Conceptual Analysis – Lesson 14
This transcript was produced automatically using artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.
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Table of Contents
- Ways of inference: deduction, induction, and analogy
- Ranking reliability between induction and analogy and reversing the relation
- Analogy as a two-stage process: induction and then deduction
- Elimination of features, scientific generalization, and the “common denominator”
- A principle derived from two verses in Bava Metzia: standing grain and vineyard
- A common denominator with halakhic features versus factual features
- The four primary categories of damages and the Mishnah’s rule in Bava Kamma
- Talmud in Bava Kamma 6a: his stone, knife, and load that were placed on the roof and fell in a normal wind
- The Rosh: exemptions regarding his stone, knife, and load, and the breaking of the symmetry
- Fire as assistance in neutralizing the involvement of wind: a derivation that is not a “common denominator”
- Spitting into the wind on the Sabbath: Rema, Mishnah Berurah, Rabbi Akiva Eiger, and Alfei Menashe
- Conceptual construction: uniting unique features versus intersecting a “common denominator”
- Subcategories derived from two primary categories in damages versus Sabbath
Summary
Overview
The speaker presents the three modes of inference—deduction, induction, and analogy—and sets out a principle of an inverse relation between how much information a conclusion adds and its level of certainty. He argues that dividing things into three modes is misleading, because analogy is built from two stages: a hidden induction from the particular to the general, followed by deduction from the general to the particular. From there he develops the concept of the common denominator as a logic of filtering out irrelevant features, connects this to Talmud study in Bava Metzia and Bava Kamma, and proposes an additional distinction between a derivation of the common denominator type and what he calls conceptual construction, where a third concept is created by combining unique features from two source cases.
Ways of inference: deduction, induction, and analogy
Deduction is presented as necessary inference because the conclusion adds no information beyond what is already contained in the premises. Induction and analogy are presented as inferences that add information, and therefore cannot be certain, because every addition of information beyond what is given involves speculation. The speaker presents the “price” of certainty versus information: striving for full certainty leaves you with zero information, and striving to know everything leaves you with zero certainty.
Ranking reliability between induction and analogy and reversing the relation
The speaker presents an initial intuition according to which analogy is more reliable than induction, because analogy transfers a property from one case to one case, whereas induction generalizes across a large group and is therefore more error-prone. He shows that induction can be treated as a collection of many analogies, so that error is possible in each one. He then reverses the picture and argues that every analogy contains a hidden induction, because the move from “this table” to “that table” relies on a general assumption about “all tables” by virtue of their being tables.
Analogy as a two-stage process: induction and then deduction
The speaker argues that in practice there is only one way of inference, namely analogy, and when you break it down two fixed stages emerge. The first stage is induction from particular cases to a presumed rule, and the second stage is deduction from the rule to the new particular case. He illustrates this with books that have red covers and other examples, to show that analogy works by means of generalization and then application.
Elimination of features, scientific generalization, and the “common denominator”
The speaker describes generalization as a process of filtering out irrelevant features and isolating the shared feature that explains the behavior. He illustrates this with objects falling to earth, where the material or shape of the object is irrelevant and the relevant feature is mass, and presents this as scientific elimination. He connects this to the Sages’ expression “the common denominator” as a mechanism for identifying the shared relevant parameter among cases, and adds a rule from information theory according to which removing features expands the group of objects that fit the description.
A principle derived from two verses in Bava Metzia: standing grain and vineyard
The speaker brings an example of deriving a principle from two verses, where the Talmud learns the worker’s permission to eat from standing grain and from a vineyard. He presents the move: “What about standing grain, which is subject to challah… the vineyard will prove it… what about the vineyard, which is subject to gleanings… standing grain will prove it… and the law returns… the common denominator between them is that they are produce of the ground, and at the time of completion of labor a worker may eat from them.” He explains that this process neutralizes unique features that are not shared by the two source cases, identifies the shared feature “produce of the ground,” and generalizes from that to everything that is produce of the ground.
A common denominator with halakhic features versus factual features
The speaker distinguishes between a common denominator that removes unique halakhic laws, such as challah and gleanings in the example of standing grain and vineyard, and scientific generalization, which deals with factual features of objects and events. He argues that in Bava Kamma there is a possibility more similar to scientific generalization, because one can identify factual features of the primary categories of damages, such as “its creation was initially for damage” in the pit, or “another force is involved in it” in fire, alongside halakhic features such as exemptions and payments.
The four primary categories of damages and the Mishnah’s rule in Bava Kamma
The speaker quotes the Mishnah’s rule: “The common denominator among them is that they are your property, and their safeguarding is upon you, and it is their way to cause damage; and when they cause damage, the damager is obligated to pay compensation from the best of the land.” He explains this as an inductive generalization that identifies the features relevant to liability for payment and removes factual features that cannot be decisive because they are not shared by all the primary categories. He presents the principle according to which anything that is your property, whose safeguarding is your responsibility, and whose way is to cause damage, creates liability for payment even if it does not resemble exactly one of the primary categories.
Talmud in Bava Kamma 6a: his stone, knife, and load that were placed on the roof and fell in a normal wind
The Talmud asks, “What does ‘the common denominator among them’ come to include?” and Abaye answers, “To include his stone, his knife, and his load, which he placed on top of his roof, and they fell in a normal wind and caused damage.” The Talmud rejects the possibility that the damage occurred “while they were moving,” because then “that is just fire,” and it rejects the possibility of damage “after they came to rest” when he had declared them ownerless, because then “that is just a pit.” It concludes that the case is one where he declared them ownerless after they came to rest, and nevertheless “they are not similar to a pit,” because with a pit “no other force is involved in it,” whereas here “another force is involved in them”; therefore “fire will prove it.” That derivation too is challenged, because with fire “it is its way to go and cause damage,” and finally “the pit will prove it, and the law returns.”
The Rosh: exemptions regarding his stone, knife, and load, and the breaking of the symmetry
The Rosh cites an opinion that “one is liable only for what is liable in both,” and therefore exempts regarding “damage to vessels and the death of a person, like a pit, and hidden items, like fire,” because “since they are derived by the common denominator, we assign them the lighter law of the two.” He also cites the opinion that “they were uncertain about the matter”—whether both exemptions apply or neither one does—and finally writes, “It seems to me that they have all the law of a pit,” meaning that in his view they have only the exemptions of pit. The speaker argues that the Rosh’s ruling cannot stem from the regular logic of a common denominator, because it breaks the symmetry between pit and fire and treats pit as the main category.
Fire as assistance in neutralizing the involvement of wind: a derivation that is not a “common denominator”
The speaker explains that according to the Rosh, his stone, knife, and load are essentially similar to a pit, and the only problem is that the involvement of the wind in creating the obstacle might have prevented deriving it from pit. Fire serves only to show that the involvement of wind does not exempt, and once that point is neutralized, we go back to seeing the case as an actual pit, and therefore the laws of pit apply to it. The speaker notes that the Talmud’s wording here is “and the law returns,” without an explicit formulation of “the common denominator,” and presents this as a hint that this is not a standard common-denominator derivation.
Spitting into the wind on the Sabbath: Rema, Mishnah Berurah, Rabbi Akiva Eiger, and Alfei Menashe
The Rema rules: “One who spits into the wind on the Sabbath, and the wind scatters the spit, is liable on account of winnowing. Mahari"l in the name of Or Zaru’a and the Jerusalem Talmud.” The Mishnah Berurah writes: “We have not seen anyone who is concerned about this, since he does not intend it, and all the more so because this is not the normal way of winnowing,” and refers to the Biur Halakhah, which cites Rabbi Akiva Eiger as inclining to be lenient because the labor of winnowing is similar to selecting, whereas in spit “it is all waste.” The Biur Halakhah cites the book Alfei Menashe, which explains that the Jerusalem Talmud means liability for carrying four cubits in the public domain by means of the wind, “just as in winnowing, even though the wind assists him, he is nevertheless liable,” and concludes, “and this is correct.”
Conceptual construction: uniting unique features versus intersecting a “common denominator”
The speaker proposes interpreting the case of spitting as a subcategory derived from two primary categories, throwing and winnowing, but not through a common denominator, because “there is nothing at all shared between them.” He defines an alternative move in which one takes from throwing the feature of transferring something four cubits in the public domain, and from winnowing the feature of being assisted by the wind, and combines them into a third concept. In this way, “conceptual construction” is created as a union of two source cases rather than an intersection of shared features. He argues that this is also the key to understanding the Rosh in Bava Kamma, where fire is not the source for a common denominator but rather a tool for neutralizing a disturbing feature, while the final law rests on the similarity to pit.
Subcategories derived from two primary categories in damages versus Sabbath
The speaker notes that in damages there are subcategories derived from two primary categories together, such as his stone, knife, and load, whereas in the laws of the Sabbath, with the thirty-nine primary labors, there is no example of a subcategory of two primary categories, and if an act does not resemble any one primary category on its own, it is exempt. He presents spitting into the wind as the one case that seemingly looks like an exception, and suggests that it can be understood only through the move of conceptual construction. He concludes by proposing two ways to create a third concept: the common denominator as an intersection that removes what is different and leaves what is shared, and conceptual construction as a union that specifically joins the differing sides.
Full Transcript
[Rabbi Michael Abraham] Okay, last time I spoke a bit about the three ways of inference: deduction, induction, and analogy. And I said that deduction, deriving a particular from a general rule, is a necessary inference because the conclusion contains no information that wasn’t already implicit in the premises. It doesn’t add information for me, and therefore it’s necessary, with the joke about the hot-air balloon and so on. Induction and analogy are inferences that add information for us. And since that’s the case, they can’t be certain. The moment you add information beyond what you have, there’s some element of speculation there, conjecture, something uncertain. Either it’s true or it’s not true. Either you made a good analogy, or your analogy may not be good, right? It’s not certain. So there’s always a price: you have to pay for information, you have to pay in the currency of certainty, and vice versa. Someone who wants complete certainty will remain with zero information. Someone who wants to know everything will remain with zero certainty. You have to play some kind of game, to pay in the currency of certainty in order to allow yourself to gain more information. I want now to continue. We started with Bava Kamma, but before I move on to Bava Kamma, I want to complete one more point that really concerns induction and analogy. Induction, because it directly touches the topic in Bava Kamma as well. The relationship—when I laid out this principle of certainty, what I called the relation between the amount of information and the level of certainty—so now we can ask: among the inferences, let’s say deduction is certain. Wow, there are explosions outside, battles. Deduction is certain. Analogy and induction are not scientific—well, not certain. Can I rank them? Which one is stronger, more reliable, more persuasive? Are you just talking to me? I’ll mute here. So apparently, at first glance, induction is weaker. Why? Because it adds more information. Right? Induction basically takes examples and creates from them a general law about a large collection of situations or cases or objects. Analogy is from one case to one case. So analogy adds a small amount of information; induction adds a lot of information. So apparently the degree of certainty of analogy should be higher than the degree of certainty of induction. Because it’s always an inverse relation. Or in simpler language: the moment you say something about a large group of things, clearly the chance that you’re wrong is greater. If you say it about one thing—say I say about this table that it has four legs, therefore all tables have four legs—the conclusion that all tables have four legs has a pretty good chance of being mistaken; just find one table that doesn’t, and you were wrong. But if I say this table has four legs and that one is also a table, so that one also has four legs—here there’s a better chance I’m right. It’s just one table. Maybe I’m wrong, maybe I’m right, but it’s not certain—but it’s more certain than if I’m talking about all the tables in the world, right? Therefore with a greater level of information, there’s a lower level of certainty. But if you look at it more carefully, then you’ll see that the relation between analogy and induction isn’t so simple. What I assumed until now is basically that induction is a collection of analogies. Because what am I saying? If this table has four legs, then all tables have four legs. Let’s break that down into small change. This table has four legs, so that table has four legs, and that one has four legs, and that one has four legs, and that one—and in the end all tables have four legs. Meaning, I made lots of analogies. Right? Induction is basically a collection of lots of analogies. That’s how I presented it until now. Therefore induction is less certain than each individual analogy on its own. Because simply, the chance of error in induction is the chance of error in each of the analogies. Right? Let’s say if they’re independent, then it’s the sum of the probabilities or something like that. But okay,
[Speaker C] In induction, the probability is that the hypothesis will be correct in most cases, while here—here if you’re wrong in the analogy, then you can be wrong in this one with one hundred percent error.
[Rabbi Michael Abraham] Right, but the chance that you’ll be wrong is smaller. If you were wrong, then you were completely wrong, but the chance of being wrong is smaller.
[Speaker C] No, but that also has weight, doesn’t it?
[Rabbi Michael Abraham] It does too, no problem. I’m not campaigning here on behalf of analogy; you can… defend it, that’s perfectly fine. I’m just describing the disadvantages and the advantages. You’re right, correct? But now I want to point to the opposite relation between analogy and induction. Good grief, wow, it looks like tanks are coming in here. Anyway, there’s also an opposite relation between analogy and induction. What do I mean? When I say this table has four legs, and therefore that table also has four legs—what is that “therefore”? How do I know? What do I know about that table that makes me think it also has four legs? All I know about it is that it’s a table. Or in other words, when I make an analogy between this table and that table, there’s actually a hidden induction here. I’m really assuming it about all tables, and in particular about that table. Because when I assume it about that table, I assume it only because it is a table, not because of anything else I know about it. So if so, it’s true of every table, not only of that table. Which means that analogy is actually a practical expression or specific expression of a hidden induction. When I say this frog is green, therefore that frog is green too—how do I know? Because I’m actually assuming that all frogs are green. So this one too will be green. Right? I don’t know anything about that frog besides the fact that it’s a frog. So what I’m really doing here is induction that all frogs are green. Right? But then it turns out that it’s not correct to say that induction is a collection of analogies. On the contrary. Induction is more fundamental. Induction is the basis for the analogy I’m making. Without induction there would be no analogy. Now how does this work? Basically my claim is the following. Contrary to the ordinary view that there are really three ways of inference here—analogy, induction, and deduction—in fact there is only one. And that one way is analogy. Only analogy. Except that when you break analogy down into its components, you see that analogy is done in two stages. One stage is the move from the particular cases to the general rule. This table has four legs; apparently all tables have four legs. That’s induction. Now, once I know that all tables have four legs, then in particular that specific table also has four legs. What is that? Deduction, right? From the general to the particular. Okay? So in fact the way to make an analogy is to make an induction followed by a deduction. Or in other words, it’s not three ways of inference. There’s really only one, analogy, only if you break it down into stages, you understand that analogy is built from two stages: induction followed by deduction. Let’s say, I don’t know, I saw one book with a red cover and inside it there are white pages. Okay? I see another book with a red cover, I say, so apparently it too has white pages. How did I reach that conclusion? Because I’m really assuming that every book with a red cover has white pages, and in particular I apply that to this specific book. So implicitly I made an induction here about all books, and afterward from all books I came back down to that specific book, which is deduction. So induction followed by deduction is really just the breakdown of the analogical process. Therefore when I make an analogy between things, I’m really exposing some shared property. Let me put that differently now. Suppose I made an analogy between two tables. This table has four legs, therefore that table also has four legs. Now that table is in the yard and this table is in the house. So they’re not exactly the same; there’s a difference between them, their location is different. When I make an analogy, what am I really saying? That location doesn’t matter. Right? I’m really saying that this is true of every table; I don’t care what its location is. So what does it depend on? It depends on its being a table, let’s say, on the fact that it serves for writing or eating or whatever people use a table for. Okay, for example, not important. So understand what happens when we make an analogy. When we make an analogy, we’re really eliminating features. Let’s think about scientific induction, okay? I saw one body fall to the earth—this phone, I let go of it and it falls down. So I say, apparently all objects made of plastic, when you let go of them, fall to the earth. Then I take, I don’t know, a shoe, let go of it, and it also falls to the earth. Well then, it’s not only objects made of plastic; it’s also objects made of leather that fall to the earth. But then I say to myself, wait—why assume that? There’s something simpler. Let’s assume that everything that has mass falls to the earth; I don’t care what material it’s made of. The question of what material it’s made of is a parameter that distinguishes the shoe from the phone, but it’s not a parameter relevant to gravity, right? So when I now look at the objects falling to earth, I’m really trying to isolate, from among their features, which is the shared feature by virtue of which they all fall to the earth. And then it’s clear to me that it’s not the plastic of the phone, because the shoe also falls and it isn’t made of plastic. And it’s not the leather of the shoe, because the phone also falls and it isn’t made of leather. So apparently it’s some other property they have. That’s scientific elimination. So what am I saying? That’s their common denominator. You see how now we get to Bava Kamma? That’s their common denominator. What is the common denominator of the shoe and the phone? That both have mass. So apparently the parameter of mass is what determines whether the object falls to the earth or not, not whether it’s made of leather or plastic or whether it’s square or round or whatever else. All those are irrelevant features. Which means that whenever I generalize, I take cases and then establish a general scientific law—that all bodies with mass fall to the earth—what am I really doing? I take bodies, each of which has its own features, but if they all behave the same way in this context, then apparently the particular features each one has are not the relevant features. What is the feature that is important? What they all share. That is what, in the language of the Sages, is called the common denominator. When we establish a common denominator among particulars, among particular cases, what we’re really doing is looking for the relevant parameter because of which these two particular cases are similar. After I find that, then I say, okay, if so, all objects that have that same relevant feature—for example here, that they have mass—will fall to the earth. This is a rule in information theory. You know that the more I reduce the number of features, the more I increase the number of items in the set or the objects in the set. For example, when I say “the first prime minister of the State of Israel,” only one person fits that description, right? If I said “the first prime minister of a state,” not necessarily Israel, more people would already fit that description, right? If I said “the first prime minister” not of a state—the first head of a government, maybe of a city—then even more people fit. If I said just “prime minister” without “the first,” then many more people fit. If I said just “head,” not prime minister, just the head of something, then many more people fit. What does that mean? That the more features I remove, the more objects fit the description I’m left with, right? The more features I have, of course, the description fits fewer objects. That is really the meaning of scientific generalization. What we do in scientific generalization is strip away the irrelevant features of the objects, remain with the relevant feature, and thereby we have made an induction. Why? Because I see the phone fall to the earth, I see the shoe fall to the earth. They have all kinds of features in which they differ. The phone is made of plastic; the shoe is made of leather. The phone is for making calls; the shoe is clothing. They have lots of uses. The shoe is on the floor; the phone is on the table. Okay? They have many different features. But since both fall to the earth, I assume that the differing features between them are not important for this discussion. What is important is what they share, the common denominator they both have, namely that they have mass. And then what do I say? I basically strip away all the features of the phone and remain only with the feature that it has mass. If I defined a phone the way I defined “the first prime minister of the State of Israel,” I’d say a phone is an object made of plastic, it has mass, it is made of plastic and serves for communication. Now I remove the feature that it serves for communication. Then I remove the feature that it is made of plastic. I’m left with the fact that it has mass. That feature, because it is thinner, contains fewer features, obviously fits many more objects—objects with mass. That is the process of generalization. The process of induction, of generalization, is ultimately just filtering out irrelevant features. Okay? That’s really what we do in generalization. That’s induction. But understand that if I make an analogy between this table and that table or between this frog and that frog, then when I make the analogy, what am I saying in that analogy? That the fact that this table is here and is a writing table, while that table is in the kitchen and is a dining table—those are features in which the two tables differ, but they are apparently not relevant. Or not relevant to the question whether they have four legs or not. And when I make an analogy, I’m basically assuming that the table’s location and its use for eating or writing are not relevant parameters to the discussion. What is relevant? The fact that it’s a table. And that is the common denominator of these two tables, and therefore notice—suddenly you see that analogy too is induction. After all, what I did here is really induction. I reached the conclusion that all tables have four legs, not only that table in the kitchen. I said it only about the table in the kitchen, but actually in my thinking I passed through an induction that concerns all tables. The table in the kitchen is only a particular example of that. Now this is really the root, and here I get to the topic of the common denominator, that a principle derived from two verses. The common denominator is really exactly such a process. Let’s take, for example, an example. I chose an example from Bava Metzia here. The Talmud wants to learn from what a worker is allowed to eat—a worker who is working, from what is he allowed to eat. Okay? So the Talmud wants to derive what a worker may eat from two source cases—this is a principle derived from two verses: standing grain and vineyard. It says, “When you come into your neighbor’s vineyard…” and so on, so one may eat. From standing grain too one may eat. The question is whether there are other things as well. So the Talmud derives it through the common denominator. What does that mean? It says as follows. They derive it from standing grain; they want to derive from standing grain that a worker may eat from anything, so they say, what are you talking about—standing grain is subject to challah, it has a unique feature, so maybe only something subject to challah is permitted to the worker to eat. The Talmud says: the vineyard will prove it. For from a vineyard too a worker is allowed to eat, and a vineyard is not subject to challah. You see the gravity model—it’s exactly the same thing. The Talmud asks: what about a vineyard, which is subject to gleanings? And standing grain is not subject to gleanings. So the Talmud says: standing grain will prove it. And the law returns: this is not like that, and that is not like this; the common denominator between them is that they are produce of the ground, and at the time of completion of labor a worker may eat from them; so too anything that is produce of the ground, at the time of completion of labor a worker may eat from it. What are they really doing here? Exactly the scientific process I described before with gravity. I have two source cases, standing grain and vineyard. From both I know that a worker may eat. Now each of them has its own features. Standing grain is subject to challah, vineyard is subject to gleanings, and each lacks the feature of the other. But they share one common feature: both are produce of the ground. Both grow from the earth, yes, both sprout from the ground. Then the Talmud says it’s obvious that the unique feature of standing grain is not relevant—the fact that it is subject to challah. How do I know? Because vineyard is not subject to challah, and yet in a vineyard too the worker may eat. Therefore that isn’t relevant. The Talmud says yes, but vineyard also has a unique feature; maybe only something subject to gleanings is permitted to the worker to eat? Then suddenly standing grain proves that’s not so, because standing grain is not subject to gleanings, and therefore we really see that neither the obligation of gleanings nor the obligation of challah is relevant to our discussion. So what is? I ask, okay, then what is the common denominator? What is the shared feature that exists in both standing grain and vineyard? The answer is that both are produce of the ground. Therefore a worker may eat from anything that is produce of the ground. Exactly the same logic as the law of gravity and like any scientific generalization. Really, deriving a principle from two verses, or the common denominator, is scientific induction—it is scientific generalization, and scientific generalization means finding the common denominator, neutralizing the unique features of my two source cases, my two examples, and remaining with the feature they share, and then I understand that the phenomenon depends on the shared feature. Once I know that, I already know I can apply it to anything that has the shared feature. Now I say: okay, what about peaches? That’s neither standing grain nor vineyard. Right, but it’s produce of the ground. Anything that is produce of the ground I can now permit the worker to eat from, because I have already reached the rule by means of induction. What is the rule? Anything that is produce of the ground. Okay?
[Speaker E] Is that the broadest possible common denominator? I can’t hear. Do you check the broadest possible common denominator?
[Rabbi Michael Abraham] No, the opposite, the opposite. The broadest possible one makes no sense; you have to look for the narrowest one, because after all you’re looking for evidence for something. The evidence you have is for the narrowest possibility, because beyond that, you don’t know—maybe yes, maybe no. The narrowest is certainly correct. What goes beyond that, maybe yes, maybe no.
[Speaker F] So who says that “produce of the ground” is the narrowest thing that is common to both?
[Rabbi Michael Abraham] Maybe there’s something even narrower? I don’t know—if you have another suggestion, but of course one that’s relevant. Not something like that both milk and vineyard—I don’t know—have the same letter in them, or something like that, but something that seems relevant to the discussion. So right, if you have such a suggestion, you have to check it. Relevance is a very important rule, because this is not pure formalism. We have to use our heads and see what seems reasonable, what is a relevant parameter and what is not a relevant parameter. Okay? In any case, that’s the common denominator. But still, there is a difference between the example I gave here of standing grain and vineyard and scientific induction. You know what the difference is? The difference is that the common denominator of standing grain and vineyard is what I call a common denominator with halakhic features. Because what were the features of standing grain and vineyard that I eliminated? That one is subject to gleanings and that one is subject to challah. In scientific generalization, we deal with factual features of the events or the objects, not laws that apply to them, not legal properties that apply to them. In the Talmud in Bava Kamma, the example is more similar to scientific generalization. The example—the Talmud we began dealing with last time. Why? Because the Talmud there speaks about the four primary categories of damages: the ox, the pit, the maveh, and the fire. Let’s talk for a moment about the common ones. We’ll speak about horn, tooth and foot, pit, and fire. Okay? Now each of those categories of damage has halakhic features—legal features. Horn pays half-damages for the first three gorings; fire is exempt for hidden items; pit is exempt for vessels; tooth and foot are exempt in the public domain. So each has a certain halakhic property. But each also has certain factual properties. For example, pit—the Talmud says: its creation was initially for damage. The moment it’s there in the public domain, it’s already a potential source of damage. Right? Tooth and foot are not. An animal is not initially made for damage. It can happen that it causes damage, but it’s not something that by its nature is a damaging thing. Or fire—another force is involved in it, because the fire advances by means of the wind, so another force is involved in it. So all these categories of damage have factual features. Now I know that in all four primary categories the Torah obligates payment. If my property caused damage in one of these four ways, I have to pay. I ask myself: what is the general law? I want to make an induction. The common denominator. So the Mishnah in Bava Kamma—we saw this Mishnah—the Mishnah in Bava Kamma itself does the work for us. “The common denominator among them is that they are your property, and their safeguarding is upon you, and it is their way to cause damage; and when they cause damage, the damager is obligated to pay compensation from the best of the land.” So the Mishnah itself tells us what they all have in common: they are your property, they tend to cause damage, and their safeguarding is your responsibility. If so, I now have the general law; I’ve made an induction. Namely: anything that is your property, whose safeguarding is your responsibility, and whose way is to cause damage—if it causes damage, then even if it doesn’t resemble one of these primary categories, you are liable to pay. Just like we saw regarding permission for the worker, and all the previous examples, or gravity. This is a common denominator more similar to scientific generalization. Why? Because here I’m looking for the factual features that my source cases, my primary categories, have. I make a selection. I say: which features are irrelevant? What exactly is the feature responsible for the obligation to pay? It certainly can’t be the feature that its creation was initially for damage, right? Because otherwise only pit would have to pay. Why does fire have to pay? Why do tooth and foot have to pay? So it’s clear that “its creation was initially for damage” is not a relevant feature. And if I say about fire that another force is involved in it—is that a relevant parameter? No. Because in a pit another force is not involved in it, and still one has to pay. So that means that the fact that another force is involved, or that its way is to go and cause damage, are also not the determining features. So what remains? What remains for us is only the common denominator, meaning the feature shared by all the examples. And that feature is that it is your property, its way is to cause damage, and its safeguarding is your responsibility. And here I’ve reached the general law—that is the induction. Therefore what the Mishnah says—“the common denominator”—is really doing induction and determining what the general law is. And now we come to the Talmud in Bava Kamma on page 6, which we started last time.
[Speaker G] And “their safeguarding is upon you”—does that mean that all these things, all these forces, are under your control?
[Rabbi Michael Abraham] What? I didn’t understand.
[Speaker G] And “their safeguarding is upon you”—does that mean that all these things, all these forces, are under your control?
[Rabbi Michael Abraham] It’s my property, so the responsibility is on me. The Talmud in Bava Kamma 6a—we started reading this last time, and I started speaking a bit about the status of rules in the Talmud; leave that aside for now. The Talmud says as follows: “The common denominator among them…” wait, can you see this? Did I share it here or not? No—wait, I’ll share it. “The common denominator among them”—what does it come to include? Right? Why does the Mishnah conclude with “the common denominator”? Last time I noted what bothered the Talmud. After all, the Mishnah presented us with the rule, the way it should always have done. So we spoke about casuistry and about the fact that the Talmud doesn’t have much trust in rules. Fine. So the Talmud asks: what does it come to include? Abaye said: what does this come to teach? Abaye said: to include his stone, his knife, and his load, which he placed on top of his roof, and they fell in a normal wind and caused damage. We’re talking about my objects that I put on top of the roof; a normal wind came and knocked them off the roof and they caused damage. My obligation to pay for this kind of damage is what is learned from the common denominator. That’s what the Talmud says. The Talmud asks: what are the circumstances? How are we talking? If they caused damage while they were moving, that is just fire! If we’re talking about damage that occurred during the fall from the roof, then you can learn it from fire; you don’t need any common denominator. It’s exactly like damage caused by fire. Fire too is carried by the wind and causes damage; here too the wind carried these objects and they caused damage. Therefore for that you don’t need any common denominator. A common denominator always requires at least two source cases. Here one source case is enough—you can learn it from fire. So that can’t be it. The Talmud says: what is different about fire? That another force is involved in it, and it is your property and its safeguarding is your responsibility. Here too another force is involved in them—that other force is the wind—and they are your property and their safeguarding is your responsibility. The Talmud says: rather, then apparently they did not cause damage during the fall, but after they came to rest. Meaning, they caused damage after they were already resting on the ground. The Talmud says: if he declared them ownerless, then according to both Rav and Shmuel, that is just a pit! What is different about a pit? Its creation was initially for damage, and it is your property and its safeguarding is your responsibility. Here too their creation was initially for damage, and they are your property and their safeguarding is your responsibility. Meaning, if we’re talking about damage after they came to rest, then again we don’t need a common denominator; we can learn it from pit. A pit is initially created for damage, and it is your property and its safeguarding is your responsibility, and you have to pay. That’s it—it’s the same thing as a pit. Again, no common denominator is needed. In the end the Talmud concludes—I’m reading the conclusion here—“Actually, it is a case where he declared them ownerless,” yes? We’re talking about a case where he declared… not important to get into ownerlessness right now. And they are still not similar to a pit, and the damage happened after they came to rest, and yet it still isn’t similar to a pit. Why? What is true of a pit, where no other force is involved in it, can you say that here, where another force is involved in them? After all, who brought these things there? The wind. His stone, knife, and load. A pit—I dug it. Which means that here, the one who created the obstacle was the wind, or at least it was involved in creating the obstacle. Therefore you can’t derive the damage of these things from pit. It’s true that with a pit I have to pay because I also dug the pit, but here the wind brought them there. Who says that if they cause damage, I have to pay? You can’t learn it from pit. To that the Talmud says: fire will prove it. Right—that’s why the assistance from fire is needed. Why? Because with fire too the wind is involved, and nevertheless its owner is liable to pay for the damage it causes. So we see that in our case too, the involvement of the wind should not exempt me. So what if his stone, knife, and load fell because of the wind? I still have to pay, as we see in the case of fire. Fine. So if that’s so, the question arises: then let’s learn it just from fire; why is a common denominator still needed? The Talmud says: no. What is true of fire, whose way is to go and cause damage? But in fire there is something that his stone, knife, and load don’t have. Fire naturally goes and causes damage. His stone, knife, and load, after they are on the ground, stay there; they don’t move. It could be that with fire the obligation to pay exists because of this feature, that its way is to go and cause damage. You can’t derive from it to his stone, knife, and load lying on the ground. The Talmud says: the pit will prove it, and the law returns. We learn it by the common denominator from pit and fire. In the simple understanding, how would we derive it? The logic is the common denominator, just as we’ve seen until now, and that’s how this Talmudic passage is usually learned. What does that mean? We see that there are special features of pit—I’m going back to the same logic I demonstrated before. There is pit and fire, which are the source cases, and his stone, knife, and load that fell and caused damage—that is this subcategory, that is the learned case. The source cases, two source cases, and the learned case—it is learned from them. Okay? Now each source case has its own unique property. In pit another force is not involved in it. Both pit and fire create liability for payment, which means that apparently the property unique to fire and the property unique to pit are not the properties responsible for the obligation to pay, because clearly even without them I’m still liable. So what is? The common denominator of pit and fire. What is that common denominator? That they are your property, their safeguarding is your responsibility, and their way is to cause damage. If so, that is what creates liability for payment. If so, then his stone, knife, and load that fell from the roof—even though they are not exactly similar either to fire or to pit—they do have the feature shared by fire and pit, that same common denominator. And since that is the relevant feature for liability for payment, therefore they too create liability for payment. This is a straightforward common denominator. Okay?
[Speaker D] Now, now I’m opening the Rosh on this passage in the Talmud. And the Rosh says as follows.
[Speaker B] Wait. There, that’s it.
[Speaker D] For some reason it didn’t mark that for me.
[Rabbi Michael Abraham] “And there are some of the great authorities who wrote that one is liable only for whatever both of them obligate, and exempt from damage to vessels and from causing a person’s death, like a pit, and from hidden property, like fire. Since they come by way of the common denominator, we assign them the leniency of both.” What is the Rosh saying? We learn the damager of “his stone, his knife, and his load” that caused damage after they came to rest, from pit and fire, right? Through the common denominator. Now, we know that for every— we spoke about the essential characteristics, and now I’m moving to the halakhic / of Jewish law characteristics. A pit is exempt for vessels and for causing a person’s death. And fire is exempt for hidden property, for damage to things concealed inside something else. Okay? Now I ask: “his stone, his knife, and his load” that caused damage—are they exempt for hidden property? Are they exempt for vessels? Are they exempt from nothing? Are they exempt from both? What kinds of exemptions should that damager, which I learned through the common denominator, have? So there are some great authorities who write—this is the first opinion in the Rosh—that in fact they are exempt both for hidden property and for vessels. Meaning, they have both the exemptions of the first source text, the pit, and the exemptions of the second source text, the fire. That’s the simple logic, right? Why? Because after all, they are not similar either to pit or to fire. If I want, for example—let’s formulate it this way—suppose damage was caused by “his stone, his knife, and his load,” and they damaged something that was hidden. Now I want to obligate payment for that. In order to obligate, I have to learn it from pit and fire, right? The liability of “his stone, his knife, and his load” is learned from pit and fire. But fire is exempt for hidden property. And from pit alone you can’t learn it. So you can’t learn liability for hidden property. And of course, by the same logic, you also can’t learn liability for vessels, because pit is not liable for vessels, and I’ll only have fire, but from fire alone you can’t learn it; you need both in order to learn it. Therefore in fact you can obligate neither for vessels nor for—nor for hidden property, sorry. Okay? That’s the simple approach. Some of the great authorities understood it that way, and that’s the straightforward understanding. But what’s interesting in the Rosh is that he brings two more opinions. “And there are those who were uncertain about the matter”—that’s a second opinion. Now before I keep reading: uncertain between what and what?
[Speaker C] It’s pretty clear that—sorry—about vessels.
[Rabbi Michael Abraham] They were uncertain about the question whether it has both exemptions, as “some of the great authorities” held, or whether it has none of the exemptions. Right? That is, do you compare it to the smallest common denominator or the largest common denominator—do you take the union of the two source categories or the intersection of the two source categories? That’s really the dispute, okay? That’s those who were uncertain about the matter. “And it seems to me that they have every law of pit”—that’s the third approach of the Rosh. The Rosh claims that “his stone, his knife, and his load” have the exemptions of pit and not the exemptions of fire. How did the symmetry between pit and fire suddenly break? “Individual popping sounds can still be heard,” as HaGashash HaHiver say—not so individual, but they can be heard. So the Rosh basically broke the symmetry here between the two source categories, fire and pit. And how exactly? After all, we learn it from the two sources. How did you suddenly decide that pit is the primary one and fire is some kind of secondary thing, or something that doesn’t really determine it? How can you do that? After all, according to the whole logic of the common denominator as I explained it earlier, it really can’t produce what the Rosh is saying. And my claim is that the Rosh did not learn a common denominator here. He doesn’t think the derivation here is the common denominator. The derivation here is something very similar, but it isn’t the common denominator. I’ll explain to you how he learned it. In the end, when you look at “his stone, his knife, and his load” that fell onto the ground and caused damage, I ask you: what is it similar to, pit or fire? At first glance it is identical to pit—not just similar, identical to pit. Except what? In the way it got here, the wind took part. In that sense, you also need some contribution from fire to understand that it is liable. But basically, fundamentally, it is a pit. It’s simply a pit. Except what? It’s a pit in whose formation fire bears some contributory guilt, so to speak. Right? So fire serves me in neutralizing the involvement of the wind. Fire shows me that the involvement of the wind is not important. Once fire has shown me that, I forget about fire, I go back to “his stone, his knife, and his load,” and I say: this is a pit. It’s really a pit. Except what? I had trouble comparing it to pit because, after all, in a pit the wind was not involved. Along comes fire and says: don’t be bothered by that; the involvement of the wind does not exempt. Okay, so now I’m not bothered. If the involvement of the wind does not exempt, then going back—this is simply a pit.
[Speaker C] But in a pit, somebody made it; somebody created it. Here the person had no involvement at all.
[Rabbi Michael Abraham] When fire shows that it doesn’t matter. Because the fact is that even if the wind creates the damager and not just I do, even then one is liable.
[Speaker C] But you need that fire in order to understand that.
[Rabbi Michael Abraham] Of course. Again, he uses fire as an aid—the Talmud / Talmudic text uses fire as an aid—the Rosh is not disagreeing with the Talmud / Talmudic text. The Talmud / Talmudic text brings fire in order to support this derivation. The Talmud / Talmudic text itself says that you cannot learn it from pit alone. But the Rosh argues that the combination of fire and pit is not a combination of the common-denominator type, the way I described earlier. That is the approach of “some of the great authorities.” The Rosh says it doesn’t work like a common denominator; this is a different logic. We learn it from pit alone, except that regarding pit there is one small side problem: in a pit there is no involvement of wind in its formation, whereas in “his stone, his knife, and his load” there is. So know what? Let’s step aside for a moment and study the topic of fire. In the topic of fire we see that this parameter is not important. Okay, we’re done with fire, we throw it away and go back—I understand that this parameter is not important. Once I understood that it’s not important, I go back to comparing it to pit; it is really a pit. I need fire as assistance for the derivation, but after I used fire, at the end of the day what I have here is just a plain pit. Okay? And then what comes out of this is that “his stone, his knife, and his load” are not really learned from the common denominator. This is not a derivation of common denominator. “Some of the great authorities” understood that this is a derivation of common denominator—the common denominator of fire and pit. What is that common denominator? “Your property, and its safeguarding is upon you.” Right? That’s it. And that exists in “his stone, his knife, and his load.” The Rosh says, what are you talking about? We don’t learn this from the common denominator of the two of them; we learn it only from pit. Fire comes only to neutralize a characteristic that could have interfered with the derivation. And it shows that it does not interfere; it’s irrelevant. That’s all. Once it neutralized it, I went back to learning from pit, and I learn it from pit. That’s how the Rosh learns.
[Speaker C] So what is that called? What is it called? How do you define this derivation?
[Rabbi Michael Abraham] By the same name. It’s just that way. In a moment I’ll give a name to something else, and I don’t know whether this is that or not that; in a moment I’ll try to explain. If we take the middle approach in the Rosh—those who were uncertain about the matter—then as far as they’re concerned, what was the uncertainty? Either it has both the exemptions of fire and the exemptions of pit, or it has neither of the two types of exemptions. It would then always be liable—also for a person, also for vessels, also for hidden property, for everything. How did they understand the comparison? I think they understood the comparison in a third way. And what they said is what I call conceptual construction, as distinct from the common denominator. Very similar, very confusing, absolutely not the same thing. What is conceptual construction? I’ll demonstrate it through another example. Because one of the things that used to bother me a lot was that among the four primary categories of damages we find subcategories of each of the primary categories, and we find subcategories that require derivation from two primary categories together, like “his stone, his knife, and his load” in the passage we just saw. Meaning, we need the common denominator in order to derive some of the subcategories. Not every subcategory has one parent category; sometimes you need two parent categories. In the laws of the Sabbath there are thirty-nine primary categories of labor. Each such primary category has subcategories. But nowhere in the entire Talmud, in all the Sages, the medieval authorities (Rishonim), and the later authorities (Acharonim)—whatever you want; I also asked people much more expert than I am—there is no example of a subcategory of two primary categories on the Sabbath. It’s an amazing phenomenon that I’ve never seen anyone point out. In the categories of damages there is common denominator: you derive from two primary categories to a certain subcategory that cannot be learned from one primary category alone. On the Sabbath, if it is not similar to any one category on its own, then one is exempt. You do not derive it from two primary categories. There is no common denominator; there is no example at all.
[Speaker D] There is one example that on the face of it looks like a common denominator, and that example is a very
[Speaker B] interesting law that appears in the Rema and whose source is in the Jerusalem Talmud. Wait.
[Speaker D] Look here in section 17 in the Shulchan Arukh. You can see the Rema here.
[Rabbi Michael Abraham] “Gloss: One who spits into the wind on the Sabbath, and the wind scatters the spit, is liable because of winnowing. Maharil in the name of Or Zarua and the Jerusalem Talmud.” What does that mean? The labor of winnowing is a labor in which I throw grain into the air, the wind comes and blows away the chaff, and the kernels fall downward, and then I’m left with kernels without chaff. It’s basically a kind of sorting. Winnowing, selecting, and sifting are very, very similar primary categories. Winnowing is separating kernels from chaff by means of the wind. That is called the labor of winnowing. The Jerusalem Talmud says—and the Rema brings this as Jewish law—that if I spit on the Sabbath and the wind scatters the spit, I violate the prohibition of winnowing. Plainly, “liable” seems to mean liable at the Torah-level / of biblical origin.
[Speaker C] But nothing remains. Huh?
[Rabbi Michael Abraham] But—
[Speaker C] Nothing remains.
[Rabbi Michael Abraham] Good question; you’re asking a very good question. Let’s look here in the Mishnah Berurah. Do you see the Mishnah Berurah? “And we have not seen anyone who is concerned about this, since he does not intend this, and all the more so since this is not the normal way of winnowing.” Rabbi Akiva Eiger already comments on this, and see the Bi’ur Halakhah. What does Rabbi Akiva Eiger comment? What in the world does this have to do with winnowing? “With all the winds,” yes, the wind is involved here. What does it have to do with winnowing? Winnowing is an act of separating food from waste, kernels from chaff. Here, even if the wind scatters the spit, what are you separating from what? You are not left here with something while removing some waste that you don’t want. What does this have to do with the labor of winnowing? How is it even similar? And therefore, “we have not seen anyone who is concerned about this,” says Rabbi Akiva Eiger; it doesn’t belong. But there is an explicit Jerusalem Talmud. “We haven’t seen anyone who is concerned”—is he disagreeing with the Jerusalem Talmud? I don’t know, it’s… a bit strange. What do you mean, of course not?
[Speaker H] What? It’s liquid. No—
[Rabbi Michael Abraham] I understand.
[Speaker H] It waters the garden.
[Rabbi Michael Abraham] No, no, no—not watering. Let’s say in the street, on the road. No, he doesn’t write here that it waters anything; he didn’t write that he spits onto a garden. In any case, he rejects it. Now look here at the Bi’ur Halakhah. “In the responsa of Rabbi Akiva Eiger, section 20, he was uncertain,” etc., “and he strongly inclines to be lenient, because since the decisors omitted the Jerusalem Talmud, this indicates that they do not hold like it. Rather, the labor of winnowing is akin to selecting, in that one separates waste from food. But where it is entirely waste, such as spit—it is entirely waste; I want to get rid of it—then one is not liable because of winnowing.” And in the end he brings: “And in the book Alfei Menasheh”—here. “And in the book Alfei Menasheh”—this is a student of the Vilna Gaon, Rabbi Menasheh of Ilya—“he explained that the intention of the Jerusalem Talmud is where one carries it four cubits in the public domain by means of the wind. And it is by way of illustration. Meaning, just as in winnowing, even though the wind assists him, nevertheless he is liable, so too in the case of one who spits, if its movement is by means of the wind, he is also liable. And this is correct.” Interesting that in the Bi’ur Halakhah he says “and this is correct,” but in the Mishnah Berurah he brings only that people were not concerned about it, in the name of Rabbi Akiva Eiger, and that’s it. That’s strange.
[Speaker C] In any case, that’s something completely different, Rabbi. I can’t hear. If it’s carrying four cubits in the public domain, then it’s neither winnowing nor selecting.
[Rabbi Michael Abraham] Yes, yes—right away I’ll explain, right away I’ll explain. His definition is the following, and it’s brilliant. He claims—by the way, some wanted to emend the version: instead of “liable because of winnowing,” that he is “liable because of throwing.” Throwing is someone who
[Speaker B] takes
[Rabbi Michael Abraham] an object and throws it four cubits in the public domain. Then if I spit with my mouth, that’s the same as throwing, so that’s simple, right? I want to claim that the Jerusalem Talmud says “winnowing.” I want to claim there is no need to emend the text. The Jerusalem Talmud says “winnowing,” and it really is winnowing. And what I am claiming is that one who spits is learned through a common denominator—or through a joint derivation—from winnowing and throwing together. Two primary categories. I told you, this is the only example in the laws of the Sabbath that I know of where a subcategory is learned from two primary categories together. And the claim is the following. Basically, when I spit—now look at the similarity to the Rosh we saw earlier; it’s exactly parallel—when I spit, and let’s say I spit four cubits in the public domain, then basically it is like throwing in the public domain. Same thing, right? It’s a subcategory of throwing. With one difference. What is the difference? If I spit, and the wind takes it four cubits, the spit itself is not strong enough to carry it four cubits. In throwing by hand, the throw by my own power carried the object four cubits in the public domain. That is the primary category. So there one is liable. But when I speak of spitting, we are speaking about a case where the wind took it four cubits. Without the wind it would not have reached four cubits. If so, look how this is exactly like the Talmud / Talmudic text in Bava Kamma with fire. I want to learn “one who spits” from throwing. Then I ask: what about throwing, where the wind is not involved in it? But in spitting the wind is involved, so perhaps I am exempt? Then what do I say? Winnowing proves otherwise. Because in winnowing the wind is involved, and nevertheless I am liable. Right—but what about winnowing, where it is a labor of separation? And here I’m just spitting; I’m not separating anything—that’s Rabbi Akiva Eiger’s question. Then I say: throwing proves otherwise. Throwing is not a labor of separation; it does exactly the same thing—throws four cubits in the public domain—and one is liable. And so the rule returns. Winnowing and throwing together teach me the prohibition of one who spits. That, in my view, is the logic behind the words of Rabbi Menasheh of Ilya. And if so, this is the only example that exists of a subcategory learned from two primary categories. Now I ask you a simple question: what is the common denominator of the two primary categories, winnowing and throwing? After all, it is learned through their common denominator. What is their common denominator? Nothing.
[Speaker C] Why? Because the wind is involved in it?
[Rabbi Michael Abraham] No, in throwing the wind is not involved, only in winnowing. I’m asking, what is the common denominator? There is no common denominator, period. There isn’t one. There is nothing shared between them. Two different primary categories; there is no equal line between them. So what is happening here? This is not a derivation of common denominator. Do you know what kind of derivation this is? This derivation is built like this: from throwing I take the characteristic that this is not a labor of separation; it is a labor of moving something four cubits in the public domain. From winnowing I take the characteristic that it is done with the aid of the wind. Each of these characteristics, by the way, does not exist in the other. The characteristic of throwing—that it is a labor of moving four cubits in the public domain—does not exist in winnowing. The characteristic of winnowing—that it is done by means of the wind—does not exist in throwing. I take these two characteristics, fuse them together, and create the labor of one who spits. Now understand: this is the exact opposite of the common denominator.
[Speaker C] Yes, in this method, in this method, if there were two such labors—wait—
[Rabbi Michael Abraham] One second, maybe—
[Speaker C] two things within one labor—wait, one second, one second—
[Rabbi Michael Abraham] One second, one second, we’ll get there; no, don’t jump ahead. What I want to say is: the common denominator, as we saw earlier, means taking the shared characteristic that both of them teach and learning from it about the subcategories. Here we do exactly the opposite. I take the unique characteristic of primary category A, the unique characteristic of primary category B, and instead of setting them aside and remaining with the shared element, on the contrary—I take this one, attach the second one to it, fuse them together, and create a subcategory. Therefore I call this conceptual construction, or in other words, I am making here a union of the two source categories and not an intersection of the two source categories. The intersection of the two source categories strips away the foreign differing characteristics and remains with the characteristics common to both. That is common denominator. What I do here is a union. I am basically saying: I take the characteristic of this one and the different characteristic that is there, and I take both together. That is what I call conceptual construction. Conceptual construction means: I build one concept from two other concepts. That’s why this is a lesson on conceptual analysis, right? So now we’ve arrived at the conceptual analysis. I take two characteristics of two concepts, each of which is unique to it and absent in the other, fuse them to one another, and create a third concept that resembles neither of the two source categories, and yet it is still learned from both of them. And that is what I’m doing here. I claim that this is exactly what the Rosh did in what we read earlier. What did the Rosh do? Exactly the same thing. He learns “his stone, his knife, and his load” basically from pit. Just as here, one who spits is really exactly the labor of moving something four cubits in the public domain—it is throwing, not related to winnowing. Winnowing only teaches you that the involvement of the wind does not exempt. The same thing there. What does fire teach you? That the involvement of the wind does not exempt. So you can remain with the resemblance to pit. “His stone, his knife, and his load” is like pit. Ah, but in “his stone, his knife, and his load” the wind was involved? Fire shows that this is not important; you don’t need to get excited about it. Same thing here. One who spits is basically throwing. True, the wind is involved here in spitting; I learn from winnowing that the involvement of the wind makes no difference. And I am left with the fact that it is one who spits. Do you see the logic of the Rosh? Exactly parallel, precisely this. That is the logic of the Rosh. And to that logic I give the name conceptual construction. Why? Because unlike the common denominator—even though, if you noticed, when I formulated it earlier, I formulated it exactly like a common denominator. Let me formulate it again, if you’ll allow me two more minutes. I learn one who spits from throwing. What about throwing, where the wind is not involved? So in spitting the wind is involved. Then I say: winnowing proves otherwise, because in winnowing the wind is involved. What about winnowing, where it is a labor of selection, of food from waste? Spitting is not like that. Then I say: throwing proves otherwise. And so the rule returns. “And so the rule returns”—but not “the common denominator of the two,” that I cannot say. Why? Because there is no common denominator of the two. “And so the rule returns” in this case means: take the characteristic from here plus the characteristic from there, connect them, fuse them, and that is what teaches you about one who spits. And I’ll conclude by returning to the Talmud / Talmudic text in Bava Kamma that we saw earlier. Wait, sorry, I apparently closed it by mistake. Ah, it’s open here for me, okay. Look at the wording—how beautiful. Wait, nice. This is the conclusion of the Talmud / Talmudic text we read earlier. “Ultimately, we establish it” and “they are not similar to pit. What about pit, where no other force is involved in it—will you say the same of these, where another force is involved in them? Fire proves otherwise. No, it is also not similar to fire. What about fire, whose way is to move and cause damage? Pit proves otherwise. And so the rule returns.” Usually, when they bring a common denominator, it doesn’t end here. “And so the rule returns: this is not like that, and that is not like this; the common denominator of both is such-and-such, so too his stone, his knife, and his load, which are such-and-such, are liable to pay.” None of that appears here. “And so the rule returns,” period. We stopped. Why did we stop? The Rosh says because this is… not a common denominator. You cannot continue to the next sentence, because this is not a derivation of common denominator. “And so the rule returns” means: I learn it from both of them; I learn it from both of them by conceptual construction, not through the common denominator. I take the characteristic of pit and the special characteristic of fire, fuse them together, and thus this damager is created, whose name is “his stone, his knife, and his load” that floated along and caused damage. This is not a common denominator. There is no common denominator; that’s not how it’s learned. Here there is a common denominator, unlike the case of one who spits, winnowing and throwing. Here there is a common denominator—“your property, and its safeguarding is upon you”—a common denominator of pit and fire, as the Mishnah says. But here it is not learned from the common denominator; it is learned specifically from the different aspects, from the joining of the two different aspects—fusion, or conceptual construction. And indeed, in the language of the Talmud / Talmudic text you can see it: the Talmud / Talmudic text does not mention a common denominator here—“and so the rule returns,” period.
[Speaker I] Suddenly, yes.
[Rabbi Michael Abraham] Okay, I’ll stop here at this stage.
[Speaker I] So “one who spits” in the Jerusalem Talmud—which labor is that?
[Rabbi Michael Abraham] Winnowing and throwing. Fundamentally, according to the Rosh, it is throwing. Winnowing only helps you say that the involvement of the wind doesn’t matter.
[Speaker I] The labor, the labor is throwing—you move it four cubits in the public domain.
[Rabbi Michael Abraham] Correct, and winnowing only shows you that the involvement of the wind does not exempt; it is irrelevant. But basically, at the end of the day, this is throwing. It’s Ezra, it’s throwing. Throwing. Exactly like the Rosh says that “his stone, his knife, and his load,” at the end of the day, is a pit. What you used fire for was only to show that the involvement of the wind does not exempt. It’s exactly parallel; it’s literally the same thing. Fine, so what we basically see here are two ways to analyze concepts and synthesize from two existing concepts a third concept. Either take the common denominator and throw away the differing aspects—the intersection of the two source categories—or the union of the two source categories, specifically taking the differing aspects and connecting them, and that is what I called conceptual construction. Okay? Good—does anyone else want to comment or ask?
[Speaker C] Thank you very much. I’d like to return to what I asked earlier: according to the Rabbi, is it impossible to expound that there are two labors and basically do that same synthesis and find some new subcategory, so to speak?
[Rabbi Michael Abraham] In principle it’s possible. If you have an idea or an example, we can discuss it. I don’t know of an example of that in the halakhic literature. This is the only example I found. I don’t think there are more.
[Speaker C] Okay, thank you very much. Happy holiday.
[Rabbi Michael Abraham] We may find other examples elsewhere, not in the laws of the Sabbath. Good, thanks. Okay, goodbye, Sabbath peace, happy holiday.
[Speaker C] Happy holiday.