Simplicity, Lesson 5

Table of Contents

• [0:00] Returning to the introduction on categories
• [1:40] The need for understanding before generalization
• [2:56] Newton’s example and the connection between phenomena
• [5:43] The cycle of induction and abduction
• [8:54] The demand to seek the reason for the verse and its implications
• [10:37] The Talmud on the four primary categories of damages
• [12:41] Defining a set: extension and content
• [14:24] The Mishnah and the definition of the four primary categories
• [27:18] The difficulty and the question of “primary category” and damages
• [30:14] Searching for derivative categories of damages in the Talmud
• [32:40] Half damages and a law given to Moses at Sinai
• [34:04] The example of the cow and the board — additional damage
• [35:07] The framework: a conceptual-learning relation versus a causal one
• [41:14] The Talmud examines the statement of Rav Pappa
• [49:44] Exemption in the public domain for pebbles propelled by an animal?
• [53:33] The rule of “it is your property and its safeguarding is upon you”

Summary

General overview

The text presents the unavoidable connection between generalization and theoretical understanding, arguing that it is impossible to ask “what” without presupposing a “why” that defines which parameters are relevant for grouping cases under a rule or law. It presents induction as generalization from an instance to a group, and abduction as the move from phenomena to a theory, and it describes theory-building as a repeated back-and-forth movement between facts and theory. Along this axis, it interprets the Talmudic topic of primary and derivative categories in Bava Kamma as a laboratory in which it becomes clear that defining a primary category and a derivative depends on essential understanding and not on mere technical similarity, and it explains the exceptional case of pebbles propelled by an animal as a causative derivative. It then connects this to understanding the “common denominator” and to the dispute among the medieval authorities (Rishonim) over the scope of liability and exemptions in a derivative learned from a common denominator.

Induction, abduction, and the movement between facts and theory

The text defines induction as the move from an instance to a group that contains it, and abduction as the move from phenomena to a theory that explains them. It argues that every induction is grounded in abduction, because deciding what the relevant parameter is for grouping facts does not arise from the facts themselves but from prior understanding. It describes science as a process in which one builds a hypothesis, checks it against the facts, refines the theory when it does not fit, and returns again and again between theory and facts with no fixed order. It illustrates this through Newton, who connected the paths of the planets with the tides, and emphasizes that dividing phenomena into groups is theory-dependent.

“There is no what without a why” and the Brisker myth

The text presents the “Brisker myth,” in the name of Rabbi Chaim of Brisk, as though one says, “You don’t ask why, only what,” and denies that this is possible as a serious principle. It argues that every determination of “what the law is” requires deciding which similarity is the relevant one, and that decision is already a “why” in the sense of understanding what stands behind the law. It connects this to the demand to seek the reason for the verse and argues that without asking why, it is impossible to interpret, impossible to define the parameters of a law beyond its explicit wording, and impossible to rule in new cases. It mentions a treatment of this issue in Rabbi Shmuel Ariel’s book Planted Within Us, and emphasizes that it is difficult to draw a sharp line between a “why” that is included in seeking the reason for the verse and a “why” that is not.

Primary categories and derivatives, essential similarity, and the definition of groups

The text explains that the primary categories of damages are types of damage written in the Torah, and derivative categories are learned from the primary ones on the basis of similarity. It argues that deciding what counts as a derivative of a primary category depends on understanding the essence of the primary category, because without that there is no way to determine which senses of similarity matter. It parallels this to extensional and intensional definitions of groups, and argues that even an extensional list of items ultimately rests on content that defines what belongs in the group. It applies this to the Mishnah that lists the four primary categories of damages and gives “this was needed and that was needed” explanations, and argues that those explanations already presuppose essential parameters such as “having a living spirit” and “their way is to go and cause damage” as relevant characteristics.

“One does not impose monetary liability through logical derivation,” the Mekhilta, and Maharsha

The text cites Tosafot, who asks how the Mishnah can sound as though “one imposes monetary liability through logical derivation,” and contrasts this with the Mekhilta on “if a man opens” and “if a man digs,” which learns from there “to teach you that one does not impose monetary liability through logical derivation.” It presents an understanding according to which Tosafot points to a dispute between the Babylonian Talmud and the Mekhilta, and it brings Maharsha in his second edition, who explains that the Babylonian Talmud also accepts the principle that “one does not impose liability through logical derivation,” except that in the case of “if a man opens / if a man digs” this is an a fortiori inference of the type “included within two hundred is one hundred,” in which “no refutation is possible.” It explains the distinction between a regular a fortiori inference, where refutations are possible, and an a fortiori inference of the “included within two hundred is one hundred” type, where the conclusion actually contains the premise, and it gives examples such as “one who offers of his children to Molekh” and “his sister, the daughter of his father and the daughter of his mother.” It connects the discussion to the fact that this kind of a fortiori inference seems like a case where one can say “what” without getting into “why,” but argues that even this is an illusion when viewed more broadly.

The Bava Kamma passage: primary categories and derivatives in damages versus Sabbath and impurity

The text presents the Talmud’s question: “Are their derivatives like them, or are they not like them?” and sets it against Sabbath, where “their derivatives are like them,” and impurity, where “their derivatives are not like them.” It cites Nachalat David, who explains that the difference is between a conceptual-learning relation on Sabbath, where the derivative is learned from its similarity to the primary category and therefore has the same laws as the primary category, and a causal relation in impurity, where the primary category produces derivatives in different degrees and therefore their laws are weaker. It concludes that the question in damages is whether the derivatives of damages are conceptual derivatives based on essential similarity, or causal derivatives produced by the primary category.

Rav Pappa, the search for “not like them,” and half damages for pebbles propelled by an animal

The text explains that Rav Pappa says that in damages there are derivatives that are “like them” and derivatives that are “not like them,” and the Talmud goes through each primary category one by one to search for the exceptional case. It emphasizes that lists such as goring, biting, crouching, and kicking are classified as derivatives of Horn not by the organ used in the act but by essential characteristics such as “its intent is to cause damage,” and it presents the Talmud’s wording, “Tooth has benefit in its damage; biting has no benefit in its damage,” as proof that the classification depends on an essential “why.” It argues that the didactic movement of the passage is meant to show that derivatives of damages are generally conceptual derivatives, and therefore “like them,” and that only one exceptional case remains as a candidate for “not like them.” It identifies that exception as half damages for pebbles propelled by an animal, as a causative derivative of Foot, because the foot causes a stone to fly and damage something, so the relation is like impurity and not like Sabbath. It explains that the law of half damages for pebbles propelled by an animal is tied to the fact that this is a novelty taught as a law given to Moses at Sinai, and it presents a dispute among the medieval authorities (Rishonim) over whether the law given to Moses at Sinai teaches the very obligation and the half-payment, or only the reduction to half.

Why is it called a “derivative of Foot” in the case of pebbles, and what practical difference does that make?

The text brings the Talmud’s question, “Why is it called a derivative of Foot?” and suggests that the term “derivative” here is not a derivative in the usual conceptual sense of damages but a derivative in the causal sense, particularly with regard to “paying from the higher-quality property.” It connects this to the distinction that Horn pays “from the body itself,” whereas pebbles propelled by an animal, even though it is half damages, is not like Horn but resembles Foot in certain respects. It notes possible follow-up questions such as atypical pebbles propelled by an animal and applications such as kicking a wooden board or plank that is transferred between domains, and hints that practical differences, such as exemption in the public domain, depend on the continuation of the passage.

The “common denominator,” the ladder of primary categories, and the dispute between Rashi and Rif

The text interprets the Mishnah’s conclusion, “The common denominator among them is that their way is to cause damage and their safeguarding is upon you,” as the focal point of a dispute over whether the general rule itself creates liability, or whether liability must always be learned from the primary categories. It presents one possibility in which the primary categories serve to build a binding general rule, while the primary categories remain mainly in order to establish the unique exemptions of each one, such as exemption for vessels in a Pit, exemption for concealed items in Fire, exemption in the public domain for Tooth and Foot, and half damages at the outset for Horn. It presents a second possibility in which the “common denominator” is only a didactic summary, and the actual liability for a new damaging force depends on learning it from a primary category or from a common denominator, and if there is a refutation from all the primary categories, it will be exempt.

Page 6: “The common denominator among them — what does it include?” and derivatives of several primary categories

The text dwells on the Talmud’s question on page 6, “The common denominator among them — what does it come to include?” and explains that the common denominator comes to include cases that cannot be learned from one primary category alone because of refutations, such as “his stone, his knife, and his load that he placed on top of his roof,” which fell in a normal wind and caused damage. It presents the novelty as a derivative learned from the common denominator of at least two primary categories, in contrast to Sabbath, where there are almost no derivatives of two primary categories, and it notes an exception mentioned in the Jerusalem Talmud according to Nachmanides and Meiri. It explains the structure of a common denominator argument, in which each primary category by itself is refuted because of some unique stringency it has, and the combination allows the derivation either because those stringencies are not the main point, or because they serve as mutual proofs that neutralize the refutation.

Exemptions in a derivative learned from a common denominator, and the language of the Rosh

The text presents the implications of the question how one learns from a common denominator: does the derivative receive the exemptions of both sources, does it receive no exemption at all, or does it receive only the exemption of one of them? It quotes the language of the Rosh: “And some of the great authorities wrote that one is liable only for what is liable in both, and they are exempt regarding damage to vessels and causing the death of a person, like Pit, and regarding concealed items, like Fire… and some were uncertain about the matter… and it seems to me that they have all the laws of Pit,” and emphasizes that the Rosh presents three practical possibilities. It concludes by saying that the dispute over whether the leniencies and exemptions are inherited from a common denominator takes us back to the question of the kinds of abstraction and generalization that underlie the derivation, and it leaves the explanation of “why specifically Pit” for later.

What I want to do today is go back a bit to things we discussed in the introduction, in the introductory sessions, about the arcs. We started talking—only now we’re really starting; good thing we chatted first. So in the introductions we talked about arcs on a few planes. Among other things, I spoke about two kinds of generalization: induction and abduction. Induction means moving from a particular to a group that contains it, and abduction means moving from phenomena to a theory. In other words, taking various phenomena and seeing what theory stands behind them. And that’s basically how you build a scientific theory too: you experiment on various cases, or you observe certain phenomena, and you build some theory that explains those phenomena. After you’ve built a theory, of course, you can also do simple induction, generalization. Meaning, you can see in what additional places there will be similar behavior according to the law you uncovered. But at the base of induction sits abduction. Or in other words, when you make a generalization—I talked about this back then—when you generalize to a group, behind that generalization to the group sits some kind of understanding. You can’t generalize to a group without understanding. Because you see a donkey that has four legs and say, fine, so all donkeys have four legs. Why? Maybe all animals in Israel have four legs. Who said the relevant parameter is that it’s a donkey? Maybe the relevant parameter is that it’s an animal in the Land of Israel. Or whatever else you can think of. And that’s an interesting question, and I talked about it back then—I don’t remember anymore—about Hempel and Carnap, about the question of how we move, if we move, from facts to theory, like the somewhat banal, somewhat naïve description of Francis Bacon, or whether it’s a back-and-forth movement. Meaning, the theory also helps us identify which facts are relevant, and only then can you move back to theory. So basically this problem reflects the fact that when you see a collection of cases, the question is, first: which collection should be assigned to the same law, to the same theory? And after that: what is that theory? Those are obviously two questions connected to each other. What is the theory? And what the theory is determines which collection of cases enters one group. Think about Newton. Newton, who discovered the law of gravitation, connected phenomena that nobody would have imagined were connected: the paths of the planets with the tides, for example. What does the phenomenon of tides have to do with how the stars move in the sky? By the same token, you could ask what theory stands behind the tides and the color of ravens in Australia. How do you know those aren’t connected? Why do these two belong to the group of things for which we should look for a common explanation? In other words, the division of phenomena into groups is itself theory-dependent. Meaning, the theory determines which group of phenomena is one relevant group. You can call that a theory, you can call it a hypothesis. You now go and test, and the hypothesis becomes a theory. Obviously, as long as it hasn’t been confirmed it’s a hypothesis, but it’s a theoretical hypothesis. You build a theory as a hypothesis, return to the facts, go back to theory, once again to facts. This happens more than once or twice—it happens many times. And every time the theory undergoes refinement, what’s called articulation, every time facts are discovered that don’t obey it, you need to change the theory. Each time you discover something new. And each time this movement between facts and theory—there’s no fixed order here, it’s always this kind of back-and-forth. Why is this on the axis of induction and abduction? Abduction is the explanation. Abduction is the move from facts to theory, and induction is the move from particular facts to groups of facts. For example, you see two bodies falling to Earth, a pen and a ball, and then you say, okay, those are two facts. Who said these are two facts that belong to the same law? Why not the color of a bird in Australia? You’ve decided that yes, there’s probably some reason. Obviously you have some theoretical intuition saying that this probably belongs to the same type, there’s a chance it belongs to the same type of phenomena. Then you ask, okay, and what unifies them, what stands behind this? You say, ah, there’s a law of gravitation. What does the law of gravitation say? The law of gravitation says that any two bodies with mass attract each other. Ah, if so, then it’s not just a ball and a pencil, it’s also a lectern, a chair, a picture, a clock, all kinds of things—anything that has mass. So I go to theory, come back, organize the group of facts, check other facts again, or perhaps in these facts something in the law doesn’t hold, or there are additional facts in which it does hold, but not exactly according to what… then I return to theory, correct it, refine it, change it, whatever it may be. Then I return to the facts again, and so on. Now the move from facts to theory is abduction. When you descend from the theory and define the group of facts, there’s basically a process of induction here, because you took two specific facts—say, about the ball and the pencil or the pen—and then suddenly reached the conclusion that all objects with mass basically behave the same way. That’s induction, but behind it sits abduction. So behind induction there always sits some kind of understanding: what stands behind the group? What is the relevant parameter that defines a group here? Now here we can maybe see these things in the topic of primary categories of damages, which I touched on a bit, but today I want to expand on more. There, I think, you can see this very clearly. And I’ll preface that with the well-known Brisker myth, in the name of Rabbi Chaim of Brisk: they say that we don’t ask why, only what. In other words, we don’t do abductions, only at most inductions. We ask what the law says, where it applies and where it doesn’t apply. The claim that follows from what I said earlier is: there’s no such thing as asking what without why. Behind every what there always sits a why. Meaning, you can’t make generalizations from particular facts if you don’t have some idea what theory stands behind it. Why should the generalization be to this group rather than some other group? In other words, why is this the relevant parameter and not that? You have to assume that this is the parameter that determines the law for our purposes. Therefore there’s no such thing as what without why—that’s an illusion. Now one of the examples, I think one of the nicest ones on this matter—why do I say this? Because it’s all a question of dosage. This was never really formulated as a conceptualized and orderly philosophical theory. If they had done some kind of work—actually, in general in the analytic yeshiva world there isn’t much reflection. In Brisk there’s relatively more. There isn’t much looking at the meaning of the rules by which we operate. People are just used to working in certain ways and so we work that way. We don’t really give ourselves much of an account: wait a second, where did these rules come from? What exactly do these rules say? Where do they apply and where not? The whole concept of literature of rules is relatively new. There’s a bit of it in the period of the medieval authorities (Rishonim), much more in the period of the later authorities (Acharonim), but it’s a new concept, this idea of literature of rules. And simply put, I think what Rabbi Chaim really wanted to say is that we supposedly do not expound the rationale of the verse, something we also know in the context of Torah-level laws: we do not expound the rationale of a verse, or interpret the verse according to its rationale, but rather we look at what is written in it. Supposedly that’s really the what without the why. But even there that’s not true. Maybe it’s out of concern—yes, many explain it because of concern, I’m not sure that’s the right explanation. But the point is that it’s an illusion. That’s why there’s a major problem defining what it means to expound the rationale of the verse. By the way, I saw a pretty good treatment of this in a book by Rabbi Shmuel Ariel called Neta Betokhenu; in general, he’s a very interesting person. You gave a series of lectures on this in Ra’anana? The topic of the rationale of the verse? Yes, yes. So the claim is that in fact, if you do not expound the rationale of the verse, you won’t be able to interpret it. Without asking why, you won’t be able to define what. How can you define the parameters of a law without understanding what stands behind it? The Torah writes a law. How can you define what that law means beyond what is explicitly written? You want to understand the principle here, on which cases to apply it and on which cases not to apply it. Behind all of that there is always some kind of why. Now the question of which why counts as expounding the rationale of the verse and which why does not count as expounding the rationale of the verse—that’s hard to draw a sharp line around. There are indications; I spoke about them there in Ra’anana. And so too in the context of dealing with the Talmudic text. Dealing with the Talmudic text is the same idea. There too Rabbi Chaim basically meant to say that we do not expound the rationale of the verse—the rationales of the Talmudic text; we are too small for that, supposedly we’re not capable of understanding. We need to describe what’s written there, focus on the facts, not engage in speculation. There is no such creature. You also can’t rule correctly, because if a case comes before you, you need to draw distinctions too. You need to say this belongs here and that doesn’t belong here. So Rabbi Chaim, in a naïve conception… you just look at what resembles it and what doesn’t resemble it. I just take it as is: if it resembles it, I’ll apply it; if not, I won’t. But that’s nonsense. In what respect is it similar? Everything is similar to something else in some respect, and dissimilar in other respects. Now you need to decide which respects of similarity are the relevant ones. But in order to know which kind of similarity is relevant, you need to decide what determines the law. Otherwise what—how will you determine the relevant parameter of similarity? Therefore there is no such thing as what without why. That’s an illusion. It’s a directional cue, something you can take from Brisk. It’s not really a rule you can take seriously. And one of the clearest examples of this, I think, is the Talmudic text at the beginning of Bava Kamma, which discusses primary categories of damages. What happens there is that the Talmudic text defines four primary categories of damages. Rashi here says: what are the primary categories of damages? These are the primary ones—the Mishnah defines—the types of damages that appear in the Torah; those are called primary categories. Secondary categories are what don’t appear in the Torah but which we derive by similarity from the primary categories. Now the relation between primary categories and secondary categories appears in other contexts too: in the laws of the Sabbath, it also appears in the Sabbatical year, even in the case of the heifer whose neck is broken there are secondary categories regarding the prohibition to plow a rough wadi—what happens with derivatives of plowing? Are you allowed to do there… there are discussions like that. And in various places, the issue of primary categories and secondary categories comes up, and also primary and secondary categories of ritual impurity, which is what is discussed here in the Talmudic text. The relation between primary categories and secondary categories obviously invites the discussion we’re having here. Because the secondary category is determined by its similarity to the primary category. And if you don’t understand the nature of the primary category, how will you decide what resembles it and what doesn’t? On what basis? You have to say it has the same foundation that the primary category has, and therefore it is similar. Which foundation is the relevant one for the law—say, in this context, for liability for damages? What is the determining parameter in an ox’s goring, because of which one has to pay? Until you decide that, you won’t know that you also have to pay for a dog bite. How will you know that a dog bite is similar to an ox’s goring? You need to decide what characterizes an ox’s goring, what the essential characteristics are, such that you can extend it also to a dog bite. Fine, but even that can be called what; you don’t have to call it—it doesn’t have to be why. It’s not why the law is like this. It’s what—what is the determining parameter? And how will you answer that? What’s the parameter? And if you ask: and how do you answer that at all? I say: according to understanding. I try to understand what stands behind liability for damages. I ask what my logic says, which parameters are relevant to liability for damages, and then I make the analogy. I can’t relate to it—it’s like what we said about definition; this was really the whole topic in our introductions. I spoke about defining groups, extensional and intensional definitions of groups. Meaning, how we define a group through its extension and through its content. Now you can define the group of democratic states just by listing all the democratic states. Just point: England, France, Israel, the United States, whatever—simply list them. But obviously you can’t start there. How did you determine the list of those states? Why did you decide they are… You have to understand what democracy is, look at each of those states and ask whether it fits those characteristics or doesn’t fit them. In other words, even definition through extension ultimately rests on definition through content. You can’t ignore the content and look at the extension as a substitute. The extension is a result. Meaning, if there’s no content behind it, then the extension is arbitrary. You can define any group you want—there’s no meaning to it, there’s no right and wrong here, and you’ll do whatever you want. If you say there is such a thing as a correct and incorrect definition, then you’re really saying that behind the extension there sits content. Behind the list of democratic states there sits a definition of what democracy is—you need to understand that. As I say, the same thing applies to primary categories of damages. And therefore, after the Mishnah lists the four primary categories of damages—the ox, the pit, the grazer, and the fire—there is a dispute among the amoraim what exactly these four are. One interpretation is that the ox is goring, and the grazer and the fire are fire and tooth and foot, so this is horn, tooth, and foot, fire, and pit. Some say human beings. This is a dispute between Rav and Shmuel. But these are the four primary categories of damages, and in the Talmudic text some discussion begins about what exactly the characteristics of these primary categories of damages are. Now in the Mishnah there are several aspects to this passage; I’ll point to a few of them. So in the Mishnah itself it says like this: Four primary categories of damages: the ox, the pit, the grazer, and the fire. Then the Mishnah starts making necessity distinctions. The ox is not like the grazer, and the grazer is not like the ox, and neither of these, which have life in them, is like fire, which has no life in it, and neither of these, whose way is to go and cause damage, is like the pit, whose way is not to go and cause damage. The common denominator among them is that their way is to cause damage. Their way is to cause damage, and their safeguarding is upon you, and when they cause damage, the damager is obligated to pay compensation from the best of the land. The Rif adds here: that they are your property—that their way is to cause damage, and their safeguarding is upon you. So all kinds of characteristics of the primary categories of damages arise here: that its way is to go and cause damage, that its initial creation was for damage, that its way is not to go and cause damage, that it has no life in it, all kinds of things of this type. So already in the Mishnah itself there are hints as to what really defines the primary categories of damages. What is the why that sits behind the what—in other words, what is really the essential definition of the primary damage category of horn, or of tooth and foot, or of pit, or of fire. And then the Mishnah makes various necessity distinctions. Necessity distinctions means: why do we need all four? Tell me one and I’ll learn the others; tell me two and I’ll learn the others. In other words, the Mishnah assumes that if something is similar enough, it need not be written; I would have learned it from the other one, or from the other two. That itself already, of course, assumes that I have some understanding of what the relevant parameters are. In other words, the Mishnah assumes—for example—if none of them had life in them, there would be no issue that these have no life in them and this one does, let’s say all of them had life in them. So the Mishnah says: if so, one of these things would have been unnecessary. It didn’t need to be written in the Torah; I would have learned it on my own. How would you have learned it? Who told you that the relevant parameter is specifically having life in it? That’s not written in the Torah; you’re deciding that those are the relevant parameters. Because obviously I ask myself what is the relevant parameter that defines a primary damage category. Apparently whether it has life in it or not is a relevant parameter. We’ll see later exactly what that does. So that’s already in the Mishnah itself. There’s an interesting comment of Tosafot here that brings us into another aspect of the issue. Tosafot asks: and it’s a bit difficult, because it implies that we impose monetary liability by logical derivation. The Mishnah implies that if indeed there were no refutation of the derivation, and it were possible to derive one primary category from another or from two other primary categories, then it wouldn’t need to be written. Why? Because we would have learned it ourselves. Tosafot says: learning it ourselves is all very nice, but we do not impose punishment by logical derivation. So how would we obligate payment through a derivation by a fortiori or by an archetypal derivation? After all, we do not impose punishment by logical derivation—at least as to a fortiori; archetypal derivation is another question. So Tosafot says: from here we see that monetary liability is indeed imposed by logical derivation. The Mishnah has no principled problem with the idea that if it could have been learned, then we would have learned it and the verse really would have been unnecessary, and we would have obligated payment on the basis of deriving one primary category from another. So Tosafot says: but in the Mekhilta it should read that it was taught: “If a man opens a pit” and “if a man digs a pit”—if one is liable for opening, then surely for digging, all the more so? Rather, this teaches you that monetary liability is not imposed by logical derivation. It says “if a man opens a pit or if a man digs a pit”—why is it necessary to write both opening and digging? Obviously if one is liable for opening, then one is certainly liable for digging. Why? Because digging includes opening too. Opening means removing the cover from an existing pit. Digging means creating the pit; among other things, you remove its upper layer, meaning it includes opening too. It is certainly more severe than opening. So if one is liable for opening, then for digging all the more so. Why then does the Torah write both opening and digging? To teach you that monetary liability is not imposed by logical derivation. Because if it had not written digging, only opening, and I had learned digging by a fortiori, that would not be enough; I wouldn’t have been able to impose liability because it came from a fortiori reasoning. That’s why the Torah writes it explicitly. And from here they also derive a general principle, that monetary liability is not imposed by logical derivation. Now, “we do not impose punishment by logical derivation” is an agreed-upon principle, but here the discussion is about money, because money is not a punishment, ostensibly; it is compensation. So the question is whether something like that is included in the rule that punishment is not imposed by logical derivation, or not included in that rule. Tosafot says there is a difficulty from the Mekhilta against what appears in our Mishnah. However, in the chapter of the cow it is expounded for a different exposition. In other words, Tosafot says that apparently this is a dispute between the Babylonian Talmud and the Mekhilta. That is how the later authorities understand Tosafot. Meaning, the Babylonian Talmud really holds that monetary liability is imposed by logical derivation, and “if a man opens a pit or if a man digs a pit” is expounded for a different exposition, later here on 51a and 49b. And the Mekhilta holds that monetary liability is not imposed by logical derivation. Now the Maharsha, in his later edition there on the Talmudic text on 49b, where it brings the other exposition, explains the dispute. He argues that the Babylonian Talmud too says that monetary liability is not imposed by logical derivation. Except that in the case of “if a man opens a pit or if a man digs a pit,” this is an a fortiori where two hundred includes one hundred. And in an a fortiori where two hundred includes one hundred, liability is imposed by logical derivation. Why? Because in an a fortiori where two hundred includes one hundred, there cannot be a refutation. That’s already an interpretation, but simply speaking, in an a fortiori where two hundred includes one hundred there cannot be a refutation. The concern in imposing monetary liability by logical derivation is maybe there is a refutation of the a fortiori. How can you punish if you’re not sure that the derivation is airtight? To be stringent and prohibit, you allow yourself. But to punish—that’s something irreversible. You don’t allow yourself to punish on the basis of an argument that might be refuted, that might collapse. Is that in all cases of punishment by logical derivation or only in monetary cases, where he says this rule of two hundred includes one hundred? No, in every case. Meaning, he argues that money is no different from punishments. That is the whole idea of the Maharsha. Money is no different from ordinary punishments; punishment is not imposed by logical derivation. In this specific case, because it is an a fortiori where two hundred includes one hundred, then liability is imposed—even in ordinary punishment. There is the well-known Kesef Mishneh on one who offers from his children to Molech. There the exposition is: “from his children,” but not all his children. The Kesef Mishneh asks: but this is an a fortiori where two hundred includes one hundred. If you offer from your children to Molech—one or two out of the five you have—you are liable to death. But if you offer all five, then not? After all, if you offered all five, then among them you also offered two. Besides, you offered another three. So the fact that you offered another three exempts you from the death penalty on the two? That’s absurd. Fine? So the well-known Kesef Mishneh gives two answers there. Yes, “his sister, daughter of his father and daughter of his mother” is the same idea. There too it is an a fortiori where two hundred includes one hundred; the same question arises there. So what does the term mean, “included in two hundred”? “Two hundred includes one hundred.” Ordinary a fortiori reasoning, ordinary a fortiori reasoning, is an a fortiori of: if what… just as, exactly, that too. Ordinary a fortiori, say: “Behold, the children of Israel did not listen to me; how then will Pharaoh listen to me, seeing I am of uncircumcised lips?” That is one of the ten a fortiori arguments in the Bible; the midrash counts ten a fortiori arguments. There it is not an a fortiori where two hundred includes one hundred. It’s ordinary a fortiori. What stands behind it? If the children of Israel don’t listen to me, then Pharaoh, who is certainly less likely to obey Moses than the children of Israel are, certainly won’t listen to me. Now that is not an a fortiori where two hundred includes one hundred, because Pharaoh is less likely to listen, and if the children of Israel don’t listen then Pharaoh certainly won’t. In an a fortiori where two hundred includes one hundred, the derived case is not more severe than the source case—it simply physically contains the source case, actually contains the source case. Two hundred includes one hundred. And two hundred is not more than one hundred in the relevant sense; it contains the one hundred, just with something added. Fine? Therefore it’s a different type of a fortiori. On the first type of a fortiori there can be refutations, says the Maharsha. There can be refutations. It could be that there is a reason Pharaoh would in fact listen—he has something to lose. Moses will strike him with plagues; he has something to lose, so he might indeed listen to Moses. The children of Israel won’t listen because they have nothing to lose—what can he do to them? Their condition is already a total mess; it can’t get worse. Okay, I’m just making this up, but there can be refutations. In an a fortiori where two hundred includes one hundred, there cannot be a refutation. Because in an a fortiori where two hundred includes one hundred—when you offer from your children to Molech and you offered two, or you offered five sons—in particular you also offered two. It’s not that five is more severe than two. You offered two, you just added another three. So punish for the two; forget the other three, I don’t know what to do with that. But for the two you need to punish. There can be no refutation to that. In any event, in my lectures I said that even here there can be a refutation. It’s not true; there can also be a refutation even in an a fortiori where two hundred includes one hundred. But that is how some later authorities take it. So the Maharsha argues that here only specifically the Mekhilta says that monetary liability is not imposed by logical derivation because this is an a fortiori—sorry, only the Babylonian Talmud says that here liability is imposed by logical derivation because here it is an a fortiori where two hundred includes one hundred. But on the principled level, the Babylonian Talmud also agrees that monetary liability is not imposed by logical derivation. That is not the plain meaning in Tosafot. What? That’s not the plain meaning in Tosafot. Tosafot is the opposite, against Tosafot. Yes. He’s not on Tosafot here; this is his later edition on the passage on 49b, on the Talmudic text that Tosafot quotes here. What is this a fortiori where two hundred includes one hundred? Through this I want one more aspect. Why can there not be a refutation there? Because fundamentally there is no abduction. It’s an inference, a generalization, or an analogy behind which there is no why. You don’t need the why. If offering two sons incurs the death penalty, then offering five sons incurs the death penalty without getting into the question of why offering two incurs death. You offered two. You also offered another three, but that changes nothing. They’ll punish you for the first two that you offered. After that you did another three—I don’t know what to do with that. But you don’t have to get into the question of why one is liable to death when one offers two. “Behold, the children of Israel did not listen to me; how then will Pharaoh listen to me?” Who told you there is an a fortiori from the children of Israel to Pharaoh? You have to build a theory. You do abduction. Why really don’t the children of Israel listen to me, and why Pharaoh? So let’s see who is less likely to listen to me, and then I can establish the a fortiori or refute it. But I need to ask why in order to state what. And the a fortiori where two hundred includes one hundred—that’s it. There you can say the what without the why. You don’t need to get into the why. Now, the Brisker dream of learning is a deceptive dream, because even inside a fortiori, within the what, you also have to ask why. But I won’t get into that here; I spoke about it in the past, so I won’t go into it here. There’s no place where you don’t need to ask why; there’s no such creature. There is no what without why. But I just want to use this to illustrate that behind every explanation sits a why. You cannot ask what and say okay, this derives from that, or a generalization of that, without getting into the question of what exactly is the relevant parameter here, the important parameter. Fine. So now I continue to the Talmudic text. The Talmudic text says: from the fact that it taught primary categories, it follows that there are secondary categories. Primary categories in damages—so apparently there are also secondary categories. And then it asks: are their secondary categories like them or not like them? Do the secondary categories have the same law as the primary one or not? If it’s the same thing. So it starts discussing. Regarding the Sabbath we learned: the primary labors are forty less one. Primary categories, from which it follows that there are secondary categories. Their secondary categories are like them. It makes no difference whether it is a primary category and one is liable to a sin-offering, or a secondary category and one is liable to a sin-offering. It makes no difference whether it is a primary category and one is liable to stoning—inadvertently it’s a sin-offering, intentionally it’s stoning—or a secondary category and one is liable to stoning. So what difference is there between a primary category and a secondary category? Then why define primary and secondary at all? The practical difference is that if one performed two primary categories together, or two secondary categories together, one is liable for each separately. But if one performed a primary category and its own secondary category, one is liable only once. Yes, in one lapse of awareness. If you do a primary category and its derivative, then you are punished once. If you do two different primary categories, or a primary category and the derivative of another primary category, then you are liable twice. But there is no difference in law between a primary category and a secondary category. There is a point in defining who is a primary category and who is a secondary category, but there is no difference between them. That’s why it is called: their secondary categories are like them. And according to Rabbi Eliezer, who holds one is liable for a secondary category in place of the primary one—never mind—there they say something else. Now the Talmudic text says: regarding ritual impurity we learned: the primary categories of impurity are the creeping creature, semen, and one impure from a corpse. Their secondary categories are not like them. For the primary category imparts impurity to a person and vessels, but the secondary category imparts impurity to foods and liquids; it does not impart impurity to a person and vessels. So in the secondary categories of impurity, the laws of the secondary category and the laws of the primary category are different. Not only when they come together, like on the Sabbath, but the law of the primary category and the law of the secondary category are different. The secondary category is not like the primary category. Okay? And then all this is part of the difficulty and the question. Then the Talmudic text says: what about here? Here, regarding primary categories of damages, what about them? The Nachalat David explains here: what does “what about here” mean? Does it resemble the Sabbath or does it resemble impurity? That is really the question here. And that is why it brought both sides. Because the primary categories of the Sabbath are like them, and the primary categories of impurity are not like them. What happens with the primary categories of damages? Now here there is a very interesting point that the Nachalat David puts his finger on, and it is connected to many disputes among the medieval authorities (Rishonim) and a lot of yeshiva-style conceptual grinding. But I think it explains very well the passage at the beginning of the chapter. What really is the difference between primary and secondary categories of the Sabbath and primary and secondary categories of impurity? Primary and secondary categories of the Sabbath: the relation between the primary category and the secondary category is one of derivation. I derive the secondary category from the primary category because the secondary category resembles the primary category. Right? In that situation, obviously the laws of the primary category and the laws of the secondary category will be the same. The secondary category is just another application of the primary category, and it’s the same principle. In primary and secondary categories of impurity, I do not derive the secondary categories of impurity from the primary categories of impurity. The primary categories of impurity generate the secondary categories of impurity. The relation is not one of derivation; it is causal. A primary source of impurity—when you touch it, you become first-degree impurity. A first-degree impurity—when you touch it, you become second-degree impurity. So the relation between the primary category and the secondary category is not that they are similar and you derive the secondary category from the primary category. It’s not a derivational relation. It’s a causal relation. In other words, the secondary category is generated by the primary category. The primary category, okay, the primary category creates the secondary category. And therefore there really can be a difference in law between the primary category and the secondary category, because the secondary category does not resemble the primary category. Why should it have the same law? The secondary category is produced by the primary category. Who says the level of impurity in first-degree impurity is the same as in a primary source of impurity? It’s one level lower. Exactly. So behind the question of the Talmudic text here there are basically two types of relation between primary categories and secondary categories. That is what the Nachalat David explains. The question is whether this is a derivational relation or a causal relation. And now look at something interesting. If that’s so, let’s go back for a moment to primary and secondary categories of damages. When the Talmudic text asks regarding primary and secondary categories of damages whether this resembles primary and secondary categories of the Sabbath or primary and secondary categories of impurity, according to this we need to continue and ask ourselves: who are the secondary categories of damages? Are the secondary categories of damages those things that resemble the primary category of damage? Then of course they will be like it, because if they resemble it then their law too will be the same. Or is the secondary category of damage produced by the primary category, as in the secondary category of primary and secondary categories of impurity, and then perhaps its law will not be like the primary category? Now look at this beautiful thing. In the end the Talmudic text looks for who the secondary categories of damages are. Rav Pappa here says: some of them are like them and some of them are not like them. In damages there are two kinds of secondary categories. There are secondary categories that are like the primary category, and there are secondary categories that are not like the primary category. In the end, the Talmudic text looks for who the “not like them” are, and it doesn’t find them. In a moment we’ll get into that search a bit more, but it doesn’t find them. It found one. Who is it? Pebbles causing half-damages. What is half-damages of pebbles? That it comes out from the foot, sort of? The pebble? Right. That is the only case of a secondary category that is a caused secondary category, not a derived secondary category. All the examples that the Talmudic text rejects along the way—goring, pushing, crouching, kicking—that’s all horn. It’s like horn. Why is it like horn? Because this one intends to damage, and that one too intends to damage. It’s not that horn creates the goring, pushing, biting, and kicking, but rather that it resembles them. This one intends to damage, and that one too intends to damage. This one is unusual, and that one too is unusual. So why should the law be different? Therefore their secondary categories are like them. The only case the Talmudic text finds where Rav Pappa says their secondary categories are not like them is the only case in the laws of damages where the secondary category is a causative derivative of the primary category, and not a derivational derivative of the primary category. And there, really like impurity, their secondary categories are not like them. Strong. What is a causative derivative as opposed to a derivational one? What is half-damages of pebbles? It’s a derivative of foot, right? Why is it a derivative of foot? Because the foot kicks the stone, then the stone flies and causes damage. So it’s not that the damage by the stone resembles damage by foot; it is caused by the foot. That’s exactly the relation between primary and secondary categories of impurity, not the relation between primary and secondary categories of the Sabbath. Right? Is it because it comes from its force? No. Why is it not like foot? It happened through its normal walking. No. Well then why is it not like foot? The pebble doesn’t damage through its normal walking? The pebble does not damage through its normal walking; the pebble is not mine. Why am I liable for it? It needs to be my property. The pebble is caused by the animal’s kick. That is what obligates me. This is a causal derivative, not a derivational derivative. Pebbles is a derivative of foot not because it resembles foot, but because it is caused by the foot. Then really the relation between it and foot is like the relation between a derivative and a primary category of impurity, not like the relation between a derivative and a primary category of the Sabbath. And therefore this is the only case where their secondary categories are not like them. And what is the difference in law? What? So what is the difference in law? The difference is that one pays half-damages. Ah, because it is caused? Yes, because it is a derivative that is not like it. It is a law perhaps similar to foot, but not identical to it. Why? Because the derivation of half-damages for pebbles is also a law to Moses from Sinai. Why is it a law to Moses from Sinai? Because I cannot really derive it from foot. If it were a derivational derivative, why would I need a law to Moses from Sinai? A derivational derivative resembles foot, therefore one is liable for it. But it does not resemble foot. Why are we liable for it? Because the foot causes it. Who says that if the foot causes something, then just as the foot is liable, so too that thing is liable? This isn’t a matter of similarity; it’s cause, so what? So the law to Moses from Sinai says that one is also liable for this. This is, of course, a dispute among the medieval authorities (Rishonim): what exactly is the law to Moses from Sinai. That’s the debate. There is a dispute: with half-damages, whether half-damages are punitive, that’s a dispute among the amoraim. Regarding pebbles, that is a dispute among the medieval authorities (Rishonim). The question is whether the law to Moses from Sinai teaches that pebbles are liable and teaches that they are liable for half-damages, or whether the fact that they are liable is obvious and it only reduces it to half. Okay? I’m obviously going in the first direction in the explanation I’m giving here. So pebbles could have many other examples too. What? Pebbles could bring in many more examples. I know. There’s a wooden plank and the cow kicks the plank and the plank falls and hits a person on the head. So? If the cow kicks it, then the question is whether that will be pebbles. Because pebbles is a derivative of foot when the animal is walking in its ordinary way. But if the cow kicks—we’ll see this in a moment—that’s horn, not foot. Because that is damage it does intentionally. It doesn’t matter that it was done with the foot. Then when it sends something flying, if it kicks and sends a stone flying, then that stone is pebbles of horn, not pebbles of foot. Then the question is whether there is an unusual form for pebbles, and that brings us into totally different passages. Or if it stepped on the wood, on the plank, because it was there in the area, and at such an angle that… No, that’s the question of the Rivam in Tosafot. What happens with a plank lying between the public domain and the private domain, and the animal walks in the public domain, and in the public domain foot is exempt. But it moves the plank and the plank causes damage in the private domain. The question is whether it is liable or not. In any event, the point here, I’m saying, the framework of the discussion—we’ll get into it more in a moment—the framework of the discussion is basically that when I speak of the ordinary relation between primary categories and secondary categories, usually it is a derivational relation. And a derivational relation means their secondary categories are like them. Why? Because the fact that something is not written in the Torah—so what? It resembles what is written in the Torah, and the same law in the Torah applies to it. Why should there be a difference? Unless there is some specific source saying nonetheless to make a distinction, but absent that, if it resembles it, then I place the same law on it. Therefore the assumption is that their secondary categories are like them. We’ll also see this later in the Talmudic text, that the Talmudic text assumes it; it doesn’t bring proofs for it. Obviously their secondary categories are like them. And once you understand this framing story, the whole passage falls beautifully into place, every line. Without it, every line is difficult in this passage; there isn’t a single line there that isn’t difficult. You can’t get through a line there. So the claim in the end is that with derivational secondary categories—and these are the secondary categories I’ve spoken about until now—basically I’m saying that after I ask why, I derive from the why the what. These are derivational secondary categories. Consequently, the law of the secondary category will be like the law of the primary category. I have full confidence in abduction. And if I reached some conclusion through abduction, I have no problem with that; that’s perfectly fine. In causal secondary categories, the whole matter is different. So I said, this doesn’t concern us all that much, because here we aren’t talking about generalization at all. We’re talking about some novelty saying that if something is caused by foot, one is also liable for it. Like secondary categories of impurity: something caused by a primary source of impurity is also impure. Fine, impurity of another kind, because it was caused by it. And for that, of course, you need a source—a law to Moses from Sinai or a verse or something. Because for something derivational you don’t need a source. If it resembles it, then I derive on my own that since it resembles it, it has the same law. For a causal derivative you need a source, because this is not an abstraction, not an inference that we make. The Torah introduced that there is another type of derivative: caused derivatives, not derivatives learned from the primary category. Okay, that is basically the point. Now look how one reads the Talmudic text, the passage. The Talmudic text starts looking for who the secondary categories are that are not like them. So it starts going primary category by primary category. The Sages taught: three primary categories were stated regarding the ox—horn, tooth, and foot. There are four primary categories of damages, but within ox there are sub-primary categories, yes? Horn, tooth, and foot. Why are they primary categories? Because they appear in the Torah. I said that this is Rashi on the Mishnah. From where do we know horn? As the Sages taught: “If it gore”—goring can only be with a horn, and so on. Now the Talmudic text asks: what is the derivative of horn? I’m skipping a bit because the details don’t matter to us. Every line here, by the way, is connected to our topic, but I’m giving the highlights. It says: what is the derivative of horn? Pushing, biting, crouching, and kicking. Notice: pushing is done with the body. If anything, I would have said this was foot, because if an animal walks and causes damage by its foot—or say by its shoulder too, or something like that—if at all I needed to assign it somewhere, it would be foot, right? But no, here it is a derivative of horn. Biting is done with the tooth, right? A derivative of tooth, right? Crouching—again with the body—and kicking is with the foot. All of these are foot except for biting, which is tooth. But no, all four are derivatives of horn, says the Talmudic text. From where—why is that? The Talmudic text asks: what is different about goring that it is called a primary category? Because it is written “if it gore.” Pushing also is written “if it push.” That pushing is goring—never mind, that’s a discussion not relevant to us. The Talmudic text asks: is biting a derivative of tooth? The Talmudic text says no. Tooth: there is benefit in its damage. Biting: there is no benefit in its damage. There’s the why. You see why biting is a derivative of horn and not of tooth. It depends how you understand it. The why is what determines what tooth is. If you say tooth means something from which there is benefit in the damage, some abstract definition like that, then right: biting is not that. Biting is not done for benefit, just to damage. Right? But if you… tooth is what is done with the teeth. If we ask, as the Briskers do, only the what and not the why, then you cannot read this Talmudic text if we ask only what. What is written in the Torah? Tooth. And what is biting? A derivative of tooth. Finished. What’s the problem? This speculation that it means there is benefit in its damage—where did you get that from? Where did this why come from? We only ask what, don’t we? Fine, the Briskers say that the amoraim are allowed to ask why; only we are forbidden. They have answers for everything. But the Talmudic text itself—but the whole flow of the passage comes precisely to clarify this issue of abduction, the abstraction that stands behind the analogy or behind the… So this is like foot again. If you take only the what without the why, then it is a derivative of foot. Then the Talmudic text says: absolutely not. Foot is common; these are not common. So the Talmudic text says: then are these the secondary categories that are not like them that Rav Pappa spoke of? So what was Rav Pappa talking about when he said that among the secondary categories there are some that are not like them? I said: this is about pebbles, but that’s on the next page. We’re on the way there now; I only brought the framework. About what? If you say these—then perhaps he was speaking about these four, derivatives of horn? How are they different from horn? Horn intends to damage, is your property, and its safeguarding is upon you. These too intend to damage, are your property, and their safeguarding is upon you. I don’t understand. Rav Pappa tells you that among secondary categories there are some that are not like their primary categories. Now they tell you that these four are derivatives of horn, right? Okay, maybe Rav Pappa was talking about that? It can’t be, because it’s like the primary category, so of course the law will also be like the primary category. What do you mean, the derivative is like the primary category? Exactly. And to that Rav Pappa says: even though a derivative is learned from the primary category, nevertheless there are some among them that are not like them. The Talmudic text here assumes what it needs to prove. The Talmudic text is looking for what Rav Pappa was talking about, and assumes he wasn’t talking about this, and then asks: so what was he talking about? He was talking about this—who says he wasn’t? What do you say? What? Who says? Because derivative—why is it called a derivative? Because it is a derivational derivative and not a causal derivative. The whole passage is going on this. If the derivative is a derivational derivative, it would never occur to anyone that Rav Pappa would say it is not like the primary category. If it resembles the primary category, then its laws are like the primary category. Now the Talmudic text is clarifying exactly this point: are these derivatives causal derivatives, or I don’t know, technical ones, or are they derivational derivatives? If you were to say that biting is a derivative of tooth simply because it is done by the tooth, there is really no similarity to the damaging action of tooth, but it’s the same thing—I don’t know, it’s kind of like causal, really caused by the tooth, if you like. It’s not really, but let’s say. It is certainly not a derivational derivative, because there is no similarity: in the relevant parameter there is no benefit in the damage here whereas there is benefit there. It doesn’t resemble it. So they tell you: absolutely not. The proof is that this baraita says these four are derivatives of horn. What does that mean—how can that be a derivative of horn? Apparently these derivatives are derivational derivatives, even though they are not done by the horn, but they resemble horn and therefore they are derivatives of horn. Ah, if so, then obviously they are like them. You don’t need proof; it’s obvious. We are only looking for a derivative that is not a derivational derivative, one about which Rav Pappa could say that it is not like it. The whole discussion revolves around this. Now look at the continuation. The Talmudic text says: the derivative of horn is like horn, so from horn we won’t find salvation. Then what was Rav Pappa talking about when he said among the derivatives there are some that are not like them? And if Rav Pappa was talking about tooth and foot? Maybe it’s on tooth and foot? Where are tooth and foot written? Never mind. The Talmudic text asks: what is the derivative of tooth? Long story, irrelevant, doesn’t concern us. Continuing the passage: what is the derivative of tooth? What—what are the derivatives of tooth? Exactly as we asked about horn before, we’re looking for candidates for whom Rav Pappa was speaking, yes? It rubbed itself on the wall for its pleasure and dirtied produce for its pleasure. That is a derivative of tooth: it rubs itself on the wall for its pleasure and the wall falls with its body, yes? Or it dirtied produce for its pleasure—it steps in them, sits in the produce like this, there’s fruit juice, and it sort of bathes in the fruit juice. What does that have to do with tooth? If anything, it’s foot. It’s done with the body. Why is this tooth? So the Talmudic text says: how is tooth different? Because there is benefit in its damage, it is your property, and its safeguarding is upon you. These too involve benefit in their damage, are your property, and their safeguarding is upon you. Therefore the derivative of tooth is like tooth. And therefore it cannot be that this is what applies to derivatives of tooth—again, assuming what it needs to prove. Who told you? Maybe this itself is what Rav Pappa was talking about—who says not? Exactly like with horn. Once we reached the conclusion that these are not derivatives—it’s of course all a rigged game; the Talmudic text knows everything in advance—but this is its didactic way of telling us the matter. It wants to tell you that the derivatives of damages are derivational derivatives, and for derivational derivatives it is obvious that the derivative is like them. And it teaches us this by simply going primary category by primary category and showing us for each primary category that the lists of derivatives are derivational derivatives, not causal derivatives or derivatives of technical similarity, but of essential similarity. Consequently it is obvious. And it looks for where there is a derivative that is not derivational, so it brings a list of derivatives, and in all of them it is obvious that they are derivational. How do I know? Because if they were not derivational, they really would not resemble them, so why are they derivatives? Sorry, there is essential similarity, but they are not done by the tooth. So why is it a derivative? Only because they conceptually resemble it; that is why it is considered a derivative of horn, of tooth, or something like that. So if that’s the case, then obviously it is also like it. It’s not assuming what it needs to prove; it’s obvious. The whole thing already begins with the question: what does “like it” and “not like it” mean? Then they move on to foot, same idea. Yes, with foot too: it damaged with its body while walking, and with its hair while walking, and with the saddle upon it, and with the bridle, and with the bell on its neck, and so on. Then the Talmudic text says that there it really does look like derivatives of foot, by the way, and therefore they already skip the possibility that it might be derivatives of horn, because there it really is foot, even in the ordinary sense. And once again the Talmudic text says: true, but it also resembles foot in the essential sense. Because foot means in the course of its ordinary walking, and all these things are also in the course of its ordinary walking. Therefore it is obvious that this too is like it. In short, we’re stuck. Rav Pappa is speaking neither about derivatives of horn, nor derivatives of tooth, nor derivatives of foot. So what was he talking about? The conclusion of the Talmudic text on page 3b: the derivative of pit is like pit, and all the things—the same whole move. Derivatives of a human being, and when Rav Pappa said a derivative of foot, we established it and so on—half-damages for pebbles are learned by tradition as law. Fine? Then they ask: why is it called a derivative of foot? What do you mean, why is it a derivative of foot? To pay from superior property. What do you mean, why is it a derivative of foot? Because it is done by the foot. Derivatives are derivational derivatives in damages. So why is this called a derivative of foot at all? What connection is there between pebbles and foot? Because the foot caused the pebbles. Right, but that’s not what derivatives are. Derivatives in the ordinary sense—the all the derivatives we went through until now are derivational derivatives. So this is called a derivative of foot only because it pays from superior property, that’s all. It’s not really a derivative of foot in the full sense. Or for our purposes: it is a derivative of foot in the causal sense. Yes, but not in the accepted sense in the laws of damages. Why doesn’t the Talmudic text say that it is foot because it is caused by the foot? Because the derivatives in damages are derivational derivatives. There is a result, there is a derivative, there is a derivative. Exactly. So the Talmudic text says it’s a derivative in that sense only in order to tell you it also resembles it in law. So it is considered a derivative also in the accepted sense in damages with respect to what? Only with respect to paying from superior property. Unlike the half-damages of horn, which are paid from the animal’s body. What? What does horn pay from? From the animal’s body. Of course—you ruled out its being horn. Right, that’s what we came to say: it is a derivative of foot only in the sense that it is not horn. Half-damages, but not horn. Why isn’t it simply foot because it is a causal result of foot? That’s obvious, that was already stated by the Talmudic text at the outset. But the derivatives in damages are not derivatives of that type. Derivatives on the Sabbath are derivational derivatives; derivatives in impurity are causal derivatives. The derivatives in damages—the concept of derivative in damages—is like the Sabbath, a derivational derivative. There is one exception. Not that there are two kinds of derivatives—there is one exceptional case. Why is it called a derivative at all? It’s not really the concept of derivative that belongs to damages, except with respect to paying from superior property. And that is basically the only aspect. That’s how I understand it at least. But it pays from superior property because it is causation, no? Yes, but paying from superior property matters only so that it won’t be like horn, because horn pays from the animal’s body. No matter; this is another type of half-damages in the laws of damages. So what is the difference, really, between causal and derivational in terms of the result? There is no difference—it is half-damages and not full damages. No, it says the reason is different. No, it is half-damages and not full damages because it really does not resemble foot. The laws are not like foot. There is a certain similarity to foot: that this half-damages is not punitive but monetary, and it is paid from superior property and not from the body. That is what he meant. That is all Rav Pappa meant. And only about this did Rav Pappa speak. Now the whole movement here—once you look at it this way, you see how the whole structure of the first two pages of Bava Kamma is completely clarified. It’s clear what the question is, it’s clear why they made this whole rigged game the whole way through—the derivatives are of this and of that, and how do you know? It’s all assuming what it needs to prove. Nothing there works. If you read it this way, it all blossoms. Everything is simple; every line falls into place. All they wanted was to show you systematically how one learns primary and secondary categories of damages, what the meaning is of the relation between primary category and secondary category, namely that it is like the Sabbath and not like impurity. They went through all the primary categories to show you that, and all of this was done just in order to clarify what Rav Pappa was talking about. That was not really the purpose of the passage. The purpose of the passage was to provide an introduction to Bava Kamma. They used Rav Pappa because through him they went through all the primary categories and derivatives and showed you what the general idea of primary and secondary categories in damages is. That is really the meaning of the passage. Now, what about exemption in the public domain for pebbles? What? Is there exemption in the public domain for pebbles? Simply speaking, yes; it is a derivative of foot. I don’t remember whether it is stated explicitly, but I think so. No, then you could say there is also a practical difference for exemption in the public domain, not just for paying from superior property? The Talmudic text—meaning, that is the intention. The intention is all the other laws too, apart from half-damages. That it is like foot—paying from superior property means all the laws are like foot except for the point of half-damages. It perhaps depends on chapter two; there is a series of dilemmas there about unusual pebbles, and maybe there it will depend on this. Okay, now one more point. In the Talmudic text on page 6, I already mentioned, let’s start from the previous Mishnah. The Mishnah concludes, after describing all the primary categories, that the common denominator among them is that their way is to cause damage and their safeguarding is upon you, and when they cause damage, the damager is obligated to pay compensation from the best of the land. So the Talmudic text basically—the Mishnah basically—ends at the end, after giving the characteristics of the primary categories, not all the characteristics but typical characteristics of the different primary categories, and says: but they also have a common side among them. They are all your property, which the Rit inserted here—the term before us doesn’t appear—your safeguarding is upon you, and when they cause damage, then he has to pay. From the best, he has to pay. So that is the summary, basically. After there are all the primary categories, I also know there is something shared that encompasses them all. And on this point there is a famous teaching from the Rabbi of Brisk, which people in yeshivot deal with through all of Bava Kamma: a dispute of the medieval authorities (Rishonim), Rashi and the Rif. He hangs it on the question of why—what exactly is written here. Is what is written at the end that after you have all the primary categories, you can basically use the ladder, climb the tree, and throw away the ladder? The primary categories are just the way to generate the common denominator. Now that you have the common denominator, anything that meets this general criterion is liable to pay. Fine? And another possibility is no. In fact they have a common denominator, but this common denominator by itself does not obligate. Meaning, you need to resemble one or two of the primary categories in order to be liable. In other words, if you bring me something that is my property and whose safeguarding is upon me and it causes damage, I am not necessarily obligated to pay. Even though there is here a rule that anything that is your property and whose safeguarding is upon you, if it causes damage, you have to pay—that depends on whether you can derive it from one primary category or from two primary categories or from whatever primary categories are written in the Torah. If you can’t derive it from them, if there is some refutation against all of them, then it will be exempt. The first view says: what are you talking about? If it is your property and its safeguarding is upon you, you are liable. So why distinguish among the primary categories? And the Talmudic text here says: for their laws. Meaning there are special exemptions. In a pit there is an exemption for vessels: ox, and not a human being; donkey, and not vessels. In fire there is an exemption for hidden items—what is hidden inside something else and gets burned, then the owner of the fire or the one who ignited the fire is exempt for what was hidden inside. Tooth and foot are exempt in the public domain, and horn is exempt from full liability, paying only half-damages in the first three gorings. In each of the primary categories of damage there is a special law, some leniency, some exemption. Fine? Now according to the first method, what really obligates is that it is your property and its safeguarding is upon you. Anything that is your property and its safeguarding is upon you—you are liable. If you belong to one of the four categories of primary damages, you will have the exemption of that category. Meaning, the primary categories now still remain; the ladder has not been completely thrown away—it’s at a 45-degree angle. They didn’t throw it away completely. The ladder was used to generate the common denominator. The rule says that if it is your property and its safeguarding is upon you, you must pay—anything. Now ostensibly you could have remained in a situation where you could throw away the whole Mishnah. Now I already have the rule; I learned it from the four things in the Torah that couldn’t have been learned with fewer than four—that is what the Mishnah proves. So it needed all four. But after I have all four, I have a rule. Anything that is my property and whose safeguarding is upon me, I need to pay. So now a case comes before me—what do I need to do with it, whether it is liable or exempt? Simply see whether it is my property and its safeguarding is upon me—if so I have to pay if it caused damage, and if not then not. How would he pay in that case the Rabbi said—so suppose there is such a case where it doesn’t resemble, there would be a refutation, whatever, never mind. According to this view that makes no difference. Full damages? Yes. In principle you pay by virtue of the fact that it is your property and its safeguarding is upon you; you no longer remember that the four primary categories helped you climb this tree or generate this rule. So why do we need the four primary categories? Why didn’t the Torah simply write that directly? Because each of the primary categories has exemptions. Suppose now this new damaging thing that I am obligating is my property and its safeguarding is upon me. Now I ask: it caused damage in a hidden item, it damaged vessels—is it exempt? Depends. If it resembles pit, then I will exempt it as to vessels. If it resembles fire, I will exempt it as to hidden items. As for the exemptions, there it is important whether you resemble one of the primary categories. As for the basic liability: if it is your property and its safeguarding is upon you, you are liable to pay. The rule determines it; that rule already covers all the cases. You don’t need to go back to the primary categories. The four primary categories of damages built for us when you are exempt—exactly, they come to be lenient. They do not come to obligate. According to the second approach, no. The liability is learned from each of the primary categories. The summary is only a didactic summary, but in the end the liability is learned from the primary categories. In order to impose liability for some damaging agent, you need to derive it from a primary category or from two primary categories together, the common denominator or something like that. Without this, you can’t impose liability. And what is the relation between this new general rule and derivatives? Couldn’t there be a contradiction between them? And that will depend exactly on the point I just made. Now look. On page 6a the Talmudic text asks: “the common denominator among them” comes to include what? I already mentioned how that question is very funny, because the Mishnah usually brings us examples, not rules. And here the Mishnah did us a favor: it gave us the rule. Ox, pit—what do you want? Just tell me what needs to exist in order for there to be liability. What are all these crazy examples for? The examples, yes. Give me the rule and that’s it. Now fine—here the Mishnah did us a favor, gave us the rule, did not suffice with examples. So I would have expected the question: okay, so why do we need the examples? Tell me: for their laws. That was the answer; on page 5 they talk about it. But the question that should have been asked is: why do we need the examples? And the Talmudic text asks: why do we need the rule? As though rules are some kind of thing in which the Talmudic text has no confidence at all. Just an interesting lesson. Fine. But for our purposes, the Talmudic text says—and this is connected, connected to the lecture on forced interpretive narrowing. What? Yes, connected to the lecture on forced interpretive narrowing, and on rules and details, yes, many things. So the Talmudic text says—it brings various cases that the common denominator comes to include. For example, one’s stone, knife, and load that one placed on top of one’s roof, and they were blown by a normal wind and caused damage, whether while flying or after coming to rest, doesn’t matter. So we need the common denominator. Why do we need the common denominator? Because you can’t derive this from any one of the primary categories of damages. Whichever primary category of damages you bring me, there is some refutation, such that you cannot derive it from there. You need to use two together and derive this damage category from the common denominator of the two together. Or one who put out refuse into the public domain—there are several. The Talmudic text asks: but I learned the rule from the four primary categories of damages. Exactly. So I derive a rule from the four primary categories of damages in order to say things that are not within the four—not exactly. The rule, listen, logically the rule is a bit problematic. The rule comes to include derivatives that are derivatives of more than one primary category, which you can’t derive from one primary category but only from the common denominator of at least two primary categories, or three, or four. Without this you would have only derivatives of one primary category. This means, for example—I mentioned this in one of the lectures—but on the Sabbath there isn’t a single example of a derivative of two primary categories. Very interesting. There is no common denominator. In the laws of the Sabbath there is no common denominator. Every derivative is a derivative of one particular primary category. There is no derivative that needs the common denominator of two primary categories, unlike the examples brought here on page 6 in damages. Except for one example, as I said: one who spits in the public domain, according to the Jerusalem Talmud, according to Nachmanides and the Meiri. That is the one example that combines throwing and winnowing—a combination of throwing and winnowing. We’ll get back to that in a moment. But here what the Mishnah is really saying is that in damages there are derivatives that are derivatives of several primary categories, unlike the Sabbath. And that is what the common denominator of the Mishnah comes to introduce. Not just derivatives of one primary category—that we would have done anyway, because that is a derivational derivative. But a derivative of two primary categories is not so simple. The Mishnah comes to say that even a derivative of two primary categories can be derived. What is novel about that? The novelty is that in a derivative of two primary categories—why do we need to derive it from two? Because neither of them alone could have taught it. Why not? Because each of the primary categories has some feature, some stringency of its own, that would have refuted the derivation on its own. You need to combine two primary categories, at least two—here in this case it is two—in order to derive the secondary category. And therefore, in practice, let’s say we want to derive one’s stone, knife, and load that one placed on top of the roof—it doesn’t matter—from fire and pit. Fine? From fire and pit. If this is while it is flying, fire and pit. So the Talmudic text explains why it could not have been derived from fire: because another force is involved in it. Why could it not be derived from pit? Because its initial creation was for damage. Never mind, there are various reasons why it cannot be derived from fire alone or pit alone. Fire has one special stringency and pit has another special stringency. And those two special stringencies are not found in this specific damaging thing of one’s stone, knife, and load. So what then? If I understand that derivatives are derivational derivatives, this derivative does not resemble any of the primary categories. With each primary category there is some difference. You cannot really derive it. You need the common denominator to introduce that even if you derive from two primary categories together, although it does not resemble either one specifically, if it resembles their common denominator that too is enough. That too is a derivative, and for that we need the end of the Mishnah. Fine? That’s not really the rule described there. The plain meaning of the Talmudic text is like the view of the medieval authorities (Rishonim) I mentioned earlier. The plain meaning of the Talmudic text on page 6 is that the common denominator does not really come to create a rule that obligates. So that is what the common denominator comes to introduce. Now here there is an interesting point, because how is such a common denominator built? A common denominator like this is basically built, throughout the Talmud and especially here, in the following way. I have two teaching cases, A and B, and I have the derived case, let’s say the two primary categories and the derivative, which is C. Okay, and I need to derive C from A and B. How does that work? If I try to derive it from A, it doesn’t work, because A has a certain stringency, fine? X. Fine, so I’ll derive it from B. No, B has another stringency called Y. If it had the same stringency X as A, then you couldn’t derive it. There is no common denominator in that situation, because both primary categories differ from the derivative in the same way. But B has another stringency, so from B too it cannot be derived alone. Now the Talmudic text does some kind of hocus-pocus: if you take A and B together, then yes, you can. What is the logic? It differs from both A and B, right? So why, if you combine the two together, can you suddenly derive it? Usually now this can be understood in two ways—I’ll shorten a bit. It can be understood in two ways, and this is all connected to abstractions and generalizations; I’ll explain it next time more explicitly. You could understand that each of the primary categories teaches—or say, you could understand in the simplest way, like the two possibilities of the common denominator in the Mishnah—namely, that these two primary categories together basically tell you that if in both primary categories, in both fire and pit, one is liable, then that means that the facts that its initial creation was for damage or that another force is involved in it—that’s not the point; those are not important points. What is important is that it is your property and its safeguarding is upon you, and if that is true in the derivative, then all is fine even though it does not specifically resemble any one of the primary categories. Then we’re back to that understanding of the common denominator in the Mishnah. Another possibility is to say no—I am really deriving it from pit; it’s just that pit has a problem: with pit, its initial creation was for damage, and maybe that is why one is liable. But if not one’s knife and load? Fire will prove otherwise. Fire will show that this doesn’t matter. That parameter is not an obstacle; the proof is that in fire it does not exist and one is still liable. Fine? Then I derive it specifically from pit or specifically from fire, not that I derive it from their common denominator, which is really that it is your property and its safeguarding is upon you, but rather I derive it specifically from the primary categories. What practical difference would there be? The practical difference would be which exemptions this derivative would have. If the derivative was derived from pit and fire, and this derivative damaged something hidden—would I obligate the damager? In fire there is an exemption for that, but in pit there is liability for that. Right? If it damaged vessels, for which pit is exempt, would it be liable for the vessels or not? If you derive it from pit, then “with the source case there is only its own novelty”; in other words, “it is enough for that which comes by logical derivation to be like the source.” Pit is exempt regarding vessels; you cannot impose more liability on the derivative learned from pit than the liability imposed in pit itself. Ostensibly we would have expected it to have both exemptions, both the exemption for hidden items and the exemption for vessels. Right? Another possibility is to say no. Really, since it is my property and its safeguarding is upon me, therefore I am liable. In order to derive the leniencies, it has to resemble one of the primary categories, but it does not resemble any of them, because this is the common denominator, the second view of the medieval authorities (Rishonim)—the Rif and Rashi that I mentioned before—so therefore you cannot derive any of the leniencies. It will be liable both for hidden items and for vessels. Not fair, what? Okay, but here too you would ask how to derive that exemption, because it doesn’t resemble any of the primary categories, and in order to exempt it needs to resemble one of the primary categories. Okay, that is one possibility. Now it turns out there is also a third possibility. In the Rosh there is a third possibility. It would have the exemption of pit but not the exemption of fire. Three possibilities—let me show you the language of the Rosh and we’ll finish with this. Ostensibly there could be four. What? Yes, but that doesn’t appear in the Rosh. In the Rosh there are only three. In the Rosh, which people usually read, there are generally two, but I argue that in the Rosh there are three. “And some of the great scholars wrote that one is liable only for what both are liable for, and exempt from damage to vessels and from causing the death of a person, like pit, and from hidden items, like fire.” They have both exemptions, both of pit and of fire. “Since they come by way of the common denominator, we give them the lesser of the two.” “And there were those who were uncertain about the matter.” What does “uncertain about the matter” mean? Uncertain between what and what? Whether they benefit from the exemption or not. Which exemption? There are two exemptions here. Ostensibly both, right? So far there has not been mention of a possibility to split them. So “uncertain about the matter” is a further view in the Rosh, a second view. There is one side that says it has both exemptions of pit and fire, and one side that says it has no exemption—neither of pit nor of fire. A doubt. In other words, there is one view that says it has both exemptions, and another that is uncertain whether it has both exemptions or no exemptions at all. “And it seems to me that they have all the law of pit.” The order in which the views are presented hints that the phrase “and there were those who were uncertain about the matter” is not a doubt between the first and second views, because otherwise he did not present them in the right order. He should have brought the first view, then the third, then brought this as second, and then “there were those who were uncertain” would mean either this or that. “There were those who were uncertain about the matter”—it is clear that the uncertainty is not whether to give them both types of exemptions or only one. No. The uncertainty is either both or nothing. And he himself says neither this nor that, but rather only like pit, and not the exemption of fire, but only the exemption of pit. So if that’s the case, we need to explain here—and he explains why pit, why specifically pit. All the law of pit applies to them. Why specifically pit and not fire? We’ll talk about that—not now, next time. That brings us to the question of types of abstraction or different types of generalization that are present here. But basically, what we need for our purposes—and I’ll finish with this—is that we ultimately arrive at the fact that there are three possible methods in what comes from the common denominator: either it receives the leniencies of both, or it receives the leniency of neither, or it receives the leniencies of one and not of the other. And in this case, specifically of one and not of the other alone. But that can be discussed further. Shalom.