Rabbi Gedaliah Nadel’s Thought – Homiletics in Halakhah – Lesson 3

Table of Contents

• General Overview
• Dynamic Tradition and Halakha Given to Moses at Sinai
• The Development of the Hermeneutical Principles as Conceptualization, Not Invention
• Intuition, Formal Rules, and Examples from Language and Music
• Rabbi Daliah’s Position versus the Proposed Position, and Rav Chaim and Maimonides as Disclosure
• The Authority of the Medieval Authorities (Rishonim) and the Difficulty of the Hermeneutical Principles
• Rabbi Daliah’s Text on Page 23: The Status of the Principles and the Distinction between Logical and Textual
• Maimonides: “The Thirteen Principles or from Inclusive/Expansive Terms” and the Debate over What He Means
• Kal Va-chomer: Three Types, Refutation, and the Debate over “If Two Hundred Is Included, Then One Hundred Certainly Is”

Summary

General Overview

The text presents a dynamic conception of tradition and of Jewish law given to Moses at Sinai in relation to the hermeneutical principles by which the Torah is interpreted. It suggests that these principles developed over the generations not as a new invention but as a process of conceptualization, reconstruction, and refinement of an earlier midrashic language. It explains how the loss of natural intuition leads to the creation of formal rules that on the one hand arise out of weakness and on the other hand provide new analytical power, and it illustrates this through the development of the lists of principles from Hillel to later lists. It then offers a reading of a text by Rabbi Daliah and of Maimonides, distinguishing between logical principles and textual principles, and afterward gives a systematic examination of kal va-chomer in its various forms, including the discussion of refutation and the limits of logical necessity when an inference is applied to reality.

Dynamic Tradition and Halakha Given to Moses at Sinai

The text states that in academic scholarship it is commonly accepted that the hermeneutical principles are a historical development and therefore are not “Jewish law given to Moses at Sinai,” whereas according to the medieval authorities (Rishonim) and the Torah tradition they are indeed Jewish law given to Moses at Sinai. It argues that there is not necessarily a contradiction if “Jewish law given to Moses at Sinai” does not mean a closed and explicit list handed over to Moses our teacher, but rather a broader language of exposition that was transmitted in a living and dynamic way. It describes a situation in which the Holy One, blessed be He, teaches Moses our teacher both the plain meaning and the interpretive exposition of verses without explicitly labeling the formal “hermeneutical principle,” and after Moses’ death a process of forgetting and reconstruction takes place, as described in the Talmudic text in Temurah about “three thousand Jewish laws and one thousand seven hundred a fortiori inferences and verbal analogies were forgotten,” and Otniel ben Kenaz serves as an example of the beginning of a process of reconstruction and conceptualization.

The Development of the Hermeneutical Principles as Conceptualization, Not Invention

The text describes how the number of hermeneutical principles grew over the generations, from Hillel’s seven principles to Rabbi Ishmael’s thirteen, to Rabbi Akiva’s set, where there is dispute but a similar number, and later to lists such as the thirty-two principles of Rabbi Eliezer son of Rabbi Yosei HaGelili, while in the Talmudic text itself there are many additional methods that do not “fit into the list.” It explains that the growth does not stem from invention but from progress in conceptualization, in which what was once a single intuitive tool splits into more precise sub-rules. It illustrates this through the splitting of “general and particular” in Hillel into three principles in Rabbi Ishmael: “general and particular,” “particular and general,” and “general and particular and general,” and in the Talmudic text the language of “sides” and the radius of inclusion is further elaborated.

Intuition, Formal Rules, and Examples from Language and Music

The text compares a speaker of a language who is unaware of the rules of grammar to a process in which rules are formulated out of natural use of language, and argues that conceptualization is not the creation of a new language but the distillation of what was already operating intuitively. It presents the rules as “crutches” that are born of weakness and the loss of intuition, but that provide the power to solve new problems through formal application, similar to the advantage of mathematics where intuition fails. It also illustrates this through music and composition, and mentions the book Gödel, Escher, Bach and the analogy between mathematical structures and creation in Bach and in Escher, including the claim that in Escher’s sketches one can see conscious planning.

Rabbi Daliah’s Position versus the Proposed Position, and Rav Chaim and Maimonides as Disclosure

The text says that Rabbi Daliah proposes several legitimate possibilities and emphasizes the dynamic and historical character of the Oral Torah without being alarmed by disputes, and even claims that “very little came down to Moses at Sinai.” Opposed to this, it presents a “more conservative” position according to which this development is the bringing from potential into actuality, a “dynamic disclosure” of what already existed beforehand. It illustrates the idea of disclosure through the discussion of Rav Chaim and the criticism that supposedly “Maimonides would have fainted” and would not have recognized himself, and it rejects that criticism by arguing that Rav Chaim reveals rather than creates. It even adds that perhaps Rav Chaim understands Maimonides “more correctly” than Maimonides understood himself, using modern conceptual tools. It cites a letter of consolation attributed to Rabbi Kook to the grandchildren of the Sochatchover Rebbe, the Avnei Nezer, together with the contradiction regarding Rabbi Eliezer, that he “never said anything he had not heard from his teacher,” while also saying “things no ear had ever heard before,” and proposes an interpretation in which the disciple says in his teacher’s name things that even his teacher never heard, in the sense of deeper formulation and disclosure.

The Authority of the Medieval Authorities (Rishonim) and the Difficulty of the Hermeneutical Principles

The text argues that the medieval authorities (Rishonim) are “perplexed” when facing the use of the hermeneutical principles, and that in Tosafot one sees “terribly forced solutions” because they do not have clear information about how “this whole world of exposition works.” It states that in places where the medieval authorities (Rishonim) admit they do not understand the material, their words do not automatically carry authority for the analysis of the hermeneutical principles, unlike halakhic questions, and it raises the possibility that someone who applies systematic analysis can arrive at simpler solutions and may in such cases be “more right than Tosafot.”

Rabbi Daliah’s Text on Page 23: The Status of the Principles and the Distinction between Logical and Textual

The text quotes: “The principles by which the Torah is interpreted were given to Moses at Sinai as ways of learning new Jewish laws. All the principles are logical, but on our own we would not have been able to decide that Jewish law should indeed be established according to them…” It divides the principles into “logical” ones such as kal va-chomer and binyan av, where the text gives the data and the inference is made through reasoning, and “textual” ones such as general and particular, where the very structure of the verse indicates the mode of inference and the radius of expansion beyond the particulars. It argues that general and particular is intended to expand specifically beyond what is merely similar to the particulars, and therefore it is not an analogy in the style of binyan av. It illustrates this through the redemption of second tithe and the structure “from cattle and flock, from wine and strong drink” within a framework of general-particular-general, which expands what may be purchased with the money in Jerusalem even to things not completely similar to the particulars. It explains the phrase “all the principles are logical” as interpretive logic even in the textual principles, and brings examples of expositions of general-particular-general on texts that are not Torah, including testimony that Professor Elon cites an exposition on the wording of a responsum of Maharam of Rothenburg, while noting that the precision there is less sharp and that such a thing reflects a stage similar to that of Hillel, where the finer sub-rules have not yet been formulated.

Maimonides: “The Thirteen Principles or from Inclusive/Expansive Terms” and the Debate over What He Means

The text quotes the language of Maimonides in Sefer HaMitzvot, the second root: “The principles by which the Torah is interpreted, and the expositions derived from superfluous language and from all the ways of language, are one matter and have one force.” It presents the possibility of understanding Maimonides as equating the thirteen principles with “inclusion” as a claim that all expositions possess interpretive logic and are not some kind of “encrypted code,” but then immediately rejects that as “Maimonides’ intent,” and suggests that Maimonides means to include both methods: the thirteen principles of Rabbi Ishmael as opposed to the school of Rabbi Akiva, which expounds by “inclusions and exclusions,” together with expositions based on terms of inclusion such as the word “et” and other surplus formulations. It adds that Maimonides probably is not limited specifically to the number thirteen, but is speaking about methods of exposition in general, just as in the Sages sometimes “a fortiori inferences and verbal analogies” serve as a collective term for all the principles, as in Temurah regarding “one thousand seven hundred a fortiori inferences and verbal analogies.”

Kal Va-chomer: Three Types, Refutation, and the Debate over “If Two Hundred Is Included, Then One Hundred Certainly Is”

The text says that Rabbi Daliah chooses to illustrate his principle through two extremes: kal va-chomer, a logical principle, and gezerah shavah, a textual principle, and begins with an analysis of kal va-chomer. It argues that kal va-chomer is not “just all the more so,” nor is it merely a relation of inclusion in the style of “if two hundred is included, then one hundred certainly is.” It explains that if it were, the give-and-take of the Talmudic text about constructing the kal va-chomer and about refuting it would not be understandable. It distinguishes among three types of kal va-chomer: a kal va-chomer of “if two hundred is included, then one hundred certainly is,” in which the second case includes the first, such as “if a man opens a pit, or if a man digs a pit”; a conceptual kal va-chomer of “all the more so,” such as “Behold, the children of Israel did not listen to me, so how will Pharaoh listen to me?”; and a Talmudic kal va-chomer built out of three data points, like tooth and foot versus horn in the public domain and in the damaged party’s courtyard.

The text explains that in the Talmudic kal va-chomer, two data points are used to extract a general rationale, and the third data point serves as an anchor for applying that rationale to the case under discussion. It shows that one can derive the rationale in different directions from the same data, such as “the damaged party’s courtyard is stricter than the public domain” or “horn is stricter than tooth and foot.” It connects the very existence of refutations to the fact that kal va-chomer is not a necessary inference like a Greek syllogism, and cites Adolf Schwarz, who argued that kal va-chomer is a syllogism, but points out that in a Talmudic kal va-chomer one may accept the data and still challenge the move from them to the rationale and its applicability.

The text adds that even with “if two hundred is included, then one hundred certainly is,” there can be a refutation when one applies logic to reality, because there are always hidden assumptions about how the application works. It illustrates this with the analogy of mathematical addition as opposed to the addition of forces in physics, which is not arithmetic but vector-based, and cites “the Belgian law, the Vandervelde law,” under which workers were forbidden to buy two liters of wine, but a judge acquitted a worker who bought a larger quantity on the grounds that the purpose of the law was to prevent the squandering of a weekly salary, not to prevent commerce. It returns to the example of “one who passes of his children through to Molekh” and cites the Kesef Mishneh, who suggests reasons for exempting someone who did this with “all his children,” including the possibility that the death penalty “is not enough for him,” and shows that such reasons function as a refutation of a kal va-chomer of inclusion. So even an inference that appears logically necessary at the formal level may be breached at the level of norm and application.

We’re on page 23, the hermeneutic principles by which the Torah is interpreted. We spoke a bit about tradition, about creative interpretations and supportive interpretations, about the fact that tradition is a dynamic concept. I illustrated that through the interpretive principles, and now we’re getting to those principles themselves. I’ll just mention this briefly, schematically, let’s say. In academic research, it’s accepted that these principles developed over the course of history. From one end to the other, I think everyone agrees about that. Meaning, they’re not a law given to Moses at Sinai. But among all the medieval authorities (Rishonim), both there and here, everyone agrees that it is a law given to Moses at Sinai. Wait, what do you mean? Academic research generally says that the whole Torah is a human development over history? No, not that—but that it didn’t come that way originally; it developed later on. Yes, yes. Besides, that’s not really true either. This also includes religious scholars; independently of their faith commitments, that’s how they understand the development of the Oral Torah. And I said that I don’t think there’s necessarily a contradiction here, because the question is: what counts as a law given to Moses at Sinai? Does “law given to Moses at Sinai” mean that Moses received a closed list of interpretive principles? That the Holy One, blessed be He, told him: kal va-chomer, inference from a prototype based on one verse, inference from a prototype based on two verses, general and particular, particular and general, general and particular and general, and so on? It’s pretty clear that’s not true. There are also disputes about the interpretive principles. Different enumerations, yes. And disputes too, right? Rabbi Akiva and Rabbi Ishmael. So fine, you can say there was some distortion in the process of transmission—that the disciples of Hillel and Shammai did not fully serve their teachers, and so disputes arose. And then, if the conception of a law given to Moses at Sinai, or of tradition, is a rigid one—meaning basically that Moses received the list exactly as Rabbi Ishmael formulated it, all sealed and closed, and it just gets passed down in sealed packaging from generation to generation—that’s one conception of a law given to Moses at Sinai, and then of course you can’t reconcile the two views. But if I understand that the concept of tradition, or of a law given to Moses at Sinai in this case—but really something broader—is dynamic, then that means that when the Holy One, blessed be He, taught Torah to Moses, He taught it to him on both planes, let’s say the plain meaning and the interpretive meaning. He read him a verse, told him, “You shall fear the Lord your God”—to include Torah scholars; “these”—to exclude a slave and a woman; whatever, all kinds of things like that. But He didn’t define for him by which interpretive rule He was operating. He read the verse and explained it in the interpretive mode. And at some point after Moses’ death—as the Talmud in Temurah describes—three thousand laws and seventeen hundred kal va-chomers and verbal analogies were forgotten. Then there began a process of reconstruction, conceptualization, and reconstruction. Othniel son of Kenaz, the Talmud describes there, did part of this, but it continues throughout history. And throughout history the language that was given to Moses naturally undergoes conceptualization little by little and starts to take on certain patterns. We define different tools in the midrashic toolbox: this is called verbal analogy, this is called general and particular, this is called kal va-chomer, prototype from one verse, from two verses. In other words, these are simply definitions of forms of interpretation that already existed before; they were just defined, put into a more structured pattern, one by one over the years. And as history advances, the number of interpretive principles naturally grows. Hillel had only seven; Rabbi Ishmael already has thirteen. Rabbi Akiva disagrees with him, but it’s still more or less the same number. After that there are the thirty-two of Rabbi Eliezer son of Rabbi Yosei the Galilean; others count more. In the Talmud there are many more, of course; some never made it into the list. So the number of interpretive principles grows over the generations. It grows not because they invented them, but because the process of conceptualization advances. Meaning: what used to be, say, one of Hillel the Elder’s seven rules—general and particular—becomes, for Rabbi Ishmael, three separate rules: general and particular, particular and general, general and particular and general. By the way, there’s also particular and general and particular in tractate Nazir; that’s a fourth rule, and for some reason it’s not counted by him. So there are three rules in Rabbi Ishmael’s list. These three rules are not because they suddenly absorbed two more rules from the Hittites, yes, influenced by the Hittites or something like that—maybe there was some influence there too; such processes always involve influence. But the point is that what Hillel called the rule of general and particular underwent a split. They realized that within that rule there are actually three forms of generalization, not one. One broader, one narrower, one in between, depending on the style the Torah uses. One style is general and particular; one is particular and general; and one is general and particular and general. Then suddenly they understood that what we had been calling general and particular—that when the Torah moves from plural language to singular language, or from examples to a general formulation, then you have to generalize—Hillel already understood that? What? Hillel didn’t formulate it that way, but he did the same thing. Here he made a small generalization, here a large one, here a medium one. I’m saying again, this is all a model; I don’t know what Hillel understood. But on the theoretical level there’s no obstacle. Meaning, Hillel simply acted this way. He said, look, when the Torah moves from singular language to plural language, you have to generalize. Meaning, you have to draw a wider circle, not just the examples the Torah gives. But Hillel himself, in different forms of transition from singular to plural, made different generalizations. Now his students—or whatever, the later generations—suddenly say: wait a second, we can actually define a rule here. Whenever the structure has two links, meaning a general term followed by a particular term, then the generalization is the narrowest. If it’s particular and then general, the generalization is the broadest. If it’s a three-part structure, meaning general and particular and general, then the generalization is medium. And then the Talmud starts defining three. This is already in Rabbi Ishmael’s thirteen principles, but the Talmud even explains the difference among the three principles and uses the language of aspects. It says: how many aspects are you extending by? We talked about that, right? That the number of aspects basically determines the radius of the generalization, and there it becomes completely explicit. But that’s not because the Talmud invented new principles, or at least not necessarily. The Talmud simply formulated in explicit rules what Hillel did naturally. It’s like someone who speaks a language. The example I gave: someone who speaks an ordinary language doesn’t know that certain letters take a dagesh at the beginning of a word, or what subject, predicate, direct object, and indirect object are—but that’s how he speaks. Now if someone has to distill rules out of the way we speak, he produces a list of explicit grammatical rules. Some of us don’t know those rules at all; it doesn’t matter. But we speak the language. So the fact that someone invented rules doesn’t mean he invented a new language. He conceptualized what people before him were doing intuitively. He defined it more explicitly and put it on the table. That has many advantages. It’s an aid for the weak, for those who don’t know the language. But once you’ve done that, it gives you a tool that earlier people didn’t have. So here too, the process of conceptualization on the one hand comes from weakness—meaning, from the fact that I’ve already lost the simple intuition of how to use the language of interpretation, which maybe Moses had more of, or Joshua, or the Elders. As the historical process advances, we feel it less intuitively, we’re less close to the source, and so we create crutches or aids for ourselves. We define things, distinguish among types of generalization, define this as general and particular, that as particular and general. We can’t read the language naturally and understand that when there is a three-part structure this is the kind of expansion, and when there is a two-part structure it’s either a small expansion or a large one. Someone who read it naturally simply spoke the language, so when he read such a verse he generalized accordingly; it was obvious to him. But at some stage someone came and said, wait, let’s pay attention. Whenever he made a medium generalization, it was a three-part structure, and when he made a very small or very large generalization, it was a two-part structure. Then I say, okay, now just from reading the verse I don’t know what generalization to make, but I do know how to distill from what he did these three sub-rules, and now I too can speak this language even though I’m not a native speaker of it, I didn’t get it from my parents, from home, from birth. The general system helps me. My advantage over Moses, say, or over those in earlier generations, is that if there are things he doesn’t know how to solve because he lacks intuition for them, if I have a system of rules I can propose a solution, because I understand how it works and apply the rules formally to the new problem. That’s the advantage of mathematics over intuition. Someone with stronger intuition is more right than the mathematician. Seems the other way around, no? The one who can prove it mathematically. No—I mean “more right” in the sense of more successful. Mathematics won’t always succeed. Intuition tells you what’s right and what isn’t. And by contrast, what’s the advantage of the person who works with mathematics? Where you don’t have intuition, I can at least try to offer a solution. Can it also correct intuition? Fine, afterward—after I have the rules. Of course. Then I go back again: rules create or refine an existing intuition; there’s feedback between those two ways of working. But in the end, each has its advantage and its disadvantage. Rules are born out of weakness. They’re born out of weakness, but in the end they give a kind of power that someone without the rules just doesn’t have. It’s like someone who has an intuition for how to play music. He can play beautifully even without knowing notes, reading music, and so on, without having studied music. But if he studies music, then first of all even if he has no talent, maybe up to a certain level he’ll at least be able to function formally. And in a place where that first person won’t succeed—say you have some compositional problem you don’t know how to solve intuitively—someone equipped with formal tools might be able to do it. They say that Bach’s compositions have logical, mathematical structures, quite sophisticated ones—loops and paradoxes and things like that. Gödel, Escher, Bach. So was that intuitive or mathematical? What? Was that intuitive or mathematical for him? For him it may have been intuitive. What, obviously it was intuitive, he didn’t… Yes, but that’s exactly the point. So there’s an advantage to people equipped with formal tools even though those formal tools were born out of weakness. There’s a book called Gödel, Escher, Bach. Gödel, the famous Austrian mathematician, Gödel’s theorems. Escher, the Dutch painter. And Bach. He finds some kind of mathematical similarity—everyone knows that. Who? Escher? Escher was a painter. Exactly. No, no, it was all mathematics. No, it’s not mathematics. From bird to swan, black and white. It’s not mathematics, but he had very good mathematical intuition, and maybe he really did know mathematics. In his sketches, for example, you can see that in his case it was quite conscious, with Escher. It wasn’t just intuition from which we later distilled the mathematics; with Escher there was apparently actual mathematical understanding—you can see in the sketches, when he built the drawing, that he planned it. Meaning, it wasn’t something that just came out of his sleeve and then we analyzed it. He wasn’t Picasso. Huh? Yes. Fine, Picasso wasn’t dealing with mathematical things, I think. Yes. Is this whole explanation just the Rabbi’s own explanation, or is it also supposed to be an interpretation of Rav Dalia? No, no, this is the picture I think is correct. Rav Dalia in this matter is actually a little exceptional. He talks about several possibilities, all legitimate, all acceptable. He doesn’t emphasize the dimension of continuity within this dynamic. Meaning, he’s in favor of dynamism, but he doesn’t explain that the dynamism is really just bringing into actuality things that were already there earlier. Rather he says: look, there are several possibilities; it’s human intellect; there are disagreements; and therefore everything is fine. We’re all legitimate, and there’s no need to panic over the fact that there are disagreements. And it’s obvious that things arise over history, and there’s no need to panic about that either. Not everything descended to Moses at Sinai; very little descended to Moses at Sinai. All that he says. In this respect I’m actually presenting a somewhat more conservative side. Meaning, I want to say that these things are not born over history, but develop over history; but really this is the conceptualization of things that existed potentially even in the earlier stages. They come into actuality. A kind of unveiling. Yes, exactly. Dynamic unveiling. If you asked Rabbi Akiva himself, I’m not sure he would formulate it as I do, or even agree with me. I understand it’s not simple to extract what was in Rabbi Akiva’s innards. Like with Rav Chaim—the standard criticisms of Rav Chaim; I think we talked about that once too. The standard criticism of Rav Chaim is that if Maimonides saw this, he’d collapse—whether from laughter or from crying, I don’t know, but he’d collapse. He wouldn’t recognize that Rav Chaim is offering an interpretation of Maimonides. Fine? Because it’s just not… Now I disagree with that. I don’t agree with it at all. You can argue with one insight or another of Rav Chaim, even with many of them, but I think Rav Chaim performs an act of unveiling, not an act of creation. Rav Chaim defines in a modern way what is genuinely present in Maimonides. Meaning, if Maimonides had lived in the twentieth century and not the twelfth, and he saw Rav Chaim, I think he would agree with a large part of what Rav Chaim wrote. You can say the same thing about the medieval authorities, about the Talmud. Yes, right, the same thing. It’s just that Rav Chaim and Maimonides is very sharp because it looks so different. Rav Chaim is a completely different method, and the claim is that he’s trying to force Maimonides, to convert him into Brisker analysis. And I don’t think that’s true. Again, he does a little bit of that, but everyone does a little of this and a little of that. But overall, Rav Chaim unveils, he doesn’t create. And Maimonides himself would also agree with what Rav Chaim says about Maimonides, in my opinion, in some cases. And of course you can miss, you can certainly argue. By the way, even if Maimonides himself didn’t agree, that wouldn’t mean Maimonides is right and Rav Chaim isn’t. I say that too. What is genuinely in Maimonides—not in Jewish law; in Maimonides—it’s not certain that Maimonides is right, because with Rav Chaim’s tools, Rav Chaim is stronger than Maimonides. Meaning, if you want to fit Maimonides’ view into our conceptual tools, Maimonides himself may not know how to do that as well as Rav Chaim does. Therefore Rav Chaim may be more right in understanding Maimonides than Maimonides understands himself. I think Rav Kook writes about this—Rav Kook wrote to the grandchildren of the Sochatchover when the Avnei Nezer died; he wrote them a letter of consolation. He says there that it says about Rabbi Eliezer that he never said anything he had not heard from his teacher, and on the other hand it says that he said things no ear had ever heard before. So the difficulty is weak, but the answer is better. Meaning, the difficulty is weak because he said things no ear had heard. What he means is that Rabbi Eliezer said things in the name of his teacher that no ear had ever heard before—including his teacher’s. And I’m telling you, someone who studied under a rabbi and was really close to him knows this and feels it very clearly: that sometimes I can explain him better than he understood himself, or differently from how he understood himself. I think maybe it can even be better, and that doesn’t mean he is right and I am wrong, because when I try to put it into my own pattern, my own way of thinking, my own conceptual templates, and I take his ideas, maybe I formulate them better than he does. And if he argues with me, then he doesn’t understand himself. His intuition was correct; his conceptualization was not. When he tries to define for himself what his intuition was, he may get it wrong. You don’t even have to go far; this happens within a person himself. A person has some idea, and after several years the idea is much more developed. Now, several years earlier he didn’t know that development. No, I’m saying more than that. It may be that later on he won’t agree with the development—but they’re right and he isn’t. That’s actually what lies behind his intuition. You know, many people intuit a lot of things. Now because of some logical problem they think what this thing is supposed to mean is some particular conclusion, whatever it may be, and that becomes their conclusion. Now you can try to explain it to them differently, and they suddenly discover that in their intuition it wasn’t that at all, it was something else—they simply missed something in the logical analysis. These are everyday occurrences; I can show examples of such things. Meaning, people who think their outlook must lead them to a certain place—many of the people who don’t believe in God, in my opinion, are the result of something like that. Meaning, in their intuitions, when they decode those intuitions, they arrive at the conclusion that they’re apparently not believers. But if you analyze their intuitions differently, you discover that there really is faith there. They’re not unbelievers; they reach the conclusion that they are unbelievers, but that conclusion is the result of a logical process that isn’t necessarily correct. Fine, and very often I think you can see this. A person not interpreting himself correctly is something that happens quite a bit. And once you have developed logical tools—I’m returning now to the dissonance I spoke about, between logical tools and intuition—once you have developed logical tools, you have a chance to understand or uncover something in the person who said it or spoke about it, in a way that is more correct than his own understanding. Meaning, you know better how to explain it; it’s sharper; you understand better what he means. And he himself doesn’t understand; it’s vague for him; it’s not sharply defined. So in simple problems he’ll know what it means, he’ll tell you. But in a complex problem he can be mistaken about his own position, about what his own position implies regarding a complicated problem. Therefore I think that in the end this process, if you relate to it correctly, has a great advantage. Because basically you lose the intuition—meaning there is something about setting a rule that causes you to miss the ability to go beyond the rule, like in the grammar example. When we establish grammatical rules, we somehow impair the rhythm of intuition. Right, I think that really is the second secondary effect. Meaning, first of all we are weak—we lost the intuition, so we built rules. In a certain sense, the rules somewhat hinder our ability to internalize that intuition that our teachers are trying to pass on to us. That’s true. But on the other hand, what can you do? So should we not formulate rules, and remain without it? No, but sometimes that can also develop it. Yes, exactly, and I’m arguing that if we’re aware of this, then we can work so that the rules do the opposite: help us return and understand the intuition better. And someone who knows how both to handle it on the intuitive level and analyze it with rules has an enormous advantage over both sides. I feel this so strongly many times when I talk to people about some Talmudic topic and I try to define things very logically, very systematically. The logicians don’t understand what the Talmud is really saying; they don’t have the simple intuition. And the Talmud people don’t know logic; their logical tools are less polished. So I have an advantage over both sides. Very often I feel that I can do it better than either side alone. And that doesn’t mean—the logical analysis is a result of weakness. It started from the fact that I didn’t know how to do it without logic. Yes, the Rashba writes “exempt,” “permitted,” he says—that’s the question, “permitted.” Then Rabbi Akiva Eiger comes and turns it into a twenty-page analysis with definitions and this and if so then there, and if so then here. Why? Because the simple intuition that the Rashba had—Rabbi Akiva Eiger no longer trusts his intuition that much. He needs to define a structure, identify the idea, define the terms. But there is an advantage to Rabbi Akiva Eiger’s logical ability. Meaning, there is something here that can take you to places the Rashba won’t be able to solve. Therefore I think that in the end this process, if one relates to it properly—if one understands it and tries to neutralize its weaknesses—it can only improve our situation. Meaning, in the end it seems to me that in contexts like the interpretive principles, if I go back to them, the medieval authorities are very perplexed by the use of those principles. They try solutions; in Tosafot you see all kinds of very forced solutions. Because Tosafot continues to think in the regular way and doesn’t know—after all, he doesn’t have the information. The medieval authorities themselves say, or all the sages after the Talmud say, that we no longer know how this world of interpretation works. So in places like that you see all kinds of very forced answers in Tosafot that aren’t really necessary. If you understand, if you enter into the logic of the interpretive rule, you can suggest simpler solutions. You don’t have to reach Tosafot’s answers for that. And I think it’s entirely plausible that in such a case I’m more right than Tosafot. Because Tosafot didn’t perform this analysis; he tried to offer an intuitive suggestion in a place that’s too difficult—where intuition fails. You need to do systematic work. If you succeed in doing it systematically, you can decipher things that someone relying on intuition can’t decipher. In those places, by the way, this is also a classic point, because in those places I also don’t think the medieval authorities have authority, unlike in Jewish law. Because in places where the medieval authorities themselves explicitly say they don’t understand the material, then why exactly do I need to stick to what they wrote? They themselves—this is an admission against interest—they say: we don’t understand this business. So why should there be authority? People say to me, when I reach such conclusions, wait—then why didn’t Tosafot write it this way? That’s always the challenge, right? When you say something in Jewish law, they ask: but Tosafot didn’t answer that way. So how can that be? Now even in Jewish law you can discuss it: so what if Tosafot didn’t answer that way—does that mean I’m forbidden to say it? But here Tosafot himself says that he doesn’t understand the interpretive principles. So what do you want? He didn’t answer that way because he didn’t understand. That’s all. This automatic authority granted to the medieval authorities also has to be examined through these lenses. Okay, so let’s move to chapter 5, page 23. “The interpretive principles by which the Torah is interpreted were given to Moses at Sinai as ways of deriving new laws. All the principles are rational, but by our own intellect we could not have decided that one should indeed establish Jewish law in accordance with them, were it not that Moses our teacher grasped from the Holy One, blessed be He, that with these principles he was to operate and generate laws.” There’s a somewhat subtle point here. What does it mean that all the principles are rational? If you look at the list of principles, you can divide them into principles that are more logical and principles that are more textual. Kal va-chomer, prototype inference—those are logical principles. Meaning: “If her father had but spit in her face, would she not be ashamed seven days?” Then the Holy One, blessed be He, all the more so, right? That’s kal va-chomer. Or: “Behold, the children of Israel have not listened to me, so how will Pharaoh listen to me, seeing that I am of uncircumcised lips?” That’s kal va-chomer. Okay? Kal va-chomer is a rational principle; we use it in other contexts of our thinking too. It’s logic. Likewise prototype inference. That’s a kind of analogy or generalization; inference from two verses is probably a generalization. So those are rational principles. By contrast, general and particular, which I spoke about earlier, is a textual principle, because my generalization in relation to the particulars isn’t made on the basis of analogy. Not because something is similar to the particulars, and therefore I say that what applies in the particulars applies here too. No—the opposite. General and particular, as the medieval authorities already noted, is a generalization to places that are not similar to the particulars. Because if it were similar to the particulars, it would be enough to use prototype inference. Why do you need general and particular? Prototype inference says that what is similar probably has the same law. That’s analogy, right? General and particular tells you always to go beyond what is similar. The question is how far beyond the similar. That’s what I said earlier—it depends whether it’s general and particular, particular and general, or general and particular and general. That’s already a question of how far to move beyond the similar, but it’s always beyond the similar. In every general and particular and general there will always be an objection. There is no general and particular and general without a possible objection, and there is no general and particular and general that the Talmud overturns because of such an objection. Because the objection is built into it; that’s why the general and particular was said. To give the example: if we are redeeming second tithe, then it says there cattle, sheep, wine, and strong drink. Fine? That’s what one redeems second tithe with. So I say okay—but can it also be done with salt? Can I buy with it—meaning, I have second-tithe money and I want to do… sorry, yes, I want to bring it up to Jerusalem. My second tithe produce is too heavy, so what do I do? I sell it locally, and with the money I receive I go up to Jerusalem, and there I buy food and eat. That’s what one does with second tithe. Fine? In the end, when I buy food in Jerusalem, the question is what I am allowed to buy. The Talmud says: cattle, sheep, wine, and strong drink—that’s what the Torah says. Then the Talmud starts checking: okay, and what else? What about fish, fish brine, and things like that? In other words, what can be done with this money? Now if it really were just cattle, sheep, wine, and strong drink, and I wanted to include something else—I don’t know—some other animal that isn’t cattle or sheep, something else, but similar—fine?—then I wouldn’t need general and particular. That would be analogy. It would just need to say cattle, sheep, wine, and strong drink, and I would understand that anything similar is covered by prototype inference. But if the Torah writes a structure—“and for whatever your soul desires,” that’s the general term, and at the beginning there is also a general term, I don’t remember exactly what was there—there is some general term at the beginning, a general term at the end, and these four examples in the middle. So that’s a structure of general and particular and general. This structure tells you to go beyond what is similar to the four particulars. Because if you only needed what is similar to those four particulars, there’d be no need for the general term at the beginning and the general term at the end. You’d make a simple analogy, a prototype inference—they would write only the particulars. When a general term is written at the beginning and at the end, it is in order to broaden the generalization more and extend it to things that are not entirely similar to the particulars. Fine? Therefore general and particular and general is not a rational principle; it is a textual principle. If the text is written in the form of general-particular-general, then the text itself tells you: expand. In kal va-chomer, there is no hint in the text that I need to make a kal va-chomer. If it says that damage by tooth and foot is exempt in the public domain but liable in the injured party’s courtyard, then horn, which is liable in the public domain, is certainly liable in the injured party’s courtyard. The text does not have to tell me: do a kal va-chomer here. The text gives me the data, and from that data I make the kal va-chomer. In the textual principles, unlike the rational principles, the text has to instruct me to make the inference. Meaning, in kal va-chomer and prototype inferences, the text does not instruct me to make the inference; it gives me the data, and I make the inference with my own logic. If it’s similar, it’s similar; if it’s all the more so, it’s all the more so; if it’s a generalization, it’s a generalization. I do all that myself. I don’t need instructions from the text, from the structure of the verse saying: ah, this verse is written in such-and-such a way, so here one must make a prototype inference. There’s no such structure for prototype inference; prototype inference is simply similarity. General and particular is a way the Torah writes. The Torah writes things in a certain form, and by that it tells us: here make this kind of inference or that kind of inference. Or “a matter that was included in a general rule and then left the general rule in order to teach”—all those principles are textual. Then why do we need the first ones? What? Why do we need to define the first ones? Well, in this division, the first three principles, say, are rational, and maybe also “until a third verse comes”—perhaps that too is a rational principle; probably a dispute between Rabbi Akiva and Rabbi Ishmael. But the first three are certainly rational principles, and the remaining nine or ten are textual principles. Now he says here that all the principles are rational. What does he mean? He means that even the textual methods contain interpretive logic—not inferential logic, but interpretive logic: if something is written in a certain way, it is probably to be interpreted in that way. For example, an indication: can I read a book other than the Torah, something written in the form of general and particular and general, and understand that the author really means to tell me to generalize beyond the particulars? His claim is yes. And that also makes sense. What? It makes sense. Okay, that needs a bit of thought; it’s not so simple. But I think so too. There is logic in it. Elon brings in his book—I think I mentioned this, didn’t I?—a derivation of general and particular and general made on a responsum of Maharam of Rothenburg. Professor Elon? Yes. A derivation of general and particular and general made on a responsum of Maharam of Rothenburg. Maharam of Rothenburg wrote something in a style that began with a general term, then particulars, and then a general term again, and I no longer remember who it was—one of the later authorities, or maybe one of the early ones—who interpreted the wording of Maharam of Rothenburg: apparently one must generalize this also to the case before us, even though it isn’t exactly similar to the cases Maharam of Rothenburg mentions, because there is here a general and particular and general. And afterward I collected—I have at least ten such examples—where people make general-and-particular interpretations on texts that are not the Torah. Now obviously it is much less precise there. You can’t say: okay, by how many aspects do we extend? Did Maharam of Rothenburg write general and particular or general and particular and general? That would be exaggerated. I don’t think anyone would do such a thing. From the examples I saw it’s clear that no one made the calculation whether Maharam of Rothenburg wrote general and particular or general and particular and general. That is exactly the stage we find in Hillel the Elder, because with Hillel there is only one rule, general and particular. If someone shifts from particular language to general language, then apparently he means to broaden. Fine? Now with us, after conceptualization, it became more precise, with higher resolution. But on the fundamental level there is interpretive logic here, and that is the claim. Not that every detail would have been obvious to us independently, but on the fundamental level there is interpretive logic to making such an inference, including the textual inference. That is what he means by: “but by our own intellect we could not have decided that one should indeed establish Jewish law according to them.” Here he takes it, it seems to me, a bit too strongly. Meaning, he says that we could have derived everything by reason, but reason—as he said above—is something one can argue about. What does “we could have” mean? We could have seen such a possibility through reason, but we would not have known how to decide whether it was the correct possibility or the other one. Exactly—that’s what he says. But I’m saying he takes it even further. I would say more than that: even the very possibility is not certain we would have reached on our own. For example, if no one had given us the datum that general and particular and general is different from general and particular—that it is a broader expansion than general and particular—would I have arrived at that all by myself? I’m not sure. Fine? Meaning, the details of how the interpretive principles work may indeed have been given to us—again, “given” in the sense I described earlier. They weren’t given explicitly, but they are part of the language that the Holy One, blessed be He, taught Moses our teacher, and afterward we conceptualized it into rules and so forth. I’m not sure we could have derived all that on our own. But the very transition from particular language to general language—there there is some logic in making a generalization for that reason. So I think the point is not only whether I can establish Jewish law from that result—meaning, it’s not only a question of how sure I am of the result, as he describes it. He says, basically, I could have gotten there on my own, but maybe I wouldn’t have been sure. So the Torah has to tell me: it’s okay, you can rely on this, you can issue a halakhic ruling this way. I think that even in the method itself of the inference—not only in the question of how certain I am of the result—I need tradition somewhat. I don’t think all of this could have been derived on our own. “Were it not that Moses…” yes. “The principles by which the Torah is interpreted, and the interpretations from superfluous language and all the modes of language, are one matter and have one force.” That is Maimonides’ language in the Book of Commandments, at the beginning of the second root: everything learned through one of the thirteen principles or through amplification. What—why does he bring this? What’s the proof from Maimonides’ language? Maimonides—and this also caught my eye when I studied the second root—Maimonides, in the heading of his second root, says that laws learned from interpretations are rabbinic laws, meaning they are not counted in the enumeration of the commandments. Fine, that’s the topic of the root. Now the heading of the root is the sentence written here: everything learned through one of the thirteen principles or through amplification is not counted in the enumeration of the commandments. Now what does it mean: one of the thirteen principles or amplification? Why doesn’t he just say one of the principles? What difference does it make whether it’s the thirteen principles or amplification? So he understands Maimonides as really coming to tell us that amplification is simply understanding that if there is a superfluous expression, then it probably comes to include something—that’s interpretive logic. And then he says: if Maimonides includes the interpretive principles in the same list as amplification, that means they all contain some interpretive logic. The interpretive principles are not some coded cipher—we spoke about that. There is some interpretive logic in them, like amplification. Does that sound like general and particular? Sounds like general and particular and plain meaning applied to Maimonides? Yes, maybe. Maybe even more like juxtaposition. But I think Maimonides’ intention, in my opinion, is not that at all, of course. Maimonides means simply: the thirteen principles and amplification—that is, Rabbi Ishmael and Rabbi Akiva. That’s all. The thirteen principles are Rabbi Ishmael. Now there is another school of interpretive methods, namely Rabbi Akiva’s school. The Talmud says, yes, that there is the midrashic school of Rabbi Ishmael and the midrashic school of Rabbi Akiva, in Shevuot 26. What’s the difference? The main difference is that Rabbi Ishmael, regarding general and particular, interpreted by generalities and particulars, whereas Rabbi Akiva interpreted by amplifications and restrictions. Each received from his teacher; the Talmud describes it there. So that basically means that Rabbi Akiva had a set of thirteen principles where every place Rabbi Ishmael had general and particular, Rabbi Akiva had amplification and restriction; general and particular and general became amplification and restriction and amplification. Now these are not only different names, but a different way of interpreting these changing structures of general and particular. Did he also have thirteen like that? Same thing as Rabbi Ishmael, only with amplification and restriction instead of general and particular. At least that’s what the Talmud says. And then there are amplifications in general—the word “et,” which comes to include, and all such amplifications. Rabbi Akiva would derive laws even from crownlets on the letters, yes. Every extra detail beyond the bare text he would interpret. Maybe that was additional, but amplification and restriction is part of that too, so I don’t know whether it is simply part of Rabbi Akiva’s methods of amplification and restriction. Therefore when Maimonides writes here “thirteen principles and amplification,” he doesn’t mean to hint to us anything special about the thirteen principles. He simply wants to include both Rabbi Akiva’s principles and Rabbi Ishmael’s principles. That’s all. And he says that all of them have the status of rabbinic law. And by the way, there are more than thirteen, so I think Maimonides here also doesn’t mean specifically those thirteen. He means methods of interpretation in general. In other words, what emerges from interpretive methods has the status of rabbinic law. I already mentioned that there are several rabbinic midrashim where they refer to kal va-chomers and verbal analogies, but they really mean all interpretive methods. Kal va-chomers and verbal analogies—that’s what the Talmud I mentioned earlier in Temurah says: those seventeen hundred kal va-chomers and verbal analogies were forgotten during the mourning for Moses, and Othniel son of Kenaz restored them through his dialectic. They don’t mean specifically kal va-chomers and verbal analogies there. What about general and particular and general? They didn’t forget that? That all remained in memory, and only verbal analogies and kal va-chomers were forgotten? Maybe they hadn’t even invented those yet? Even kal va-chomers and verbal analogies didn’t exist then. In my opinion, that’s exactly the point: Othniel son of Kenaz began the process of conceptualization. He reconstructed it, but not yet as a conceptualized rule. Everyone does it. Of course—everyone understands that there is such a logic. That’s exactly the point. It’s like Aristotle—we spoke about that. Aristotle didn’t invent logic. Aristotle conceptualized the logic that his predecessors also used. Every normal person uses logical inferences, but Aristotle was the first to realize that there is a system of rules here that can be defined, conceptualized, fixed—that there is some constant rule that we use everywhere, independently of the specific contents in which it is applied this way or that. So there too they use kal va-chomers and verbal analogies to say what they really mean to say about all the interpretive methods. Kal va-chomers and verbal analogies, as I said, because kal va-chomer is rational and verbal analogy is the symbol of the textual principles. So “kal va-chomers and verbal analogies” means all interpretive methods, the rational and the textual ones. Fine? So also when Maimonides says here the thirteen principles of Rabbi Ishmael and amplification, he means all interpretive methods. He does not mean specifically those thirteen. Good. Now he moves on to something interesting: he chooses to discuss what? Kal va-chomer and verbal analogy. That’s it. Those are the two principles he chooses to use in illustrating his basic idea: kal va-chomer and verbal analogy. And maybe, as you say, I don’t want to make interpretive derivations from Maimonides, but I think the choice… It makes sense—that’s the spectrum, the two extremes, no? Yes, exactly. Those are precisely the two extremes, and therefore kal va-chomers and verbal analogies are two examples: one a rational principle and the other a textual principle. So he chooses one example from kal va-chomer and one example from verbal analogy. I once read that a newly observant woman came to Rav Amital, I think, and asked him where to begin—what should she keep first in terms of commandment observance? I no longer remember exactly what he told her. He brought the three commandments we received at Marah, and there they received honoring parents, Sabbath observance, and laws. Laws, okay, because there are versions there too; Rashi brings a different list from the sages in what he says there, I don’t remember. But three—he told her that one needs one commandment from each type: one rational, moral type, one ritual type that has no evident rationality, and I don’t remember what the third category was that he found there—he conceptualized three categories there. Something that is both? I don’t know. But one from each… What? Sabbath, laws, and honoring father and mother. Yes. So here I’m saying: it’s exactly the same thing. You take a few characteristic examples and say: okay, if I illustrate this with kal va-chomer and verbal analogy, then I basically mean that this is how it works with all the principles, because these are the two types that represent the classes of principles: the rational principles and the textual principles. Let’s see what he says about kal va-chomer. “There is much to analyze regarding the principle of kal va-chomer. Kal va-chomer is not just a simple ‘all the more so.’ That is, it does not concern two things A and B whose relation is that A contains B, such that if the law exists in B, all the more so it exists in A—as in the rule, ‘if two hundred includes one hundred.’ Were that the case, all the discussion in the Talmud about kal va-chomer would be incomprehensible: neither how the stringency creates the kal va-chomer nor how an objection refutes it.” Yes. Therefore kal va-chomer is… “Rather, kal va-chomer is a certain way of learning Torah which Moses our teacher received at Sinai,” and so on. We’ll soon see what that is. What is he trying to reject here? The authors of the rules say that in biblical kal va-chomer too there is a type of kal va-chomer called “if two hundred includes one hundred.” Example: the Mekhilta gives an interpretation—actually it’s also in the Babylonian Talmud in Bava Kamma—“If a man opens a pit, or if a man digs a pit,” yes? Then he is liable to pay for a pit in the public domain. So the Talmud asks: “If he opens” and “if he digs”—if he is liable for opening it, then for digging it, all the more so. Why does it have to obligate a person for opening a pit, meaning an existing pit whose cover I merely removed, as opposed to when I dig the whole pit? It’s obvious that if I am liable for opening an existing pit, then I am certainly liable for digging it. So everyone derives something from this—the Mekhilta derives one thing, the Babylonian Talmud another—because it seems superfluous. We could derive it by kal va-chomer. So why did the verse write it? Fine, they derive something from it. But this type of kal va-chomer is the kind that those authors of the rules call “if two hundred includes one hundred.” Why? Because here the relation between opening and digging is a relation of inclusion. Digging is a broader act that includes opening within it. After all, when you dig the whole pit you also dig the top part. In other words, when you dig, you have done an opening and something more. Therefore it is called “if two hundred includes one hundred.” It’s like the relation between one hundred and two hundred: one hundred is included in two hundred. Fine? So this is not a kal va-chomer in which the second is more severe than the first, but rather one in which the second contains the first. Let’s take another kal va-chomer so we can see one that is not of that type. Fine: “If her father had but spit in her face, would she not be ashamed seven days?” Or: “Behold, the children of Israel have not listened to me, so how will Pharaoh listen to me, seeing that I am of uncircumcised lips?” Fine? So if the children of Israel, says Moses our teacher—Pharaoh is not the people of Israel plus something extra. It is simply that reason says Pharaoh will obey Moses less than Israel will. That’s all. So if Israel does not listen, then Pharaoh certainly won’t listen. Okay? That is ordinary kal va-chomer. But the kal va-chomer of “if two hundred includes one hundred” is apparently stronger—it is necessary, really a deduction—because that form of kal va-chomer basically says that when you dig a pit, included within that is that you also opened it. You simply did an opening; it’s not just that it is more severe than opening. So say I knew that for opening a pit in the public domain one must pay. Fine? And then someone asked me: tell me, for digging is one also liable to pay? I’d say: obviously. Not because digging is more severe than opening, but because when I dig, I also open. I am liable by virtue of the opening that is included in it. So here there is no objection to such a thing; it is necessary. Fine? By contrast, with the Holy One, blessed be He, and her father—right, the Holy One is more severe—or Israel and Pharaoh: Pharaoh is more stubborn than Israel or less obedient to Moses than Israel. Fine, but there could be some particular case where an objection arises—suddenly Pharaoh has some reason to be more obedient than Israel. It’s not necessary; there is no inclusion here. Inclusion is something necessary. What’s the idea in logical deduction? This is why there are books by Adolf Schwarz, a scholar of Talmudic hermeneutics at the Rabbinical Seminary in Berlin, I think. He wrote a book on verbal analogy, a book on kal va-chomer; I think maybe something on general and particular too. I think he has three books. In the book on kal va-chomer, his main claim is that kal va-chomer is basically a Greek syllogism, meaning a necessary logical inference. That’s his claim. How is a necessary logical inference built? It parallels “if two hundred includes one hundred.” Meaning, if you say: all human beings are mortal, Socrates is a human being, therefore Socrates is mortal—that is a logical inference, a syllogism. Fine? Now here it is obvious that if all human beings are mortal and Socrates is one of them, then of course he is mortal. It is a relation of inclusion. What is true of all human beings is clearly true of one of them, right? If all balloons are yellow, then if something is a balloon it is certainly yellow. This is not an inference that expands beyond my premise. Within the premise you find the conclusion; the conclusion is contained in the premise. That’s why you can’t argue with it. Anyone who accepts the premise cannot argue with the conclusion; the conclusion is simply part of the premise itself. Therefore the kal va-chomer of “if two hundred includes one hundred” cannot be disputed. It is a kal va-chomer that has no objection. The Maharsha, in the second edition there on Bava Kamma, really says that because of this the Babylonian Talmud did not want to derive from here what the Mekhilta derived. “If he is liable for opening it, then for digging it all the more so?” The Mekhilta derived from this that one may not impose a monetary penalty based solely on an inferential argument. And why do we need this doubling? After all, if for opening one is liable, then for digging all the more so. It would have been enough to write opening; why did the Torah also write digging? To teach us that one does not impose a monetary penalty based on an inferential argument. Even with money, one does not penalize from an inference. If there is a kal va-chomer, one still does not impose a monetary penalty. The Maharsha argues that the Babylonian Talmud disagrees, because it derives something else from it there on page 50, and he says the reason the Babylonian Talmud disagrees is that in a kal va-chomer like this one does impose based on inference, because this is “if two hundred includes one hundred.” This is not “based on inference”; they already told you. Exactly. It’s not really kal va-chomer at all. If they tell you the law for opening, they’ve already told you that digging is liable. It’s not a question of penalizing from an inference. So here it doesn’t make sense to say one may not penalize from an inference. Why am I saying all this? Because it means that the kal va-chomer of “if two hundred includes one hundred” isn’t really an inference at all. It’s an inference in the logical sense, but not one that innovates anything. It’s a necessary inference. Fine? The conclusion is inside the premises; there is nothing new in it. And that is what he calls here a relation of inclusion. By relation of inclusion he means: if all humans are mortal, Socrates is included in the set of human beings, therefore Socrates is mortal. That is obvious. In a relation of inclusion, the claim is that this is something that cannot be refuted; it is necessary. What does he mean by “all the more so”? He identifies “all the more so” with a relation of inclusion, and here he misses it a bit. “All the more so” is the example of “the children of Israel have not listened to me, so how will Pharaoh listen to me?” That is not a relation of inclusion. It is a relation of plain reason saying this one is more severe than that one. That’s just straightforward reasoning. Fine? What is the third type of kal va-chomer? There are three types. One is the “if two hundred includes one hundred” type—the inclusion type. “If for opening one is liable, then for digging all the more so.” Or: one who passes some of his sons through to Molech, but not all his sons. Yes, this is how the sages interpret it. Someone who passes all his sons through to Molech is exempt. Someone who passes some of his sons through to Molech is liable to death. If he passes all his sons through to Molech, he is exempt. On that they ask: but that’s a kal va-chomer of “if two hundred includes one hundred.” He got the punishment. Exactly. Why isn’t this inclusion? Exactly—it is inclusion, certainly. Did he pass them through? If he passed all his sons through to Molech, then in particular he also passed some of his sons through, no? This is a kal va-chomer of “if two hundred includes one hundred,” yes. That’s another example of that type. So that is one type of kal va-chomer. The second type can be called “all the more so.” He identifies them, but that isn’t correct. “All the more so” is a second type, a commonsense kal va-chomer. All ten kal va-chomers that the sages bring from Scripture are all of that type. Meaning, they are all kal va-chomers based on reason: if her father, then the Holy One; or if Israel, then Pharaoh. A relation between two entities where one is clearly more severe than the other; that’s reason. The standard Talmudic kal va-chomer is a third type. Most of the kal va-chomers discussed in the Talmud are of the third type. It’s the type I mentioned earlier regarding tooth and foot and horn in the public domain and in the injured party’s courtyard, the Mishnah in Bava Kamma, chapter two, where the kal va-chomer is structured like this: tooth and foot are exempt in the public domain and liable in the injured party’s courtyard; horn, which is liable in the public domain, certainly should be liable in the injured party’s courtyard. Now what do we have in this kal va-chomer? It starts from three data points, not from one. The two earlier types start from one datum and reach one conclusion. “The children of Israel have not listened to me, so how will Pharaoh listen to me?” Israel not listening to me is the datum, and Pharaoh certainly not listening is the conclusion. Meaning, there is one datum and one conclusion. Or: “If for opening one is liable, then for digging all the more so.” That is a datum and an assumption. It’s a datum and an assumption with Israel and Pharaoh too. Maybe we didn’t say the assumption, but it’s also two data points there. The assumption that Pharaoh is… never mind, but in terms of structure we didn’t say it, though it’s there too. Fine—no, it’s one factual datum. Fine. But in the kal va-chomer of tooth and foot and horn in the public domain, there are three data points we begin with: tooth and foot are exempt in the public domain, tooth and foot are liable in the injured party’s courtyard, horn is liable in the public domain. Those are the three data points. Now the question is: what is the law regarding horn in the injured party’s courtyard? Here we derive a conclusion from three data points. This is a third kind of kal va-chomer; this is the kal va-chomer discussed in the interpretive principles, not the other types. You can call it, say, Talmudic kal va-chomer. So there is “if two hundred includes one hundred,” there is “all the more so,” and there is Talmudic kal va-chomer. Talmudic kal va-chomer begins from three data points. What is the principle? I don’t want to expand too much—we could talk about it a lot—but the principle in a three-data-point kal va-chomer is that two of them always serve to generate the reasoning for me. What exists in the biblical kal va-chomer—let’s go back to Pharaoh: “The children of Israel have not listened to me, so how will Pharaoh listen to me?” There is one datum, and as you correctly said, besides the datum there is also a reason—that Pharaoh is more stubborn than Israel or less obedient than Israel. There is the datum that Israel does not listen to me, and there is the reasoning that Pharaoh obviously will be less obedient than Israel, and then the conclusion arises that Pharaoh also won’t listen to me, right? Here we have no explicit reasoning, only three data points: tooth and foot in the public domain are exempt; in the injured party’s courtyard they are liable; horn in the public domain is liable. There is no reasoning stated. So I take two of the data points and generate reasoning from them. I say like this: let’s look at the laws of tooth and foot. In the public domain they are exempt; in the injured party’s courtyard they are liable. What does that mean? Apparently it is easier to obligate payment in the injured party’s courtyard than in the public domain, right? Whatever is liable in the public domain will certainly be liable in the injured party’s courtyard. So from here I generated the reasoning. Now we have a regular biblical kal va-chomer: horn is liable in the public domain; we now have the reasoning that if something is liable in the public domain, then certainly it will be liable in the injured party’s courtyard; therefore horn is certainly liable in the injured party’s courtyard. So this means that when I have a kal va-chomer built on three data points, two of them serve to generate the reasoning, while the third datum is the anchor we also have in the biblical “all the more so.” Same thing. So now we have a third datum and a reason. Two of the data points serve me because I don’t have the reason explicitly, so in that case they generate one. By the way, almost any two of the three—well, not every pair, but two pairs among the three. For example, if you look at the public domain laws too: tooth and foot are exempt and horn is liable, right? So what does that mean? That horn is more liability-generating than tooth and foot, right? Now I move to the injured party’s courtyard. Tooth and foot in the injured party’s courtyard create liability, and we already saw the reasoning that horn is more liability-generating than tooth and foot, so if tooth and foot create liability in the injured party’s courtyard, then horn certainly does too. That is also the same formulation. From the same three data points I can formulate the kal va-chomer that way too. Either the reasoning I derive is that horn is more severe than tooth and foot, or the reasoning I derive is that the injured party’s courtyard is more severe than the public domain. Okay? But in the end, two of the data points serve to extract a line of reasoning. Now there’s an important point about the “if two hundred includes one hundred” type, as I mentioned earlier from the Maharsha’s second edition, and there are later authorities who say this too. I don’t think they’re right, by the way, but that’s what they say: that this kind of kal va-chomer has no possible objection. Because it is a relation of inclusion—how could there be an objection? Like with Socrates, yes? That’s logic, Aristotelian Greek logic. On “all the more so” there can be an objection. If the children of Israel didn’t listen to you, maybe that’s because they’re working extremely hard. Pharaoh, true, is less obedient, but he doesn’t have hard labor hanging over his head, so maybe he actually will listen to you. Who knows? Right? And a kal va-chomer can be refuted. It is not necessary; it is not like a relation of inclusion. A Talmudic kal va-chomer with three data points can be refuted even more. Because what happens in the Talmudic kal va-chomer? Not only is the reasoning uncertain, as in “all the more so”; in the Talmudic kal va-chomer, the two data points from which I extracted the reasoning—who says the reasoning really follows from them? After the reasoning, let’s talk about what happens next. But first of all, who says the reasoning is even correct? Who says that’s what emerges from the two data points? Maybe the relation between them is accidental. Maybe it doesn’t really mean that the injured party’s courtyard is more severe than the public domain; maybe there is something specific here that caused that outcome. Therefore kal va-chomer has objections. Do you understand that there are no objections to a logical deduction? A logical deduction can’t be objected to. Who can refute the inference that all humans are mortal, and Socrates is human, therefore Socrates is mortal? You can’t refute an inference like that. If you add more data, more premises, you can. Not to that inference itself. If you accept the two premises, you have to accept the conclusion, regardless of what else you add. If you accept the two premises, you must accept the conclusion. That cannot be refuted. Okay? That is the relation of inclusion; that is the kal va-chomer of “if two hundred includes one hundred.” Regarding “all the more so”—well, unless you say Socrates isn’t human. You’d have to change the premise. Yes, fine, but assuming you accept the premises. Now, in the three-data-point kal va-chomer, you can accept all three premises, all three data points, and still not accept the conclusion. Because the move from the data points to the reasoning—taking two data points and generating a reason from them—that move itself must be examined. If I have a counterexample, then I may discover that the injured party’s courtyard isn’t more severe than the public domain. The law regarding tooth and foot may just happen to be that way because tooth and foot has some special feature—that its normal manner is to go there. On the contrary, the courtyard is not its normal place to walk. But it’s the injured party’s courtyard, so that is indeed a reason to be stringent there. There is a rationale for why the injured party’s courtyard is more severe. Yes, but in the public domain it is normal for it to walk and trample things, and therefore it is exempt. In the injured party’s courtyard it is enclosed. That’s the rationale. So on the contrary, it is a rationale. It is a rationale. But I’m saying that this rationale still might not be correct if I have some counterexample. It might not be correct. A courtyard jointly owned by both parties—they start discussing it, whatever, all sorts of such things. So that is why I say: the very existence of objections means that the inference of kal va-chomer is not the logic of inclusion, not necessary logic. Otherwise there would be no objections. Fine? So the fact that the Talmud brings objections—that’s what he writes here: “Were that the case, all the give-and-take in the Talmud regarding kal va-chomer would be incomprehensible, neither how the stringency creates the kal va-chomer nor how the objection refutes it.” Why would you need stringency in order to create it? If it’s “if two hundred includes one hundred,” that’s inclusion. And of course the objection cannot be an objection to such a thing. In inclusion there are still further assumptions—for example, with the pit and the digging, there are additional assumptions there that are already assumptions we… Of course. I said I don’t agree with those rule-authors. Maybe I’ll comment on that, but I just want to finish laying out the three types of kal va-chomer. So what he says, basically, is that once there is an objection to kal va-chomer, that means kal va-chomer is not a necessary inference. So he applies this to… he calls “all the more so” a relation of inclusion, but I think there are three kinds of kal va-chomer. The inclusion type really does, at first glance, have no objection. Maybe I’ll just add one more note. The “all the more so” type and the Talmudic kal va-chomer can be objected to, because they are genuinely not strict logical deductions. Why did I say I disagree? Let me make that point anyway—we have to finish soon. Why did I say I don’t agree with the claim of those later authorities that “if two hundred includes one hundred” cannot be objected to? Because it can. And the reason is that a logical relation, whenever you apply it to the world, always involves additional assumptions. The very application does. Meaning: in mathematics, two plus three equals five. You can’t argue with that. Fine? But when I now decide that since two plus three equals five, therefore if I added two oranges to a basket and afterward added another three oranges to the basket, then apparently there are five oranges in the basket—that could in principle be false. Why? Because the fact that two plus three equals five is a mathematical fact. When you take that mathematics and apply it to the world, you have introduced some physical assumption, not a mathematical one. The assumption that adding oranges into a basket is described by arithmetic addition. And maybe… For example, adding forces in physics isn’t done arithmetically, right? Apply a force of ten newtons to a book northward, and another force of ten newtons eastward—what’s the total? Because you’re adding different things; it’s not the same. What is the resultant force? Fourteen point five. Did we refute the mathematical statement that ten plus ten is twenty? No. We refuted the physical assumption that adding forces in physics obeys arithmetic addition. It doesn’t. It obeys vector addition. But here too it follows from the definition of addition, it seems to me. What definition? There is no fixed definition of addition here. It’s not a definition; it’s physics. Physics is measurement, not definition. We measure, and we discover that the resultant force is fourteen point something and not twenty. Now from that I learn that I have to define the relevant addition as vector addition and not arithmetic addition. In other words, I discovered—the experiment showed me—that I’m not allowed to apply the rules of arithmetic addition to forces. Before the measurement I could have told you that it doesn’t… You could have said so, and others could have said otherwise, but the experiment gives me the fact that it is not so. One cannot apply arithmetic addition here. So what does that mean? That arithmetic addition itself cannot really be refuted. And if there is an experiment that shows arithmetic addition doesn’t work, that doesn’t mean arithmetic addition is false. It means that in the context of that experiment, the situation is not described by arithmetic addition. That’s all. Therefore what do I want to say here? When we take mathematics or logic and apply it to life, there is always some additional hidden assumption. A hidden assumption that says this logic is applicable to the world to which I am applying it. And that can perhaps be refuted. Now the classic example I always bring in this context is the Belgian law—the Vandervelde law, that’s what it was called. There was some Belgian city with a law that workers were forbidden to buy two liters of wine. Why? Because the worker would take his weekly wages, go to the pub, buy two liters of wine, and not bring the money home. Then there was nothing to eat. The price of two liters of wine was about a week’s wages. So the law forbade selling workers two liters of wine, or perhaps any sale of two liters of wine. Then a worker came and bought five liters, ten liters. So they took him to court or whatever—how can you do such a thing? The judge acquitted him, despite the fact that this is “if two hundred includes one hundred,” right? If he bought ten liters, then in particular he bought two. And the judge acquitted him. Why? Because he said that the whole purpose of the law is to make sure you bring your weekly wages home. But if someone decides to invest his savings in wine and become a wine merchant, how can I forbid someone to become a wine merchant? The person took his savings and bought wine with them. Fine, legitimate. If you buy two liters, then you’re spending your weekly wages—that’s what I don’t want you to do. But if you’ve decided to become a wine merchant, then that’s perfectly fine, good health to you. Now it doesn’t matter whether we accept the argument or not. The very existence of such an argument shows us that even a kal va-chomer of “if two hundred includes one hundred,” once I apply it to life, includes some additional assumption. And perhaps even that type of kal va-chomer can be refuted. For example, the case I brought earlier that Shmuel asked about: if one who passes some of his sons through to Molech is liable to death, then one who passes all his sons through to Molech is not liable to death. Everyone asks: that’s a kal va-chomer of “if two hundred includes one hundred.” Someone who passes all his sons through certainly also passed some of them through. On this the Kesef Mishneh brings several explanations. One explanation, for example, is that someone who passed all his sons through—a death penalty is not enough for him. It is so severe that the death penalty is not enough, and therefore he is not punished by the court. That is a kind of reasoning they say more generally regarding “one does not punish based on inference,” and it comes out from there. So now that argument itself is an objection to the kal va-chomer—you need to understand that. Because there is here a kal va-chomer of “if two hundred includes one hundred.” What does “one does not punish based on inference” mean? It is itself an objection to kal va-chomer. Because if B is learned from A by kal va-chomer, and A incurs lashes, then why shouldn’t B incur lashes? We see that even though B is more severe than A, it could be that A incurs lashes and B does not. Wait, does the rule “one does not punish based on inference” also apply to “if two hundred includes one hundred”? That’s exactly the question. I said that the Maharsha in the second edition says yes; other later authorities say no. Fine? So for example the Kesef Mishneh discusses that there regarding someone who passes all his sons through to Molech—why we don’t punish him by inference. The claim there is that this very explanation—that for some of his sons you are punished, but for all his sons you are not, because that punishment is insufficient—is itself an objection to the kal va-chomer. Because from the kal va-chomer you want to infer that if, say, out of five sons, if sacrificing two of them would incur death, then if he sacrificed all five, he in particular also killed two. So he should be liable to death. Right—but it may be that for all five he already deserves such a severe punishment that death won’t help. He needs a different kind of treatment—leave him to the Holy One, blessed be He, to deal with. That just won’t help. So let the Holy One deal only with the excess? The Holy One will already deal with him, so let Him deal with the whole thing. Again, it’s not important to me whether you accept the argument or not. The mere fact that such an argument can be raised—what does that say? That the inference of “if two hundred includes one hundred” is not necessary. It can be contested. Even though “if two hundred includes one hundred” is logic. Because whenever you apply it to the world, there is an additional assumption beyond the logical one, and that is where the objection can arise. Fine? Therefore I do not accept the claim that one cannot make an objection even to a kal va-chomer of “if two hundred includes one hundred.” Good. Next week we’ll continue.