Topics in Halakhic Thought – Lecture 9

Table of Contents

• Returning after the break and Hanukkah
• The decline of the generations as moving away from the source
• Analytical thinking versus synthetic thinking, and apprenticeship with Torah scholars
• Growth in analysis and decline in intuition in halakhic ruling
• Ongoing codification and the authority of earlier generations
• Why the Mishnah and the Talmud are not a code: a canonical text without bottom-line conclusions
• The example of giving a bill of divorce and the difficulty of extracting a principle from a set of cases
• “This one benefits while that one does not lose” as a rare conceptualization in the Talmud
• The common denominator in Bava Kamma and the dismissive attitude toward rules
• Casuistry versus positivism and the Nuremberg trials
• A neural network as a model for halakhic decision-making and for the structure of Talmudic passages
• “One does not derive from general rules” as a rule meant to limit rules
• Wittgenstein and the illusion of “following a rule”
• Rules of halakhic ruling as behavioral rules in a case of doubt, and exceptions to Ya’al Kagan
• Broad coverage study versus analytical study, and Daf Yomi
• “Let a person first understand and then review” and broad study in an 80/20 style
• Conclusion, continuing next time, and comments from the chat

Summary

General Overview

The claim is that the decline of the generations comes from increasing distance from the source, not from declining intelligence, and that in Jewish law there is a tension between analytical ability, which keeps improving, and synthetic-intuitive wisdom, which is hard to transmit and therefore weakens over time. This approach also explains both the growth of codification and the norms of deference to earlier generations, as well as the non-code-like structure of the Mishnah and the Talmud, which prefer cases and back-and-forth discussion over rules and bottom lines. Within that framework, it is argued that rules are only a limited aid, that halakhic decision-making is more like training a neural network through examples than running an if-then program, and that the value of broad-coverage study is limited if it is not built on analytical study that develops a mode of thinking.

Returning after the break and Hanukkah

The speaker returns to the lecture after a break that dealt with Hanukkah and makes clear that anyone who was not there should not lose out on the continuation. He notes that there was a side touch on a topic he will get to, but not as part of the main path.

The decline of the generations as moving away from the source

The speaker argues that the decline of the generations is a result of moving away from the source, not necessarily of growing stupidity. He distinguishes between analytical thinking, which is easy to pass on and may even improve across generations, and synthetic thinking, where transmission from generation to generation is difficult, so a kind of “broken telephone” occurs and the ability diminishes.

Analytical thinking versus synthetic thinking, and apprenticeship with Torah scholars

The speaker presents analytical thinking as something like logic and mathematics, which can be formally learned from books and from the board, without needing a personal bond between teacher and student, and claims that in this area there is cumulative growth across generations. He presents synthetic thinking as art and intuition, which cannot be formalized, and brings the example of Stradivarius via Michael Polanyi to show that real learning happens as apprenticeship, through observation, practice, mistakes, and feedback. He identifies this in Jewish law as “apprenticeship with Torah scholars” and links it to reading responsa as an aspect of apprenticeship and not only study. He distinguishes between knowing the material and the ability to issue halakhic rulings, which requires a certain “feel” that cannot be acquired through lectures and books alone.

Growth in analysis and decline in intuition in halakhic ruling

The speaker argues that later generations excel in more complex and refined analysis than the medieval authorities (Rishonim), but that this does not guarantee halakhic correctness. He gives an analogy to language, where a native speaker speaks better than someone who learned rules in an ulpan, and argues that in Jewish law the medieval authorities (Rishonim) “spoke the language” more naturally, so the odds that they were right are higher even if later analytical ability is greater. He presents the development of analytical Talmudic study as a substitute built because intuition was lost, and therefore elaborate moves arise, with practical ramifications and precedents, in order to reach an answer.

Ongoing codification and the authority of earlier generations

The speaker presents codification as a process born as compensation for the decline of synthetic wisdom, like rule books for language learners, and notes that the first and only code in the history of Jewish law is Maimonides. He also describes the emergence of norms marking the close of periods and granting authority, so that later authorities (Acharonim) do not dispute medieval authorities (Rishonim), and so on, and explains this as a retrospective feeling that the earlier ones are closer to the source and therefore are “probably more right.” He clarifies that in his view the norm is not binding, but it was socially accepted, and formulates a rule of thumb according to which, in a dispute with Rashba, one should assume that Rashba is right.

Why the Mishnah and the Talmud are not a code: a canonical text without bottom-line conclusions

The speaker asks why the Mishnah and the Talmud are built as associative, ambiguous, and open-ended texts, with almost no rulings, despite their canonical status. He argues that the ambiguity creates broad interpretive freedom that allows almost any halakhic ruling without directly disputing the Talmud, by means of forced interpretations or by setting one Talmudic passage against another. He presents this as a puzzle: how do you establish a canon that does not actually establish bottom lines?

The example of giving a bill of divorce and the difficulty of extracting a principle from a set of cases

The speaker describes how a passage in tractate Gittin brings dozens upon dozens of pathological cases of valid and invalid delivery of a bill of divorce, and how the medieval authorities (Rishonim) and later authorities (Acharonim) try to extract a binding principle. He presents Kehillot Yaakov, which tries to build a definition that will fit all the examples but is forced to add ad hoc parameters until the definition becomes almost as complicated as the collection of cases itself. He also presents Ketzot, which shows that giving is not merely physical transfer, because there is also acquisition through one’s courtyard and formal transfer of ownership; but it is also not merely transfer of ownership, because a bill of divorce over items from which no benefit may be derived is still valid. From this, complicated theories develop and then get tangled up with the exceptions.

“This one benefits while that one does not lose” as a rare conceptualization in the Talmud

The speaker describes a panel at the National Library where they studied “this one benefits while that one does not lose,” and presents the opening of the passage as an Amoraic excitement over “excellent material.” He shows that the Talmud translates the case of “someone who lives in another person’s courtyard without his knowledge” into a theoretical principle of benefit versus loss, and builds an inquiry with a practical ramification around the question of whether the payment obligation is for the loss or for the benefit. He argues that this structure is banal to a later learner, but in their time it was exceptional, and from this he concludes that the Talmud usually does not operate with conceptual principles of the yeshiva-study kind, but with cases.

The common denominator in Bava Kamma and the dismissive attitude toward rules

The speaker presents the Mishnah in Bava Kamma, which brings the four primary categories of damages and then sums up with “the common denominator,” as a rule, and emphasizes the Talmud’s question on page 6, “What does the common denominator come to include?” as a question that assumes the rule is an extra addition that requires justification. He concludes that the Talmud gives greater weight to examples than to rules, and that rules are viewed there as a blunt tool that does not capture the living thing. He argues that even the Shulchan Arukh and Maimonides present decisive laws mainly by way of cases rather than by formulating a set of rules.

Casuistry versus positivism and the Nuremberg trials

The speaker compares legal systems based on cases, casuistic systems, with positivist systems based on rules, and parallels this to the tension in the structure of the Talmud. He argues that rules provide certainty and control but are not accurate in a complex reality, so appointing a “robot” to issue rulings according to rules would produce bad results. He argues that positivism “took a hit” at the Nuremberg trials, because the claim “I obeyed the law” was answered by saying that obedience to the law itself can also be judged, and he presents this as a criticism of an approach that cancels judgment and critique.

A neural network as a model for halakhic decision-making and for the structure of Talmudic passages

The speaker explains that artificial intelligence uses a neural network and not a rule system, because there is no way to describe complex tasks as a set of rules, and he illustrates this with letter recognition and person recognition. He describes the training of a neural network through examples and positive or negative feedback, and argues that this parallels the structure of the Talmud, which trains a “form of thinking” rather than feeding rules and bottom lines. He argues that halakhic decision-making is not positivist but casuistic, and that rabbinical ordination exams tend to test knowledge of material rather than expose the quality of thinking on a new question.

“One does not derive from general rules” as a rule meant to limit rules

The speaker cites the Talmud in Kiddushin regarding the rule, “All positive commandments caused by time, women are exempt from, except…” and the reply, “One does not derive from general rules, even in a place where ‘except’ is stated.” He interprets this as a statement that is dismissive of rules and warns against using them rigidly, even when the rule is formulated carefully with exceptions. He presents this as a principled approach according to which rules are a framework, but not the thing itself.

Wittgenstein and the illusion of “following a rule”

The speaker presents the later Wittgenstein in Philosophical Investigations and his claim that every “following the rule” actually rests on examples and on induction of “and so on.” He illustrates learning to count and learning formulas as activities that require examples in order to understand what the rule means, and argues that even in mathematics there is no transmission of a rule without a practice of examples. He demonstrates this through sequence-completion questions and through the possibility of constructing a function that continues any sequence in any way you want, and concludes that the psychometric exam tests conventionality more than intelligence.

Rules of halakhic ruling as behavioral rules in a case of doubt, and exceptions to Ya’al Kagan

The speaker argues that rules of halakhic ruling are meant for situations of doubt and do not replace an independent position, and he illustrates this with the rule “the Jewish law follows Rava except for Ya’al Kagan,” alongside additional exceptions where Maimonides rules like Abaye. He argues that trying to reconcile exceptions by means of sub-rules is sometimes “inventing out of thin air,” and criticizes “inventions” such as rules in the style of an anonymous view followed by “and some say.” He also compares this to Amoraim who rule like Beit Shammai, and explains that when someone has an independent position there is no reason to refrain from following it, whereas a precedent rule is meant for someone who has no independent ruling.

Broad coverage study versus analytical study, and Daf Yomi

The speaker argues that broad study that is satisfied with reciting the material without understanding its meaning does not help in halakhic decision-making or in solving new questions. He brings a story about a lecturer who asked a halakhic question to a pair studying for broad coverage and showed that the answer was in the very place where their fingers were holding in the Talmud, yet they did not know how to use it. He also cites Rabbi Shlomo Zalman as saying that his proofs come from the fact that already while studying he was thinking about potential application, not from a later scan of the entire Talmud. He argues that it is better to study a little analytically than a lot in broad coverage, describes Daf Yomi as suitable for “laymen” and as aimed more at “being righteous” than at “knowing,” and brings the joke about “let him say this and it will help for forgetfulness” as an illustration of the experience of forgetting.

“Let a person first understand and then review” and broad study in an 80/20 style

The speaker reverses the order of “let a person first review and then understand,” and argues that today the right way is to start with analytical study and only afterward broad coverage. He defines proper broad study as a pass through the material that formulates the possibilities and the practical ramifications and then moves on, without a full mapping of medieval authorities (Rishonim) and later authorities (Acharonim), but still with analytical thinking and not as superficial reading. He uses the image of “regular patrol” versus “violent patrol” to distinguish between checking that there are no problems and actively digging for problems in order to understand the passage. He presents the 80/20 rule in study and tells of an attempt to learn tractates at a rapid pace while grasping the foundational principles, and argues that this kind of broad knowledge emerges only after skill in analytical study.

Conclusion, continuing next time, and comments from the chat

The speaker stops and announces that they will continue next time so as not to begin a new topic at the end. He responds to a comment about Maimonides on the decline of the generations and interprets “they did not apprentice themselves sufficiently” as a failure in apprenticeship and in synthetic ability, not in analytical ability. He answers a question about Ya’al Kagan and about Beit Shammai and Beit Hillel as the distinction between following a rule when one has no position and acting according to an independent position, and he ends with a few short questions and wishes everyone a good night.

[Rabbi Michael Abraham] Okay, last week I took a kind of time-out where we dealt with Hanukkah-related topics, and now I want to get back to our subject. There will be some point of contact there with something I’ll probably get to today, but it’s not really on the main track. Anyone who wasn’t there shouldn’t be missing anything today either. Last time—that is, two weeks ago—we talked about canonization and codification, the decline of the generations, and the authority of earlier generations. And in short, what I’m saying is that basically the claim is that the decline of the generations is a result of—or at least the interpretation I’m offering is—that the decline of the generations is a result of moving away from the source. That doesn’t necessarily mean that we keep getting stupider over the years or over the generations; it just means that we are moving farther away from the source. What does that mean? So I distinguished there between two kinds of thinking. There is thinking—let’s call it analytic thinking and synthetic thinking. Analytic thinking is, let’s call it, logic or mathematics, something formal. And thinking of that kind, first of all, is easy to transmit from generation to generation. Teaching mathematics is no problem at all; mathematics isn’t forgotten, and if you do forget it then read the book and you’ll know. Meaning, there isn’t something here that requires a connection between the rabbi and the student, let’s call it that, or between the teacher and the student. You transmit the material, the material is well defined, and if you do it properly the student knows what you know. And even more than that, I argued that in this kind of thinking—in analytic thinking—there is actually an ascent of the generations. Meaning, our logical, analytic, and conceptual ability is probably better than that of earlier generations, and that’s a process that continues from generation to generation. In contrast, synthetic thinking is thinking built more on—yes, basically the right side and the left side of the brain. The left side of the brain is analytic thinking and the right side is synthetic thinking, creativity, and so on. So synthetic thinking is basically forms of inference or forms of thought that are not logical-mathematical in a way that can be formalized. Rather, it’s some kind of art, some kind of intuitive feel for how to do things correctly. I gave the example of Stradivarius, the famous violin maker—I think he was in the 16th century or something like that—who built violins, apparently, of very, very, very high quality. And of course he couldn’t give a closed set of rules through which he could pass on to someone else the ability to build violins of the same quality. To learn from him how to do it—and this is an example brought by the philosopher of science Michael Polanyi—to learn how to do it, you have to be an apprentice in Stradivarius’s workshop, follow him around, try to feel how he handles things, how he checks the wood, how he determines the thickness, how he deals with problems, how he stretches the strings. This is not something for which there is a closed set of rules that can be transmitted in a simple way from teacher to student. It’s more a kind of art. And you have to develop an intuition for how it is right to act and how it is not right to act. And once you’ve developed that intuition, it can serve you even in places you didn’t encounter when you were accompanying your teacher. Because that intuition, like a neural network, once it is built, knows how to operate correctly in many other contexts. But it gets built in some way through engagement in the field; this isn’t formal learning where I write on the board, you summarize, memorize, review, understand, and then you know. It doesn’t work that way. You experiment, make mistakes, get feedback, follow a bit what your teacher does, and from that you can begin to understand how the whole thing works. In the context of halakhic ruling or Torah study, this is what is called learning versus apprenticeship—serving Torah scholars—or learning in the Eastern sense. Yes, East Asia—there it’s more apprenticeship than study. The student accompanies the teacher and watches how he does things. There aren’t frontal lectures where you learn the material. The student tries, gets feedback, follows the teacher, and little by little you catch how the whole thing works. In the context of halakhic ruling this is what’s called apprenticeship. When you accompany an outstanding halakhic decisor and see how he handles questions, you learn, you acquire a kind of sense, a healthy intuition for how to approach such questions, how to handle the various considerations, how to weigh and balance them, and then you can acquire from him the way one issues halakhic rulings. But that you can only do after you know the material. The material you learn because you study; you know the material; you take exams for rabbinic ordination or for becoming a judge—I don’t know what—for some given body of material, and you know the material. The fact that you know the material does not mean that you know how to rule. Most people who finish the rabbinic exams—I wouldn’t let them issue rulings even on, I don’t know, Bazooka chewing gum. Because the ability to rule goes far beyond knowledge of the material. There’s some kind of sixth sense there that tells you when it’s right to do what, and how to weigh things, and that’s not something you can acquire in lectures and simple study from books. You learn from books, so it goes into you—but not directly. It’s not the material written in the books, but the approach, the mode of analysis, what gets rejected and what gets accepted—you somehow absorb it. People also do apprenticeship from books, not only from living people—mainly responsa, by the way. Meaning, someone who reads responsa—there is in that an element of apprenticeship and not just learning. Studying the Shulchan Arukh isn’t really apprenticeship; it’s learning the material. Okay? Now, this is what I called synthetic wisdom, and synthetic wisdom is hard to transmit. Therefore when Stradivarius needed to pass on to his apprentice how to build an excellent violin, he wasn’t all that successful, because it’s hard to transmit such a thing. You can’t formulate clear, sharp rules and then relax knowing that the other person has grasped what you transmitted. And so what happens as a result is that once a teacher passes on to a student, and the student passes on to his student, and so on, basically a kind of broken telephone emerges. Then the gap between you and the original ability or skill or craft gets bigger as you move farther from the source. Therefore the synthetic ability, which is hard to transmit as-is from rabbi to student, keeps diminishing. And in the decline of the generations, in the logical analysis we do, everyone can see that we do things much more complex, subtle, and sophisticated than the medieval authorities (Rishonim). There is no doubt about that at all. But that doesn’t mean we’re right. On the road, don’t be right—be smart; in halakhic ruling, don’t be smart—be right. I mentioned—I gave an example of language use. When a person learned it intuitively, he uses it more correctly than someone who learned it through rules in an ulpan. Because he has a certain sense of smell, so someone with that sense of smell speaks better than someone who applies mechanically the rules he learned. Therefore in halakhic ruling it’s not enough to know the rules; you need the feel. So if the medieval authorities (Rishonim) spoke the language more naturally and tried to transmit it to us but weren’t all that successful—because speaking a language is an art and not mathematical knowledge—then it’s no wonder that they, since they are closer to the source, are probably right with a higher probability than we are, if they say some halakhah, regardless of the fact that our analytic intellectual ability may be much greater than theirs. Again, there are all kinds, both then and now, but broadly speaking it seems to me very clearly that there is no chance that the medieval authorities (Rishonim) knew how to do a complex conceptual construction like Rabbi Chaim or Rabbi Akiva Eiger. No chance. That is something super-complex, and the later generations do it in more and more effective and more and more sophisticated ways, and the medieval authorities (Rishonim) couldn’t do that—but they also didn’t need to. They didn’t need to because they had some intuition that told them what the correct answer was. Precisely because we lost the intuition, we developed instead the analytic ability. We use logic and analysis as a substitute, because we don’t know what the correct answer is, so we build some conceptual structure with practical ramifications, precedents, and very, very complex analysis in order ultimately to arrive at the correct answer—just as one builds grammatical rules to teach someone to speak when that person didn’t absorb the language with his mother’s milk. He didn’t receive the intuition for how that language works, so there’s no choice: you have to define a set of rules and teach him through the rules. So Jewish law is like that too. Okay, I’ve gone on about this at length; I won’t go back over all of it again. So my claim is that the decline of the generations is a decline in the synthetic realm and an ascent in the analytic realm, which comes to compensate for the decline in the synthetic realm. Now, as a result of that, basically two things happen. First, there is a process of ongoing codification. The first codex, and really the only one written in the history of Jewish law, is Maimonides—in the 12th century. Neither before him nor after him was there a full codex of Jewish law. Arukh HaShulchan, along with the future Arukh HaShulchan, comes close to it, but he relied on Maimonides, and it’s also not built exactly in the form of a codex. And this is a late phenomenon. The Mishnah and the Talmud and so on are not built that way. So first, codices are created. And why are they created? Exactly the way grammar books are created to help people who don’t know how to speak the language. So too, codices are produced in order to stabilize determinations that have already been made, and in order to help later generations, who are groping somewhat in the dark, nonetheless make correct halakhic decisions. Therefore binding codices are established, or they are treated as binding codices. And the second aspect—the flip side of the same coin—is that norms of authority arise. Every period—the Tannaim, the Amoraim, the Geonim, the medieval authorities (Rishonim), the later authorities (Acharonim)—each period gets sealed, and from that point on it is forbidden to disagree with the sages of the generations prior to the sealing. What is the meaning of this? Why not? The claim is: I’m smarter than they are, but less right. Once I see that my distance from the source is already significantly different from the distance of the medieval authorities (Rishonim) from the source, then I say: apparently if the medieval authorities (Rishonim) said something, they are probably right. And therefore there is no point in arguing with them, even though I know how to do wonderful analyses. And that, I think, is the reason why Jewish law somehow accepted a norm like this—which I said is not binding in my view, but that’s how people accepted it—some principle that later authorities (Acharonim) do not disagree with medieval authorities (Rishonim), medieval authorities (Rishonim) do not disagree with Geonim, Geonim do not disagree with Amoraim, Amoraim do not disagree with Tannaim. The sealing of periods. That sealing stems from some kind of retrospective feeling, a looking back—it obviously doesn’t happen at the very moment; it happens after some years have passed and then you look back and say: wow, those guys from those generations are already too close; I don’t really understand how their minds work. So there’s no point in arguing with them, because it’s not… it just works differently. They speak the language naturally, and I can’t reconstruct that with the analytic rules I developed. Therefore I no longer disagree with them, because I assume they’re probably right. Not certainly, but if you need some rule of thumb—if I have a dispute with the Rashba, who’s right? Probably the Rashba is right and not me. Even though my analytic ability may be greater than his. So therefore I think this is the reason they bounded the periods and why it was accepted, somehow, that one does not disagree with the sages of an earlier period. Now I want to move on. Up to this point, more or less, that’s basically what we did. The interesting question is really why the first compositions in the history of Jewish law are not structured as a codex. For example, think about the Mishnah, or even more so the Talmud, okay? Mishnah or Talmud are very wild texts: associative, flexible, ambiguous; there are no bottom lines; they’re some kind of give-and-take, proofs in this direction, proofs in that direction; there are always several opinions; there is almost never a ruling between the opinions—almost no sugya has a ruling. The Gemara doesn’t rule; the medieval authorities (Rishonim), the halakhic decisors, later on they have to decide. But the Gemara does not decide; it’s some kind of open text—flexible, ambiguous, amorphous. What’s the point of that? Why was it written that way? Couldn’t they have written some kind of Kitzur Shulchan Arukh—meaning, with bottom lines, with decisions, giving me the complete structure and helping me stabilize things in a sensible way? Why produce texts that are canonical in the sense of their status—meaning, you’re not allowed to disagree with them—but they don’t say anything? If they don’t say… anything, then almost whatever you want you can say without disagreeing with those texts. If for a moment you ignore the medieval authorities (Rishonim) and look only at the Gemara, almost anything I want I can rule and I can show you that it doesn’t contradict the Gemara. Or I’ll turn it into a contradiction between sugyot, or I’ll interpret it, make an ukimta—the interpretive freedom is so broad, and the Gemara is so amorphous and non-conclusive, it doesn’t stay with a bottom line, that basically it’s not entirely clear. On the one hand you establish a canon—something canonical, a canonical work with which you may not disagree; it is the framework for the discussion. On the other hand that work determines nothing. Make up your mind: do you want to fix things or not? What is the meaning of this? Why are these works structured this way? Maybe I’ll give an example. I once wrote an article about this too in Limudei Yesod over there, on the Limudei Yesod page, many years ago—it was when I was a doctoral student, I think, that I wrote it. It was for the Torah portion of Ki Tetze. Just to teach you that this page has already existed for a respectable number of decades, the Limudei Yesod page for Sabbaths. Does it still come out? I don’t know, I haven’t seen it in a long time. In any case, there I discussed giving a get, the Torah portion of Ki Tetze, and I pointed there to a very puzzling phenomenon in the context of giving a get. The Gemara in tractate Gittin especially devotes many dozens of sugyot to this, with many dozens of cases of what counts as valid delivery of a get and what does not count as valid delivery of a get. He gave her the get in her courtyard and then transferred the courtyard to him, the get in her hand and the pull-string in his hand, he wrote it for her on a golden tablet—all kinds of different, crazy, and pathological cases: a get involving items from which benefit is forbidden, they wrote it on things from which benefit is forbidden. Lots and lots of cases, many dozens of cases, appear in the Gemara alone—not to mention all the cases the medieval authorities (Rishonim) and halakhic decisors bring, many dozens. And then the later ones—the medieval authorities (Rishonim), and even more so the later authorities (Acharonim)—try to extract from all this what the binding principle is. Let’s try to define what valid delivery of a get is. So for example, the Kehillot Yaakov devotes almost two full long and detailed sections to this, and he basically takes the examples of the Gemara and tries to extract from them some clear definition of what valid delivery of a get is, one that will stand the test of all the examples the Gemara brings, in both directions—the examples of valid delivery and the examples of invalid delivery. Okay, the halakhic theory I am developing is basically supposed to fit the examples the Gemara brings, and then I can rest assured that this is a correct theory. A bit like a scientific theory. A scientific theory is basically a theoretical explanation such that all the cases or experiments that have been done, or the cases we observe, are supposed to fit, or be explained by, that theory. The cases are examples that I use to build the theory, and afterward I test the theory against the examples. So too in halakhic conceptual study. I build some theory, try to define what giving a get is, and I build the theory from the examples, and I try to refine the theory and define it better, testing it against the examples in the Gemara. I want to see that from this theory it really follows that all the examples the Gemara said are valid delivery do indeed come out valid, and the examples the Gemara said are invalid delivery come out invalid. That is my test for the halakhic or conceptual theory underlying the Gemara’s rulings. But that is work done a little by the medieval authorities (Rishonim) and much more by the later authorities (Acharonim). The Gemara itself hardly does that kind of work. And if you look at the Kehillot Yaakov, he gets tangled up in it in a crazy way, with lots and lots of examples, and no definition works for him. In the end he reaches a definition whose number of parameters is more or less equal to the number of examples. Meaning, every time there’s an example that doesn’t fit, he adds another parameter to the definition. What is called ad hoc in philosophy of science. So he added more ad hoc parameters until the definition became so complicated that it’s not clear what it’s good for. The definition is roughly as complicated as the set of cases. So what did you gain from the whole theory? If the definition doesn’t simplify things, if the theory doesn’t simplify things, then what did you gain from the theory? There’s something very, very problematic here. Yes, this starts already in Ketzot, this whole discussion. Ketzot tries to examine whether giving a get is the physical transfer of the get document from the husband’s hand to the wife’s hand. So he says we see that it’s not, because after all you can place the get in his courtyard and transfer the courtyard to her. So it’s not physical transfer. Fine, so maybe it’s transfer of ownership—a monetary transfer. I transfer the get to her, move the get from my ownership to her ownership? But that also can’t be, because it says that if they wrote it on something from which benefit is forbidden, it is valid. And according to—at least according to the medieval authorities (Rishonim)—who hold that there is no ownership over things from which benefit is forbidden, then the transfer of ownership of the get cannot count as valid delivery, because there’s no transfer of ownership here. So it’s neither transfer of ownership nor physical delivery. So what is it? Then they start building more complicated theories. Maybe it’s either transfer of ownership or physical delivery, or physical delivery provided there is transfer of ownership, or transfer of ownership unless there is physical delivery—these theories keep developing, and every case you bring, if it doesn’t fit, you add another little epicycle—epicycles and deferents. You keep adding to the theory more and more laths and more laths until the theory gets terribly complicated. The Kehillot Yaakov is a wonderful example of this. So what exactly is the meaning of this whole process? What is the basic idea behind this structure? Maybe I’ll give you another example. There was once a series at the National Library that dealt with Talmudic thought. It was held at the National Library, and each time they invited several people for a panel, and viewers and so on, and it’s on the National Library website. In one of the panels I participated, with two others—actually three—and when we prepared the panel I suggested studying the sugya of “this one benefits and that one does not lose.” And indeed that’s what we did there. Now, the sugya there begins in a really fascinating way. The Gemara says that Rabbah bar bar Chana meets someone and says to him, “Too bad you weren’t in the study hall in the evening—last night in the study hall there were excellent things.” Wonderful things were said in the study hall. Then he asks him, “What? So tell me what was there.” So he says to him, “Go serve me first”—he says, first serve me, apropos what we said about apprenticeship. First serve me. Fine, so he served him, and then he told him: what they asked there was this: if someone lives in another person’s courtyard without his knowledge, does he have to pay him rent or does he not have to pay him rent? Yes, someone enters another person’s courtyard, another person’s house, and lives there without permission. The question is whether he has to pay afterward or not. When the Gemara gets into the issue, it begins to discuss it and translate it—this is a case, right? The Gemara’s way is to deal with cases. But there the Gemara translates this into a theoretical principle, into a conceptual category, and there the Gemara reformulates the question and says: “This one benefits and that one does not lose.” There it is already a rule; it is no longer a case. The case is someone living in another person’s courtyard without his knowledge, and the principal question is whether he must pay rent or not. They translate this specific case into a conceptual principle, a theoretical principle, and now a discussion begins concerning the theoretical principle. And that theoretical principle is the following question: when this one benefits and that one does not lose—say, a courtyard not intended for rent, a courtyard not meant to be rented out, but the person has no other house, he needs housing. So when he enters the courtyard he gained something, because he had no housing and now he gained housing. But the owner of the courtyard lost nothing, since in any event he was not planning to rent out the courtyard, so the fact that I occupied his courtyard caused him no loss. The Gemara says the question really underlying the case is this theoretical question: when this one benefits and that one does not lose, is he liable or exempt? Translation: when I enter and live in another person’s courtyard that is meant to be rented out—ordinary renting of a house—then certainly I have to pay, right? What the Gemara asks is why one must pay in the ordinary case. Must one pay because the owner lost something, or because I gained something, I benefited? In a case where both he lost and I benefited, it isn’t clear what the ground of payment is: my benefit or his loss. Or in other words, is it compensation for the fact that he lost the use of his courtyard, or is it payment for the benefit of the residence that I received? Okay? And then the practical ramification is what happens in the case of “this one benefits and that one does not lose.” Because there, there is benefit, but there is no lack or loss. So if the basis of payment is the loss, then you are exempt when this one benefits and that one does not lose. If the basis of payment is the benefit, then you are liable, because there is benefit here; who cares if there is no loss? In the medieval authorities (Rishonim), the dispute of Tosafot and the Rif there on the spot, the opposite case arises: this one does not benefit and that one does lose. Same thing, an opposite practical ramification—maybe that is a practical ramification, a dispute between Tosafot and the Rif. So let me go back for a moment to the movement of the sugya, to the framework of the sugya. What was he so excited about? Why is this sugya “excellent things”? Wow, what a loss—you missed out, why weren’t you in the study hall? What the later authorities (Acharonim) would call section three. Fine, so the question is whether it depends on benefit or on loss. The practical ramification is when there is benefit and no loss, or when there is loss and no benefit. Any child in a small yeshiva would formulate that for you immediately, and would even expand it further and refine and define and structure the sugya and so on. In the Gemara they stop here. There are a few more qualifications, yes, blackening of the walls and so on, that there should be a rise in the gate’s value. But this structure of a conceptual inquiry, theoretical abstraction, conceptual investigation, and practical ramification—why did it so excite the Amoraim? Because in their time this didn’t exist. It didn’t exist. Today we’re jaded about it, because today that’s how we learn every sugya. But the Gemara itself deals with cases, not conceptual principles. It deals with cases: this case is liable, exempt, forbidden, permitted, impure, pure. Cases. They discuss from here, challenge from there, but there aren’t the theoretical abstractions. Those abstractions are made by the commentators, the medieval authorities (Rishonim) and the later authorities (Acharonim). And the one time there is a theoretical abstraction in the Gemara, there is tremendous excitement. What a loss—you missed it, you weren’t in the study hall yesterday? A really banal, most basic theoretical abstraction. Okay? So the claim is that because the Gemara truly was not accustomed to doing such things, the moment it encountered even a hint of a Rabbi Chaim-style move, everyone danced around from excitement. Now this sharpens the question even more: why? Why is the Gemara built this way? Why, instead of giving me a hundred cases of a valid get and an invalid get, didn’t the Gemara give me the definition? Give me the precise definition instead of giving me the cases and forcing me to do the conceptual accounting, to extract definitions from all this and argue: these will define it this way and those will define it that way. Give the definition, that’s all—why are you making me crazy? I’ll say more than that. Maybe I mentioned this one of the previous times, I don’t remember. The Gemara in Bava Kamma, the first Mishnah—we talked about rules at some point, I don’t remember anymore. The Gemara in Bava Kamma at the beginning, in the first Mishnah, says there are four primary categories of damages: the ox, the pit, the maveh, and the fire. Then it starts doing “the ox is not like the pit, this one is not like that one,” working out the mutual necessity, what characterizes each one, what distinguishes each one, the differences between them, and so on. It works out the necessity. Then the Mishnah concludes: “The common denominator among them is that they are your property”—that is the Rif’s version—“and their guarding is upon you, and when they cause damage, the damager is obligated to pay compensation from the best of his land.” Okay? Meaning, it gives me the rule after there are four cases, primary categories of damages; they explain what characterizes each one, and then finally they also give me the rule instead of letting me take the examples, remain with the examples, and extract the rule from them myself. The Mishnah itself does the work. It extracts the rule: “The common denominator among them is that they are your property and their guarding is upon you, and when they cause damage, the damager is obligated to pay compensation from the best of his land.” This is a summary of all the laws of damages. If there is property that is yours and its guarding is upon you—you didn’t hand it over to a guardian, it wasn’t stolen, nothing like that—then if it causes damage, you have to pay compensation from the best of your land. That is the summary of the whole story. Then you come to the Gemara on folio 6, and the Gemara opens there with a question that, when you think about it not from habit—we’re too used to it—it can knock you flat. The Gemara asks: “The common denominator—what does it come to include?” On folio 6a. What is it adding? There are four examples—what does the common denominator come to include? And I’m speaking about the question, not the answer. What does it mean, “The common denominator—what does it come to include?” What kind of idiotic question is that? For once the Mishnah has already given you the rule and didn’t make do with giving you just four examples, and you ask who needs the rule? On the contrary—ask who needs the examples. After all, the rule has already been given. What do I care about the examples? The examples only serve me for building the rule. But the Gemara—no, the Gemara asks: “The common denominator—what does it come to include?” More than that: why indeed does the Gemara always, as in giving a get—let me return to giving a get—why does it always give examples and not the rules? It leaves the commentators to extract the rules. And the answer is that the Gemara has no confidence in rules. Rules are for the weak. Yes? Someone who learns the language in an ulpan needs to use rules, but we all know how he ends up speaking afterward. Why? Because rules are blunt. Again, the real thing is something that cannot be conceptualized and put into a rigid set of rules. Think about language. Can someone really teach someone else to speak by means of a set of rules, and that’s it? No chance in the world. The set of rules gives you some sort of framework, but then you have to talk with people, hear how they apply it, where it’s correct, where it’s not correct. Every rule, of course, has exceptions and irregularities. You can’t learn that from the rules. There is something living that you cannot learn from rules. Jewish law is like that too, and the Gemara—that’s what the Gemara does. Therefore the Gemara is not written in the form of the Shulchan Arukh. The Gemara is not written in the form of the Shulchan Arukh. By the way, even the Shulchan Arukh, although it brings cut-and-dried laws and not give-and-take, it presents those laws in terms of cases. It doesn’t write rules there, hardly at all. Cases: in such a case it’s forbidden, in such a case it’s permitted. It doesn’t write the rules. Give me the set of rules—why not? Even that the Shulchan Arukh doesn’t do, and neither does Maimonides. But in the Gemara they don’t even bring the bottom lines. They bring give-and-take. They bring examples. And they leave the generalizations for us to make. Why? Because the Gemara understands that if you use rules, you do not transmit the matter well. You produce ulpan students. They won’t speak the language well. They won’t understand well. Rules are an approximation. Rules do not capture the thing itself. Rules are for the weak, as I said before. Someone who doesn’t know how to speak is taught by means of rules. Therefore the Gemara in Bava Kamma on folio 6 asks, “The common denominator—what does it come to include?” Because when you bring me the rule, you have already brought me the examples. It is the way of the Gemara and the Mishnah everywhere to make do with examples. The rules are our job as commentators. The Gemara and the Mishnah bring examples. So here suddenly you also bring me the rule? The Gemara asks: who needs the rule? There are already examples. The examples are stronger than the rule. There is a major debate in the legal world—or not a debate, rather different approaches in the legal world. There are legal systems called casuistic, built on cases. There are systems built on rules, positivist systems. Usually the classic examples are the Bundesgesetz, German law, which as you can imagine is of course a set of mathematical rules, theoretically of course—it’s not really like that—and British law, common law, which is built on cases. What is the difference? I think the tension between these two systems is the tension I described in the Gemara. On the one hand, rules give you simpler methods; with analytic wisdom you can pass them on; there is legal certainty; you can control what the judge will decide in each case. There are closed rules, and the judge only has to apply the rules. Okay? In a system of examples—who knows how analogies will be made to the case before us, whether it is similar, not similar. Everyone will make a different analogy. But on the other hand, the use of rules never comes out exact. Therefore, if you appoint a robot to be a halakhic decisor or a judge, you’ll get bad results. I’m not talking about a neural network, but a robot built in the classic form, a classic program—not a neural network, that’s something a bit different. So the claim is that rule-based systems work less well. By the way, that is exactly the meaning of a neural network. Why does artificial intelligence use neural networks and not a binary tree of “if this then do that, and if not then do something else”? Because there is no way to describe it in the form of a set of rules. Try teaching a computer to see, to recognize letters, with a set of rules. If you have two lines like this and a small line here, then it’s the letter heh. But now what if the line is like this? And what if these lines don’t quite meet but have a gap? The human eye immediately identifies it as the letter heh. But how will you teach the computer to identify that this letter is the letter heh? There is absolutely no chance in the world that you will succeed. Only a neural network can do that. And why? Because a neural network is synthetic wisdom and not analytic. It is not a logical path operating by closed rules; rather it teaches the system to see like a human eye. It basically develops for it, so to speak, intuition rather than rule-based operation. It works synthetically and not analytically. And when the Gemara builds itself in such a way that it does not rely on rules but on examples—by the way, someone among you who studies computers knows how one trains a neural network. How do you build the neural network so that it works correctly? You give it examples. Say we want to recognize people. We want to build a network that knows how to identify people. What do we do? We give it a list of people, a list of pictures, and then we begin giving the network the picture. If it identified it correctly, we give it positive feedback. If it identified it incorrectly, negative feedback. It reorganizes itself, and you start again. And the more examples you give it, the better results the network will achieve. And in every case these results will be better than those of a classic rule-based program. With rules you won’t get anywhere. Meaning, complex tasks cannot be carried out by applying rules. Contrary to the widespread illusion in the halakhic world—there are people who think you can use a set of rules to decide Jewish law—there is no such set of rules. Halakhic decision-making does not operate in a positivist way but in a casuistic way. And that is the reason the Gemara built its sugyot as give-and-take, examples, and so on—not rules and not bottom lines and nothing of the sort. It is trying to teach me the way of thinking, not the bottom lines. It has more confidence in producing people with a correct mode of thought than in teaching them the material. That is exactly the mistake of various rabbinic exams and the like, which test you on the material and don’t try to see how you think about a new question, how you build an answer. Usually—I don’t know, again, I’m not expert in what exactly happens today—but usually that’s how it is. And that builds a poor halakhic decisor. Because knowing the material is the less critical part of halakhic ruling. Today everything is already written down; you can get to almost whatever you want. The mode of thinking and the mode of analysis and attitude are far more significant than knowledge of the material. And precisely that is tested less, examined less—of course it is harder to examine. In any case, the reason the Gemara is built in such an amorphous way, undefined and without rules, is, I think, because the Gemara believes in casuistry and not in positivism. And in that sense, in my view, this is not primitiveness as it might look at first glance; it is ultra-sophisticated. Legal systems today already understand that one cannot work in a positivist manner. Positivism today is something for dinosaurs. Nobody believes in positivism today, not even the Germans, really. Positivism basically took a very hard blow in the Nuremberg trials. In the Nuremberg trials, people defended themselves by saying: I obeyed the law. That’s the rule, the rule says there is a law, I worked according to the law, and that’s it—what are you judging me for? And it had to be decided there that you can judge people who obeyed the law. That is simply anti-positivist. You judge people for obeying the law. The answer is yes. You judge them legally for obeying the law. Why? Because positivism doesn’t work. Positivism produces Nazism. Positivism says you work according to the law; you don’t understand, you have no criticism of what the law says, what it means, how it should be applied. That is a clear non-positivist conception. In any event, that, I think, is the reason the Gemara is built in such a strange way, which may seem primitive to some people. To me it absolutely is not. In my view it is super-sophisticated. The Gemara’s goal is basically to draw me into the give-and-take and not give me bottom lines. To train my neural network and not to feed me material and produce a classic program. There is a Gemara in tractate Kiddushin—this is the example that always accompanies the beginning of Bava Kamma for me. The Gemara in Kiddushin brings the rule that every positive commandment dependent on time, women are exempt from, except for three exceptions. Then the Gemara asks: but what about eating matzah, which is not listed among the exceptions? So the Gemara says: “One does not derive from general rules, even in a place where it says ‘except.’” I think whoever said that sentence died laughing. The Gemara is basically saying this: if there were a rule that every positive commandment dependent on time, women are exempt from, I would say fine, that’s the generalization, but there are exceptions here and there that I too could bring. But the Gemara says no—not only is the rule written in general terms, even when the rule is written in the most meticulous way possible—every positive commandment dependent on time, women are exempt from, except for A, B, and C—that’s as meticulous as can be, right? Now you ask: but there is also D, there’s another example. Fine, don’t make a big deal—there’s another example, so why are you making such a fuss out of everything? That’s basically what the Gemara answers. So there is D as well. So what? There’s D too. I counted three and there are four. What is it saying here? It’s a kind of statement that comes to belittle rules—that’s how I read this statement. This statement basically says: I belittle rules. I establish rules and make a point of belittling them at the same time. Even as I establish them. Because one has to understand that you must not take rules too rigidly. That’s basically what the Gemara is saying. By the way, Wittgenstein has a very interesting argument. Well, maybe we’ll leave that until after the break. Let’s take a few minutes’ break, say five minutes, refresh ourselves, and then come back and continue after that. Okay. Alright, come back to us, turn on your cameras. Fine, are we back? Okay, so I just wanted to complete what I began earlier. Regarding the claim, the argument raised by Wittgenstein, one very important philosopher in the first half of the twentieth century. Some say the greatest philosopher of the twentieth century. And he basically wanted to argue that every—this is the argument of the later Wittgenstein; there are two versions in Wittgenstein’s thought—and he speaks about this in Investigations, in his work called Philosophical Investigations. There he speaks about what is called “following the rule,” meaning going after a rule. And he says: we are usually accustomed, especially in mathematics—he dealt quite a bit with mathematics and logic—to think that mathematics works with some sort of closed rules, unlike other fields. But that is an illusion, because when we teach someone a rule, we actually always use examples in order to teach him the rule. For example, say I want to teach a child to count. I tell him one, two, three, four, up to ten; then eleven, twelve, up to twenty, thirty, a hundred, one hundred and one, one hundred and two, one hundred and ten, one hundred and twenty, two hundred, five hundred, a thousand, ten thousand, and so on. Okay? In the end there is always an “and so on.” And when you teach him to count, you obviously do it through examples, and the rest he is supposed to understand by induction. But even when we symbolize something for him in a general notation that looks like a rule—say, a sequence defined by f of n equals n squared. The sequence one, four, nine, because one squared, two squared, three squared, four squared, and so on—again, “and so on.” When I want to explain to him what f of n equals n squared means, the explanation will always be done through examples. Plug in one, plug in two, plug in three, and so on; keep plugging in all the numbers as much as you see fit. And he says that this is basically so in an essential way: we can never really think and teach purely through rules, because the rules themselves are conveyed through examples. And thus, for example, that very nice argument—and mathematically it is of course a trivial claim—that says: think about psychometric tests you took. In a psychometric test, one of the common types of questions is completing sequences. You have a sequence one, two, three, four, five, six—what comes next? Everyone will say seven. Right? Now I tell you three, five, seven, dot dot dot—what comes next? Nine. It could be. Maybe eleven. Eleven, yes. Right, primes, okay. Maybe it’s primes or odd numbers, right? That’s a famous example of a sequence that can branch in a simple way. But the truth is, if you think about it mathematically, detached from what we’re used to, then you’ll see that every sequence of numbers you give me—anything you want, any psychometric test under the sun—take a sequence of numbers and ask me what the next number is, I can put in any number I want and explain to you why it is the correct number. For example, you take the sequence one, two, three, four, and I ask you what comes next. I want to claim the next one is minus pi squared. That’s next. Let me show you, I’ll prove it to you. How? I’ll simply construct some function, some sequence formula, such that at n equals one it equals one, at n equals two it equals two, at n equals three it equals three, at n equals four it equals four, and at n equals five it equals minus pi squared. To build such a thing is no problem at all. You need to build a plus bn plus cn squared plus dn cubed plus en to the fourth—five coefficients—and make sure that at one it equals one, at two it equals two, at three it equals three, at four it equals four, and at five it equals minus pi squared. That’s five equations with five unknowns on the coefficients, and as long as there isn’t some problem there with the discriminant—with the determinant—then there is a solution. And if there is dependence, then there are even infinitely many solutions. Okay? And what this basically means is that I can always build some function of n that will give me the sequence one, two, three, four, minus pi squared. And of course the same goes for any number you want and any initial sequence—I can continue it in any way you want, and I will always be able to show you that it has solid mathematical logic. No problem at all. Therefore, in principle, the psychometric test doesn’t test intelligence at all. The psychometric test tests conventionality. It tests that you think in a conventional way and not outside the box. Because someone who thinks outside the box cannot be taught. The university wants people it can teach, and therefore it selects those who will complete the sequence in the way one expects an ordinary person to complete the sequence. But if someone completes the sequence in another way, he is not mistaken, he is not stupider than the others. His mind is built differently, but there is justification for the continuation he proposes as well. But since his mind is built differently, how will I teach him? After all, my mind is built this way. How can I teach someone whose mind is built differently? I teach him to count one, two, three, four, ten, eleven, twelve, twenty, a hundred, a thousand, up to ten thousand. I tell him: good, and continue the rest on your own. I ask him: so, what’s the next number? He says minus pi squared. I say to him: tell me, were you listening in class? I explained from one to ten thousand. So I continue: ten thousand and one, ten thousand and two, ten thousand and ten, ten thousand and a hundred, eleven thousand, twelve thousand, twenty thousand, a hundred thousand. Now continue. He says minus pi squared. What do you mean minus pi squared? Then he gives me the function. All in all, ten thousand equations with ten thousand unknowns—no problem, you can solve it. And you can find the sequence whose ten-thousand-and-first number will be minus pi squared. There is no problem with this in principle, and his mind is built in such a way that this sequence looks natural to him. It doesn’t look natural to me. Does that mean he is stupider than I am? No. It only means he is built differently from me, that’s all. It’s just that such a person cannot be taught, because his mind is built differently from the minds of ordinary people. The teacher doesn’t know how to teach such a person, because you need to know how his mind works in order to be able to teach him, right? Otherwise you say to him “etcetera.” Every time you say “and so on,” “etcetera,” as I said earlier, you assume your listeners know what you mean, how to continue. But if among your listeners there are some who don’t know how to continue, or continue in a different way from the one you continue, you won’t succeed in teaching them. And here I’m talking about mathematics, not psychology or gender studies or the rest of that nonsense. Even in mathematics it’s like that. Meaning that this illusion