2019-04-22 – Between Midrash and Logic – Lesson 20

Table of Contents

• The prevalence of the hermeneutical principles and the status of the Thirteen Principles
• Why specifically Rabbi Ishmael’s principles were accepted
• General and particular as a textual principle, and the canonical Talmudic passage in Eruvin
• Redeeming second tithe: the table, the line, and the radius of inclusion
• Inclusion and exclusion versus general and particular: the school of Rabbi Akiva and the school of Rabbi Ishmael
• An editorial note in the passage: “these Tannaim mentioned below”
• The baraita expositions: general–particular–general and their results
• The practical difference: fish and birds, and the replacement of Abaye by Ravina
• The three “aspects”: product of a product, things that grow from the ground, and offspring of the offspring of the earth
• Identifying relevant properties from the verse and the assumption of the Sages
• Generalization, giving up aspects, and information theory
• The Venn diagram as a second stage: containment relations among the aspects
• General–particular–general: specifically the latter general clause versus specifically the first general clause
• Translating the structure into a numerical system of “aspects”
• Completion: particular and general and particular, and a complete “toolbox”

Summary

General Overview

The text presents the expositions of general and particular as a textual hermeneutical principle that operates on the basis of the way the verse is written, and it sets the Talmudic passage in Eruvin about redeeming second tithe as an especially canonical, early, and well-ordered example in which the rules appear in a formal and clean way. It argues that most rabbinic expositions are not explicitly labeled according to the Thirteen Principles, but Rabbi Ishmael’s principles were accepted because they underwent conceptualization and were formulated as binding rules that can be broadly applied, unlike local considerations that were never formalized. Within the passage, a dispute is presented between the school of Rabbi Akiva, which uses inclusion and exclusion and expands more broadly, and the school of Rabbi Ishmael, which uses general and particular and narrows things according to rules. It becomes clear that the radius of inclusion is determined by the number of shared “aspects” among the items in the verse and by analysis of the general–particular–general structure of the verse. At the end, the text builds a full system explaining how general and particular, particular and general, and general and particular and general are translated into expansion or restriction by means of a Venn diagram of aspects, and it proposes adding another principle, particular and general and particular, in order to complete a formal “toolbox.”

The prevalence of the hermeneutical principles and the status of the Thirteen Principles

The text states that the principles of general and particular are among the most common textual principles, whereas analogy is not common, is not one of Rabbi Ishmael’s principles, and is hard to locate because it is not consistently marked. It estimates that the two forms of paradigm construction, the a fortiori argument, the three principles of general and particular, and verbal analogy cover “98% of the expositions,” while the other principles almost never appear, or appear once or twice in all rabbinic literature. It argues that even though in the sources one does not see much use of some of the principles, at the conceptual level one can expound by means of them, and sometimes expositions that are not marked turn out in retrospect to be based on a certain principle. Tosafot points to places where a Talmudic exposition is really an instance of general and particular even though the Talmud does not say so. He adds that the number of explicitly declared expositions based on one of Rabbi Ishmael’s principles is negligible, and most expositions are hard to define in terms of any orderly principle.

Why specifically Rabbi Ishmael’s principles were accepted

The text attributes the acceptance of Rabbi Ishmael’s principles to the fact that in his period the methods of exposition were conceptualized and a “binding rule” was formulated that could be applied everywhere, whereas other approaches remained local and were never formulated as formal rules. It depicts the other expositions as point-by-point applications of considerations that were never given systematic formulation, and therefore they were not accepted as a fixed general system.

General and particular as a textual principle, and the canonical Talmudic passage in Eruvin

The text defines general and particular as a textual principle because the Torah’s mode of expression is the trigger and authorization for the exposition, unlike the a fortiori argument and paradigm constructions, where there is “no hint at all in the verse” that compels that kind of inference. It states that the canonical exposition of general and particular, as it appears in Rabbi Ishmael’s examples, is the Talmudic passage in Eruvin on redeeming second tithe, and that in this passage the rules appear “in the most orderly form possible,” unlike other passages, which are “a huge mess.” It describes this passage as one that emerged at a stage when there was already a clear conceptualization of the rules, whereas before that the expositions look “confused” because no one had yet tried to fit them into formulated patterns. Later, the formulated rules can then be used to decode additional passages.

Redeeming second tithe: the table, the line, and the radius of inclusion

The text describes a table of items that emerge from the passage, arranged from bottom to top according to their degree of suitability for redeeming second tithe, where “water and salt” are the lowest and “cattle and flock, wine and strong drink” are the definite cases because they are written explicitly in the verse. It explains that over the course of the passage “the line rises monotonically,” and the line represents the radius of inclusion of what may be bought with second-tithe money, so that whatever is above the line is permitted and whatever is below it is prohibited. It presents this rise as a classic structural feature of the passage, and explains that tracing it is meant to show how different Sages place the line in different places—that is, how they determine how far the inclusion generated by general and particular extends.

Inclusion and exclusion versus general and particular: the school of Rabbi Akiva and the school of Rabbi Ishmael

The text attributes the early stages of the upward movement in the table to opinions that expound by inclusion and exclusion rather than general and particular, and states that as a rule the school of Rabbi Akiva, which includes and excludes, gives a larger radius of inclusion than the school of Rabbi Ishmael. It says that inclusion and exclusion has no clear “logical mechanism,” and describes it as wild and intuitive: “you include everything and exclude one thing” according to various considerations. By contrast, it describes general and particular as a precise system of rules that determines the radius of inclusion, and therefore it focuses on the Ishmaelian expositions.

An editorial note in the passage: “these Tannaim mentioned below”

The text interprets the phrase “and these Tannaim mentioned below” as a hint of editing, because it points forward to Tannaim who will appear later and shows that whoever wrote this stage knew what would be integrated later. It states that such instances exist in several examples throughout the Talmud, and that writing “forward” indicates editing.

The baraita expositions: general–particular–general and their results

The text describes how Rabbi Yehuda ben Gadish and Rabbi Eliezer expound inclusion–exclusion–inclusion from the verses “and you shall give the money for whatever your soul desires” (an inclusion), “for cattle, or flock, or wine, or strong drink” (an exclusion), “and for whatever your soul asks of you” (it included again), and from this conclude: “it included everything,” with a dispute about what is excluded. According to Rabbi Eliezer, “fish brine” is excluded; according to Rabbi Yehuda ben Gadish, “water and salt” are excluded. It then moves to “these Tannaim expound by generals and particulars” and presents a baraita that interprets those same verses as “a general statement,” “a particular statement,” and “it returned and made a general statement,” and concludes: “you may judge only according to the likeness of the particular,” with the definition: “just as the particular is explicitly a product of a product and something that grows from the ground, so too everything that is a product of a product and grows from the ground.” It brings a second baraita that defines it differently: “just as the particular is explicitly offspring of the offspring of the earth, so too everything that is offspring of the offspring of the earth,” and presents the Talmud’s question, “What practical difference is there between them?” together with the distinction offered between the two definitions.

The practical difference: fish and birds, and the replacement of Abaye by Ravina

The text describes Abaye as establishing that “fish are the difference between them,” and explains that according to “product of a product and things that grow from the ground,” fish count as things that grow from the ground, while according to “offspring of the offspring of the earth,” fish “were created from water.” It brings an objection from Abaye’s own words in the laws of lashes concerning the pottita, and from there comes Ravina’s rejection, replacing the distinction and establishing that “birds are the difference between them,” with the explanation that according to “product of a product and things that grow from the ground,” birds are included, while according to “offspring of the offspring of the earth,” they “were created from the mud” and not from the earth. It describes this move as completing the ascent along the table, until the question becomes whether the line includes birds as well or not, and the whole thing is presented as a consequence of the rules of general and particular.

The three “aspects”: product of a product, things that grow from the ground, and offspring of the offspring of the earth

The text defines “aspects” as the Talmud’s term, as opposed to “items,” which is his own term, and presents three aspects that emerge from the expositions: “product of a product,” “things that grow from the ground,” and “offspring of the offspring of the earth.” It cites Rashi’s explanation in Bava Kamma for the reasoning behind “product of a product” as “offspring from offspring, and a vine from grape seeds,” along with the exclusion of “water and salt and truffles and mushrooms,” and explains that “product of a product” means something born from something else. It explains that “things that grow from the ground” are things that “are nourished and grow from the ground,” and that “offspring of the offspring of the earth” are things that were created from the earth, as reflected in the distinction that fish were created from water and birds from mud.

Identifying relevant properties from the verse and the assumption of the Sages

The text describes a process in which one looks at “cattle and flock, wine and strong drink” and asks which relevant properties are shared by the items, while rejecting accidental properties and treating “food” as a trivial aspect that does not distinguish anything. It states that the Sages assumed that the relevant properties are these three aspects, and suggests as a conceptual backdrop that second tithe originates in produce that grows from the ground, so there is logic in buying with its money things “connected to the ground,” while expressing puzzlement at the idea of buying water and salt. It presents the stage of identifying the aspects as a given working assumption from which one proceeds to the rules of inclusion.

Generalization, giving up aspects, and information theory

The text argues that generalization means lowering the number of required characteristics and thereby broadening the group, and illustrates this by moving from a specific description to a more general one—human being, prime minister, and so on. It explains that the more aspects one gives up, the larger the radius of inclusion becomes, and therefore the question “where does the line pass” is equivalent to the question “which of the aspects are you giving up.” It describes this insight as the basis for interpreting the differences between the results “product of a product and things that grow from the ground” and “offspring of the offspring of the earth.”

The Venn diagram as a second stage: containment relations among the aspects

The text presents a second stage in the exposition: after identifying the aspects, one builds a Venn diagram in order to represent relations of containment, overlap, or separation among the groups. It states that in this case one gets a nested diagram in which “offspring of the offspring of the earth” is the innermost group, inside “things that grow from the ground,” inside “product of a product,” and explains that these relations are learned from the passage itself and from comparing examples like fish and birds. It defines checking these relations as, in principle, an empirical task of going through “all the creatures in the world,” but presents itself as reconstructing the way the Sages saw those relations from within the passage.

General–particular–general: specifically the latter general clause versus specifically the first general clause

The text explains that deciding the radius of inclusion depends on how one analyzes the triple structure general–particular–general through two basic principles, general and particular versus particular and general, and through the dispute over whether to begin from the end or from the beginning. It cites the language of the Talmud that the one who includes birds “holds that specifically the latter general clause is decisive,” and explains that the analysis begins from “particular and general,” which expands, and then the first general clause serves to exclude what is not similar “in two respects,” yielding inclusion based on similarity in two aspects. It also cites the language of the Talmud that the one who excludes birds “holds that specifically the first general clause is decisive,” and explains that the analysis begins from “general and particular,” which narrows until “the general statement includes only what is in the particular,” and then the final general clause re-expands in a more limited way, so that one gets inclusion based on similarity in three aspects rather than two.

Translating the structure into a numerical system of “aspects”

The text connects each verse-structure to the number of aspects by which one judges: “particular and general” generates the maximal inclusion of “one aspect,” while “general and particular and general,” according to “specifically the latter general clause,” gives “two aspects,” whereas according to “specifically the first general clause” it narrows to “three aspects.” It describes “general and particular” as a situation that blocks even the kind of inclusion generated by a paradigm construction, and therefore gives the most restrictive result, which he describes as “four aspects” in a mathematical-technical sense of sticking to the written particulars themselves. It argues that the passage is built almost like a “recipe” that teaches the order of the work and the transition from the language of the verse to the placement of the line in the Venn diagram.

Completion: particular and general and particular, and a complete “toolbox”

The text raises the point that one further form is missing from the system, “particular and general and particular,” and argues that it has a necessary appearance in tractate Nazir, and that without it the halakhic language cannot describe every required radius of inclusion. It calculates that in “particular and general and particular,” according to “specifically the latter general clause,” we would get a result of “three aspects,” and according to “specifically the first general clause” we would get a result of “two aspects,” and in this way a symmetry is obtained that completes the table of the principles of general and particular. It suggests that in modern formulation he would add this principle to the baraita and make them “fourteen” principles, and presents this as a continuation of a historical process in which one principle in the teaching of Hillel the Elder was broken down by Rabbi Ishmael into three, and in later generations additional formulations were added until there were “more than seventy principles of exposition” in Rav Sherira Gaon and Sefer HaKeritut—not as a new invention, but as a detailing and formalization of earlier intuitions.

Okay. So remind me where we were, and we’ll continue. After we did general and particular, I gave some introduction about the hermeneutics of general and particular, about logical interpretive rules and textual interpretive rules. And the rules of general and particular, aside from gezerah shavah, are the most common textual rules. Hekesh is not very common. Hekesh is not one of Rabbi Yishmael’s rules, and I also don’t think it’s nearly as common. I don’t remember exactly; you’d have to count a bit. Hekesh is also hard to identify—what exactly counts as hekesh—because it isn’t always labeled in the same way. In any case, out of Rabbi Yishmael’s thirteen rules, it seems to me that the two forms of binyan av and kal va-chomer, which we did in the first part of the series, the three rules of general and particular that we’re doing now, and say also gezerah shavah, together cover, in my opinion, 98% of the interpretations. “Something that left the general category in order to teach” maybe appears a few more times, but all the rest—some of them appear once or twice in all of rabbinic literature. They barely appear. So why claim at all that this is a rule by which the Torah is interpreted in general, that you can interpret the Torah this way, if it appears only once? In our sources we don’t find much actual use of it, but in principle it’s possible. Sometimes there are interpretations where we can’t really identify what they’re based on, but at root they began from some interpretive rule. Tosafot in several places, for example, points out that a certain interpretation the Talmud gives is actually based on general and particular. The Talmud itself doesn’t even say that. So sometimes some of the interpretations before us—if we dug into them—we’d find that one of the rules was used there, just without saying so explicitly. In Daf Yomi now there’s something—general and particular and particular and general, page 53. Anyway, and fine, I think I already said that among the interpretations of the Sages, the number based on one of Rabbi Yishmael’s rules is completely negligible. Most interpretations are on all kinds of things where it’s hard even to define what interpretive rule is being used there.

Okay, but for our purposes—why specifically Rabbi Yishmael’s rules were accepted as… I don’t know, I don’t know. Maybe these are the rules that underwent some kind of conceptualization in Rabbi Yishmael’s time, and he succeeded in defining some binding principle. The rest are more local things that they either hadn’t yet found, or hadn’t yet formulated, into a binding rule that you can apply wherever you encounter it. They’re just local considerations that hadn’t yet been formulated, hadn’t yet been formalized.

Okay. So regarding general and particular, I said that this is a textual rule, whose basis is really the Torah’s mode of expression. The Torah’s form of expression is what creates the trigger for the interpretation. Unlike kal va-chomer and binyan av, where there is no hint in the verse, in the biblical text, telling us to make from this a kal va-chomer or a binyan av. In general and particular, the Torah’s way of writing is what gives us the authorization, or the trigger, to carry out—here, there’s a page here—to carry out an interpretation of general and particular. That’s why I called it a textual rule.

I said that the interpretation that appears in the scholion, in the baraita of Rabbi Yishmael’s examples—the canonical interpretation, so to speak, of general and particular—is this sugya, the sugya in Eruvin. I think that means, on the one hand, that it’s early, relatively early. On the other hand, it seems to me that by that point this tool of general and particular, these tools of general and particular, were already organized. And we’ll go through the sugya, and we’ll see that in this sugya it appears in the neatest possible way. In all the other sugyot it’s a huge mess, and once we understand from this sugya how the whole thing works, we can start trying to decipher. And this is a sugya that was prepared in advance, by definition, in order to create formalization? Apparently it was prepared, but that’s just how it came out. Meaning, this is a sugya with a really ideal, orderly, fully systematic formalization of interpretations of general and particular. And is that why we claim it’s earlier? I don’t know. I just happen to be saying it’s also earlier. I mean, what does “earlier” mean—there are earlier things. But I think it was formed at the first stage in which there was already a clear conceptualization of the rules. From there on, these are somewhat later interpretations. What came earlier was confused material. It looks confused to our eyes, meaning because the Sages weren’t even trying to fit it into some formulated pattern, because formulated patterns didn’t yet exist. They just did what they thought made sense in that particular place. Once we have the rules, which we’ll formulate from this sugya, we’ll be able to take them and try to decipher additional sugyot. So this sugya, in my view, is very, very central—precisely because it appears in such a clean form. In almost no other sugya does it appear this cleanly. So I’ll try to show that.

So what we started discussing was the topic of redeeming second tithe. That’s the sugya in Eruvin. I remind you of the table below, which already summarizes the items that emerge from reading the sugya. I made that table after reading the sugya. And basically there are items here that go from bottom to top, because water and salt are the least suitable for redeeming second tithe with, while cattle and flock, wine and strong drink—those are the things explicitly written in the verses. Those are certainly included in what one may buy with second-tithe money. Everything in the middle—each one is a step above the previous. How do I know it’s one thing above another? Simply from the flow of the Talmudic discussion, as we’ll now see. Last time we started moving upward from the bottom. We started reading the sugya and saw that the sugya basically moves upward and each time places the line a bit higher. First above seven, then above six, above five, above four, above three—where that line marks what things I’m allowed to buy with second-tithe money. Meaning, from cattle and wine—which are written above—down to the line, those are the things one may buy with second-tithe money. What’s below the line one may not buy. And over the course of the sugya the line rises monotonically, always upward. And that’s a classic structure of a sugya. In single steps. Yes, that’s a classic structure of a sugya. It rises in single steps simply because I took the units from the sugya itself, so of course it rises in single steps. I took the list from here; it’s not a list I took from somewhere else. So obviously every time one more thing was added, that just means the line moved up by one. But what I’m trying to do is help you track the progression schematically. What we’re actually trying to define here is: what is this line? This line defines the radius of inclusion. Right? In the Torah it says, “with cattle and flock, with wine and strong drink.” We’re now making a generalization, because the rules of general and particular create a generalization. Generalization up to what point? What gets included in this category, so that it too may be bought with second-tithe money, and what does not? That’s the line. The line says: up to here the generalization reaches, beyond here it doesn’t. Later we’ll see how the line is determined, but for now we’re just following different views of the Sages, each of whom places the line somewhere else.

So I’m not going to go back again over the first part of the sugya that we already covered. We basically reached the words: “And these tanna’im interpret general and particular.” You see that in the third block, third paragraph. Okay? What happened up to there—just to remind you. What happened up to there is that the line rose above seven, above six, above five, and the Talmud linked that to views that interpret via amplification and limitation, not general and particular. And I said—that’s always true—that the school of Rabbi Akiva, which interprets by amplification and limitation… the school of Rabbi Akiva, yes, which interprets by amplification and limitation, has a broader radius of inclusion than the school of Rabbi Yishmael. That’s always so; it’s a rule. Now, amplification and limitation—I already said I don’t have a logical mechanism for it. I didn’t find one there, and I’m not even sure there is one, because amplification and limitation is built in a somewhat wild, somewhat intuitive way. You include everything and exclude one thing, and you decide what to exclude on all kinds of considerations. But basically you include everything and exclude one thing. General and particular, by contrast, has a very precise system of rules for what the radius of inclusion will be, how far we include. Okay? That’s why I’m dealing with what scholars call the Yishmaelian interpretations, from the school of Rabbi Yishmael, not from the school of Rabbi Akiva.

Okay. “And these tanna’im interpret general and particular.” So the Talmud says—maybe we’ll start from the third block—“What is the point of dispute between Rabbi Yehuda ben Gadish and Rabbi Eliezer and these tanna’im mentioned later?” And here I noted that “the tanna’im mentioned later” is a clue to the editing of the sugya, right? At an earlier stage it says there will be tanna’im later on. So that means whoever wrote this stage of the sugya already knew what he was going to place later. There’s someone editing the sugya. If you write backward, that doesn’t yet prove there was editing. If you write forward, that does prove there was editing. And there are a number of examples like that in the Talmud—not very many, but a few.

Rabbi Yehuda ben Gadish and Rabbi Eliezer interpret by amplification—amplification and limitation—while these tanna’im interpret by general and particular. In other words, the dispute is whether we belong to the school of Rabbi Yishmael or the school of Rabbi Akiva. I already mentioned that in Shevuot 26 it says there’s some fundamental dispute here between two schools: do we interpret by amplification and limitation, or by general and particular. So that is also the dispute between Rabbi Yehuda ben Gadish and Rabbi Eliezer and the tanna’im who come later. Rabbi Yehuda ben Gadish and Rabbi Eliezer interpret by amplification and limitation. “You shall give the money for whatever your soul desires”—that is amplification. “For cattle and flock, for wine and strong drink”—that is limitation. “And for whatever your soul asks of you”—that is a return to amplification. Amplification, limitation, and amplification: you include everything. What is included? Everything. And what is excluded? According to Rabbi Eliezer, brine is excluded, and according to Rabbi Yehuda ben Gadish, water and salt are excluded. So they have a dispute over what is excluded here. Are we above five, or are we above six? That’s the dispute, right? It’s in the table below. What happens with what is excluded? What is excluded cannot be bought with second-tithe money. This cannot be bought—that was excluded. Cattle and flock, wine and strong drink are written in the Torah itself. Everything adjacent to them was included; what lies beyond the line was excluded. Okay, so there’s a dispute here over how many things we exclude. With Rabbi Akiva it’s always tiny little odds and ends that get excluded at the edge. The question is how large those odds and ends are. So they say: what was excluded is six and seven, or what was excluded is five, six, and seven. So for now we’ve reached the stage of above five, right? Those are the disputes we’ve seen so far. That’s the most stringent one, sure—the one that excluded the most things.

“And these tanna’im interpret general and particular.” As it was taught: who are these tanna’im? They appear only here. We didn’t see them earlier. These are the ones we were told earlier would appear later on, but they’re not tanna’im we already met, and that’s why I’m saying this reflects editing. As it was taught: “You shall give the money for whatever your soul desires”—general. “For cattle and flock, for wine and strong drink”—particular. Now it’s all just a change of terminology, right? With Rabbi Akiva we read amplification, limitation, amplification. Here they say general, particular, general. At this stage that still doesn’t tell us anything. “For cattle and flock, for wine and strong drink”—particular, or it particularized, however you want to define it. General and particular—some understand it that way. “And for whatever your soul asks of you”—it returned and generalized. General and particular and general: you may infer only what is similar to the particular. Just as the particular is explicitly a product from a product and something that grows from the ground, so too everything that is a product from a product and something that grows from the ground. And therefore, besides cattle and flock, wine and strong drink, everything that is a product from a product and something that grows from the ground is included. In a moment I’ll explain more what that means. “And another baraita taught”—that’s one tanna, the later tanna, and there are several tanna’im, so until now we saw the first tanna. And this is another general-and-particular interpretation? This “product from a product”—is that a different general-and-particular interpretation? No, why? “Product from a product and something that grows from the ground” is the result of the interpretation. Anything that is a product from a product and something that grows from the ground can be bought with second-tithe money. That doesn’t appear in our table at all. Right, because “product from a product and something that grows from the ground” are characteristics, not items. The table contains items, okay? So in a moment we’ll see.

“And another baraita taught: just as the particular is explicitly offspring, offspring of the earth, so too everything that is offspring, offspring of the earth.” So another baraita says the radius of inclusion is different. It’s not yet clear to us whether it’s smaller or larger, but it’s different: “offspring, offspring of the earth.” Okay, that’s the radius of inclusion of the second tanna. We still don’t understand why, how it got to “product from a product and something that grows from the ground,” and how it got to “offspring, offspring of the earth.” For us that’s the million-dollar question, right? How exactly does general-and-particular interpretation work—how do you decide the radius of inclusion? For now it’s just descriptive. How do you decide which characteristic to put the… Not just which characteristic, but yes—what to exclude and what to include. I’ll spell it out more in a minute. “What is the practical difference between them? Abaye said: fish are the difference between them. According to the one who says ‘product from a product and something that grows from the ground,’ these fish are considered things that grow from the ground. According to the one who says ‘offspring, offspring of the earth,’ fish were created from water—they were formed from water.” Okay? So fish are the practical difference between these two tanna’im. Both interpret general and particular. Both basically belong to Rabbi Yishmael’s camp. Until now we saw Rabbi Akiva’s camp—and notice, we’re moving upward in the table. To add fish or not add fish. Exactly. Do we move above four or above three? Right? So notice, the line keeps climbing. Before we were above five, above six, now we’re above four and above three. Basically, the dividing line between Rabbi Yishmael’s school and Rabbi Akiva’s school passes above four. Yes. That line we just discussed—“product from a product and something that grows from the ground”—does that basically mean everything that comes out of this, only living things? No, no, in a moment I’ll explain. In a moment I’ll explain how we get to “product from a product,” but for now, just so you can track the schema: where we now stand with the line according to these two baraitot is this—according to one baraita the line is above four, and according to the other baraita the line is above three. Okay? According to “product from a product and something that grows from the ground,” and according to the one who says that—yes, I still don’t know how it connects to this—but that’s what the Talmud says. The Talmud says the practical difference is fish. Meaning, one puts the line below fish and one above fish. Okay? Fish are the difference between them. How does that connect to “product from a product”? Four is fish brine and fish innards—how does that connect? I don’t understand the… Fish brine and fish innards is already connected to brine. No, why would… yes, it’s connected to brine, and fish brine—what is it made from? Fish innards. Right, but that’s without actual pieces of fish. And there’s brine with pieces of fish, so that’s more like food. That’s just contact with food—it’s basically water, fish brine. So that’s contact with food, but here there are actual pieces. And the one who says “product from a product and something that grows from the ground,” does he take fish as things that grow from the ground? Yes. In a moment we’ll see how this connects to the characteristics. But first, as far as the table goes, that’s how it works. So there’s some dispute here. We already understand that it’s a dispute in the laws of general and particular, yes? How to apply the general-particular-general interpretation, and its implication is whether we stand above four or above three. That’s what the Talmud says.

Now, in order to understand a bit more how this whole thing works, the Talmud raises here three—now we’ll already call them by their explicit name—three “sides.” Three sides, as opposed to the items that appear here in the table. “Items” is my term; “sides” is the Talmud’s term. The Talmud raises three sides: product from a product, something that grows from the ground, and offspring, offspring of the earth. That’s the terminology we’re going to use now. Yes.

Now, what is each of these? “Product from a product”—that basically means something born or produced from something else. That’s how Rashi explains in Bava Kamma, in a parallel sugya on page 63: “offspring from offspring, and a vine from a grape seed, excluding water and salt and truffles and mushrooms.” “Product from a product” is anything born from something else. Notice what that excludes: water and salt and truffles and mushrooms. Anything born from something else that was born from something else. What? Anything born from something else that was born from something else, because it’s sort of familial like that. That’s always the case. It’s always the case. If I was born from something, then my father must also have been born from something—he’s like me. So it’s always recursive. You could say maybe salt is born from water, but water isn’t… No, no. Salt is not born from water; that’s not what we call it. We separate it from water; it’s not born from water. But “born” means really born, like an animal, or even a plant. But not salt. Why are fish “things that grow from the ground”? One second—I haven’t yet explained what “things that grow from the ground” means. So Rashi says that “product from a product” is “offspring from offspring, and a vine from a grape seed, excluding water and salt and truffles and mushrooms.” That already tells us—this is not Rashi here in our sugya, but Rashi in Bava Kamma—that “product from a product” is something broad. Mushrooms already tell us that. Anything that is born, anything that comes out of something of its own kind. And living things—but everything that is born—how do they reproduce? They don’t mention all plants here; they mention truffles and mushrooms because those are things that pop up without… Exactly. He excludes truffles and mushrooms because they’re not born from anything. No one planted them, they have no seeds, they’re born from nothing. Yes, that’s the assumption. Ordinary plants are born from something. So “product from a product” is in fact the broadest circle. Okay.

Good. What does “something that grows from the ground” mean? The three sides are: product from a product, something that grows from the ground, and offspring, offspring of the earth. Now, “something that grows from the ground”—Rashi here explains that all of them are nourished and grow from the ground. So anything nourished by the ground is called “something that grows from the ground.” Okay. And what is “offspring, offspring of the earth”? That you can see from the Talmud itself. “Offspring, offspring of the earth” means something created from the earth, right? That’s why fish aren’t included in it, because fish were created from water, as the Talmud says. Okay? In other words, “offspring, offspring of the earth” means something created from the earth. “Something that grows from the ground” means something nourished by the earth, not created from the earth. And “product from a product” means something produced from something of its own kind. Okay?

Now, what are these three sides, really? We look at the items that appear in the verse. In the verse it says cattle and flock, wine and strong drink, and we ask ourselves: what are the characteristics of these four items appearing in the verse? What relevant characteristics do they have? Obviously they can have all sorts of characteristics—they have four legs, or they weigh a kilo—but clearly there’s some kind of sorting of what the relevant characteristics are. We don’t take accidental characteristics. This is similar to what we saw in the first part as well, but here we… use reason to assume what the relevant characteristics are. And the Sages—and again, right now I still don’t know exactly why this is so—but the Sages assumed that the relevant characteristics are these: product from a product, something that grows from the ground, and offspring, offspring of the earth. These are the characteristics that connect the four examples that appear in the Torah. Okay? These are the relevant characteristics. In principle, one could have raised another side: that they are food. Yes, but that applies to everything. Exactly. Food is the trivial side. The trivial side is that the Torah says we’re supposed to buy it to eat with second-tithe money. Okay? So of course food is the trivial side; we don’t take it into account. For us there are three sides. Okay.

Good. Now, what exactly led the Sages to decide that these really are the relevant characteristics? You can raise all kinds of possibilities. I assume it’s connected both to textual hints from the passage itself and to understanding the underlying idea. We’re talking here about eating things bought with second tithe. Second tithe is a tithe taken from things that grow from the ground, right? So if you redeem it into money, the Sages’ assumption is that presumably with that money too you should buy something connected to the ground. Why on earth would you use it to buy water and salt? After all, we’re really supposed to bring tithe from things that grow from the ground. But even so, some abstraction is being made here. It’s not just “ground”; it’s product from a product, something that grows from the ground, and offspring, offspring of the earth. That means it’s something a bit more abstract than just “things that grow from the ground.” Exactly how they got there, I don’t know. In any case, let’s assume for now that this is the given.

The Sages proceed—so we see the first stage of what the Sages do. They read the four items appearing in the verse and ask themselves: what are the relevant sides? “Sides” meaning: what are the relevant characteristics of those four items? The result of this stage of the interpretation is three things: product from a product, something that grows from the ground, and offspring, offspring of the earth. Those are the three characteristics.

Now what do I do with the characteristics? Come on, let’s try to think logically now. These are the three things that characterize the four items in the verse. If the assumption is that interpretations of general and particular are meant to generalize, what does it mean to generalize? To create a rule such that anything included in it can also be redeemed with second tithe. The characteristics. What did you say? The characteristics are there to include, not to exclude. No. The characteristics define what is written in the verse. They aren’t there to do anything yet. The question is: now I want to include more—what will that do to the characteristics? It will drop some of them, right? When you include more, you’re really giving up one of the characteristics. What do you mean? After all, the verse says it has to be broader. A smaller common denominator, which means a larger set. Fine. Information theory, right? The broader the set, the less information is contained in identifying that set. Right? If I say David Ben-Gurion was a human being, I didn’t give much information—though some people would dispute even that. If I say he was a prime minister, I’ve already given more information. If I say he was prime minister of the State of Israel, I’ve given still more information. If I say he was the first prime minister of the State of Israel, then I’ve given the full information, because there’s only one such person. Okay? Each set I passed through along the way was a set getting progressively smaller. The more information I give, the smaller the set. If I want to generalize to a set—say the verse says “David Ben-Gurion,” and now they tell me: generalize. I can generalize to all prime ministers of Israel. So what did I give up? I gave up the fact that he was the first prime minister of Israel, and instead made it any prime minister in Israel. That’s already a broader set. Right? Now I generalize again. I say: he was a prime minister, not necessarily of Israel. An even broader set. There are more prime ministers, right? Then I say: no, he’ll just be a human being, not only a prime minister. That’s a much broader set. Right? So the fewer defining characteristics I keep, the broader the set becomes. Right? So the radius of inclusion—another way to ask what the radius of inclusion is—is really to ask which of the sides we’re giving up. If the items are product from a product, something that grows from the ground, and offspring, offspring of the earth, then I say: okay, let it be only everything that is a product from a product and something that grows from the ground, without “offspring, offspring of the earth.” That’s one generalization, right? Or let it be only product from a product, and not something that grows from the ground. That’s another generalization. So the radius of inclusion—and that’s the rule—the radius of inclusion…

Now before we see how the Talmud says this, there’s another passage in the Talmud. “And did Abaye really say that fish are considered things that grow from the ground? But Abaye said: one who ate a potita receives four lashes, an ant receives five, a hornet receives six. And if you say potita should also receive lashes because of ‘creeping thing that creeps upon the earth’?” Potita is a fish, yes? So if fish are things that grow from the ground, then one who ate potita should also get lashes because of “creeping thing that creeps upon the earth.” So therefore Ravina rejects that. Then it would be five total? No, then it would be more—yes, five, because of “creeping thing that creeps upon the earth.” One who ate potita gets four, so yes, then it would be five. Anyway, it doesn’t matter for our purposes; that’s just a side point.

“Rather, Ravina said: birds are the difference between them. According to the one who says ‘product from a product and something that grows from the ground,’ these too are things that grow from the ground.” Why? Because they are nourished from the ground, right? “According to the one who says ‘offspring, offspring of the earth,’ meaning what was created from the earth, birds were created from mire, not from the earth.” Let’s assume that for the moment—that’s the assumption. I don’t know, some sort of mosquito, from an egg, from something that isn’t the earth itself. Okay? Some kind of bonus category.

So now notice the table: we’ve reached the maximum, right? Ravina takes us upward. We previously stopped above three—only what’s written in the verse. Okay? That’s what Ravina says. So we’ve finished the journey along the table. Now we need to understand it. He saw the radius of inclusion as including exactly what’s written—meaning the common denominator is exactly that, it points to specific things. Okay?

So now we ask ourselves how this works. We see that it rose along the table, and we see that it depends on the question of how many sides—soon we’ll see how it depends—but we still haven’t explained how to determine the criterion of how many sides to include and how many not to include.

So here’s how. First of all, the first stage in a case like this is that we need to make the following diagram. Product from a product, something that grows from the ground, and offspring, offspring of the earth—excuse me—cattle and flock, wine and strong drink: that is included, that has all three characteristics, right? That’s what’s written in the verse. All three characteristics are found in all these items. Now what happens with the characteristics? Yes. Now I want to characterize the relationship among the characteristics—that’s always the second step in the interpretation. First, identify the characteristics; second, build a Venn diagram. You know what a Venn diagram is? A Venn diagram—say I have sets. Let’s say I have here the set of animals, okay? And I have the set of birds. So birds are included within animals, right? All birds are animals; it is not true that all animals are birds. So the drawing looks like this. Sometimes you have a situation like, say, the relationship between priests and members of the Sanhedrin. Then the relationship is like this: there are priests who are members of the Sanhedrin, there are members of the Sanhedrin who are priests, but there are also priests who aren’t, and members of the Sanhedrin who aren’t. Healthy food and tasty food is the Venn diagram on the right. No, it’s not like that—it’s like this and this, so this is healthy and this is tasty, and together they cover everything with no overlap. Okay? That’s what in mathematics is called a complete partition.

Anyway—what? These are all Venn diagrams. Everything is Venn diagrams. It’s just a technique for presenting relations among sets. So this is a relation of inclusion, this is partial overlap, this is disjointness. Okay? Disjoint sets—there’s no shared element between them, and so on. What we need to do in the next stage is draw a Venn diagram of the sides. A Venn diagram of the sides in our case looks like this. In our case it’s simple, and that’s why this interpretation is so good for analysis. This is the Venn diagram of the sides, where this is product from a product, this is something that grows from the ground, and this is offspring, offspring of the earth—the innermost circle. Why? Because offspring, offspring of the earth—say birds and fish—it’s a dispute between Abaye and Ravina, but birds and fish are not offspring, offspring of the earth, but they are things that grow from the ground, right? That’s what the Talmud says. What does that mean? That there are things—sorry—they are things that grow from the ground but they are not offspring, offspring of the earth, and therefore they remain outside. What does that mean? That offspring, offspring of the earth is included within things that grow from the ground. Meaning there are things that grow from the ground but are not offspring, offspring of the earth.

In principle, to build a diagram like this you have to examine the relationships pairwise. Meaning: we check what the relationship is between offspring, offspring of the earth and things that grow from the ground; what the relationship is between things that grow from the ground and product from a product; and what the relationship is between product from a product and offspring, offspring of the earth. Okay? After doing that pairwise, you can also draw a general diagram. I’m skipping a bit here because the technical details are less important. We basically draw this, and then you can see: product from a product actually contains cattle here—let’s write the list—cattle and flock, of course from the verse itself, wine and strong drink also from the verse itself, and fish and birds. Notice what I’m writing here: I’m writing the items included in the side, in the category—this characteristic includes these, right? Of course they aren’t really located only here; they’re also here. Right? Since offspring, offspring of the earth includes all this, and things that grow from the ground also include all this, I’m just writing it here off to the side. It includes these? What? Offspring, offspring of the earth? No, sorry, no, my mistake. Wait a second. Things that grow from the ground include birds and all the legumes, right? And fish are disputed—right, whether they count as things that grow from the ground or not. So fish you can mark with a question mark. Okay, so it’s clear they are inside product from a product, because both fish and birds are product from a product—that’s clear according to everyone. That means that things that grow from the ground are inside product from a product. Right? And offspring, offspring of the earth doesn’t contain them, so it’s even more inward. Okay, so this is clearly the Venn diagram. Okay?

So up to here we’ve basically identified two stages of the interpretation. We identified the relevant sides—and they are offspring, offspring of the earth, things that grow from the ground, and product from a product—and we drew the relationships among them. The relationships among them are a matter for scientists, not for halakhic people. You now have to check whether everything that is offspring, offspring of the earth is also something that grows from the ground, or not. You’d have to go through every creature in the world and see whether it’s so or not. Since I’m not familiar with these matters and I don’t know exactly the definitions the Sages used, I’m just trying to understand it from the sugya. I’m trying to see how the Sages saw it, because as far as I’m concerned I’m reconstructing what the Sages did. But when we come to interpret the Torah ourselves, we don’t have that information. We have to gather that information ourselves. We have to decide now what the relation is among these characteristics; you just need to look around and see what includes what, and so on. It’s just that here I’m reconstructing what the Sages did, so I have the privilege of using that.

Good. The next stage, what we now need to do—and we’re almost done—is decide where the radius of inclusion passes. Now look what happens here. It’s obvious that here, “offspring, offspring of the earth” includes the four items of the verse; they’re all inside it. Right? This is one. What? Here you can say one? Yes, one. Right? They’re all inside. When we now make a generalization, we can simply see it visually. We have the option of making a generalization like this—maybe including also things that grow from the ground. We have the option of making a generalization like this—maybe including also product from a product. Once we’ve drawn the Venn diagram, we immediately see the options for generalizing. But how do we know which option to choose? We do that according to the way the verse is written. If the verse is written as general-particular-general, that tells us one thing. If it says general-particular, it tells us something else. If it says particular-general, it tells us a third thing.

So let’s continue reading the Talmud, and it says as follows: “What is the reason of the one who includes birds, and what is the reason of the one who excludes birds?” The one who includes birds—notice, that’s this one, right? Birds are here, and he contextually thinks this line—notice, this line is the line below birds. Where is that? It’s the line below two. This is one, right? Now I’m translating the table into the Venn diagram. This is one, this is two. Right? And then there are fish, where it could be that this also includes fish or doesn’t include fish—that could be three. That’s disputed. Okay?

Now I ask myself: okay, but where really does the line pass? What is the result of the interpretation? So the Talmud says: “What is the reason of the one who includes birds, and what is the reason of the one who excludes birds? The one who includes birds holds that the latter general term is the decisive one. Particular and general—it becomes a general term adding to the particular, and thus all things are included. And the first general term serves to exclude whatever is not similar to it in two respects.” Up to here—for a moment we’ll continue. Only, the one who excludes birds—notice, excluding birds means he’s located here, right? The one who places the line here, the minimal line, excludes birds. How did he get to this as the radius of inclusion? So the Talmud says—you see how the sugya is built? It just teaches us the order of work. It’s almost like a recipe. Right?

Now, the one who draws the line here—the sugya now explains to us how. How did it come out that he drew the line here? So the Talmud says this: after all, we have this structure in the verse, simply the wording of the verse, right? This opinion says: the latter general term… latter or first? First. The first general term is decisive. What does that mean? That I analyze this triple structure by starting with the first pair. “The latter general term is decisive” means starting with the second pair and then adding the third component. In other words, I basically have two fundamental interpretive rules: general and particular, and particular and general. And I use those interpretive rules to know what to do with the triple form: general and particular and general. How do I do that? It depends on the dispute. The question is whether I start from the beginning or start from the end.

“The first general term is decisive” means—okay, just to remind you where we were and continue. In interpretations of general and particular, I had given an introduction about the interpretations of general and particular, about logical rules and textual rules. And these general-particular rules, aside from gezerah shavah, are the most common textual rules. So these three rules basically more or less… hekesh is not very common. Hekesh is not one of Rabbi Yishmael’s rules, and I also don’t think it’s nearly as common. You could count more carefully later. It’s also harder to identify hekesh; it isn’t always branded in the same way. In any case, out of Rabbi Yishmael’s thirteen rules, it seems to me that the two forms of binyan av and kal va-chomer, which we did in the first part of the series, the three general-and-particular rules we’re doing now, and say gezerah shavah as well, cover in my opinion ninety-eight percent of the interpretations. Meaning, “something that left the general category in order to teach” maybe there are a few more. All the rest—there are some that appear once or twice in all of rabbinic literature. They hardly appear. So why nevertheless claim that this is a rule by which the Torah is generally interpreted, that you can interpret the Torah this way, if it appears only once in our sources and we don’t find much actual use of it? In principle, you can. Sometimes there are all sorts of interpretations where we can’t really identify what they’re based on, but at root they began from some interpretive rule. Tosafot in several places, for example, points out that a certain interpretation the Talmud makes is actually general and particular. The Talmud doesn’t even say so. Meaning, it’s general and particular. So sometimes some of the interpretations before us—if we dug into them—we’d find that maybe one of the rules was used there without explicitly saying so. In Daf Yomi now there’s something. What? In Daf Yomi now there’s something—general and particular and particular and general and things like that. Ah, okay. Nazir 33. Anyway, I think I already said that among the interpretations of the Sages, the number based on one of Rabbi Yishmael’s rules is completely negligible. I mean, there are hardly any. Most interpretations are on all sorts of things where it’s hard even to define what interpretive rule is being used there.

Okay, but for our purposes—why specifically Rabbi Yishmael’s rules were accepted as… I don’t know. There’s the question of rules that… from the prayer? Underwent some sort of conceptualization by the time of Rabbi Yishmael, and he managed to define some binding rule. The others are kinds of local things that either hadn’t yet found, or hadn’t yet formulated, a binding rule that you can apply wherever you encounter it. These are local considerations that hadn’t yet been formulated, hadn’t yet been formalized.

Okay, so regarding general and particular, I said this is a textual rule whose basis is really in the Torah’s mode of expression. The Torah’s wording is what triggers the interpretation, unlike kal va-chomer and binyan av, where there’s no hint in the… stop, in the biblical text telling us to make a kal va-chomer from it, to make a binyan av from it. In general and particular, the Torah’s style of writing is what gives us authorization or a trigger to perform—if there is here an interpretation—to perform a general-and-particular interpretation. That’s why I called it a textual rule. I said the interpretation that appears in the scholion, in the baraita of Rabbi Yishmael’s examples, the almost canonical interpretation of general and particular, is this sugya, the sugya in Eruvin. I think this means, first, that it is early—relatively early—and second, it seems to me that there the tool of general and particular, the rules of general and particular, was already organized. And we’ll go through the sugya, and we’ll see that in this sugya it appears in the neatest possible way. All the other sugyot are huge messes, and after we understand from this sugya how the thing works, we can begin trying to decipher a sugya that was prepared in advance, by definition, in order to create formalization. They prepared it, but that’s just how it came out—meaning, it’s a sugya with a really ideal, orderly, fully systematic formalization of interpretations of general and particular. And maybe that’s why we claim it’s earlier? I don’t know. I’m just incidentally saying it’s also earlier. Meaning, there are earlier ones, but I think it was created at the first stage where there was already a clear conceptualization of the rules. From there on, these are somewhat later interpretations. What came before were confused things—confused to our eyes, meaning because the Sages didn’t even try to fit it into some formulated pattern, because there were not yet formulated patterns. They simply did what they thought in that place. Once we have the rules that we’ll formulate from this sugya, we can take them and try to decipher additional sugyot. Therefore this sugya, in my eyes, is extremely central, precisely because it appears in such a clean form. In almost no sugya does it appear so cleanly. So I’ll try—we’ll try—to show that.

So what we began discussing, the topic of redeeming second tithe, this is the sugya in Eruvin. I remind you of the table below, which already summarizes the details that emerge from reading the sugya. Meaning, I made this table only after reading the sugya. And basically there are items here that go from bottom to top. Because water and salt are the least suitable for redemption of second tithe, and cattle and flock, wine and strong drink, those are the things written in the verses themselves. Those are certainly included in what may be bought with second-tithe money. All those in the middle are one stage above another. How do I know it is one stage above another? Simply from the flow of the Talmudic discussion, as we’ll now see. Last time we started going upward from the bottom—that I start with general and particular—and afterward revise because there is another addition of a general term, and I need to correct something. “The latter general term is decisive” means I start from particular and general, and then the correction is the first general term. For that we needed to know what general and particular does and what particular and general does. So for that Rashi explains here—I brought you Rashi, I’ll read it to you if you want—“and it becomes particular and general, and the general term adds to the particular and includes all things.” What does that mean? What does particular and general do? It includes everything. It includes everything, right? Meaning, if it only said particular and general, Rashi already tells us, the line would pass here. Right? It includes everything, if it only said particular and general. But it doesn’t only say particular and general; there’s also a general term at the beginning. Right? So you have to lower a level, you have to come down to here. Meaning, the correction created by adding another general term tells us: don’t do full particular-and-general; make it narrower. Not such an expanded generality. Okay? That’s what Rashi says.

“And the first general term comes to exclude.” Why does the first general term exclude and not include? A general term ought, seemingly, to include. Because if you have everything and you need to single out something… No, sure, but what’s the idea? The idea, afterward, is very simple. Look. There is here particular and general. Like some sort of “and also” system of conditions or something? No, even simpler. First you have to understand this. Particular and general. What is particular and general? The general term comes and adds to the particular; it adds everything. So if the verse contains a particular and after it a general term, the result is everything. Everything that is similar in one of the respects. But if before that there was a general term and after it a particular, it’s clear that that came to reduce, and therefore here too it has to reduce, right? So here the general term appearing after the particular comes to include it. A general term appearing before the particular is there to exclude. The particular basically narrows the general term. You can even put it that way. The particular says: don’t go all the way to the general term; do less. Okay? We’ll still see later exactly what it does, but particular and general includes everything. Adding a general term at the beginning moves in the direction of exclusion—you have to remove one characteristic.

Now notice, and this is also why he works from the end to the beginning, because it’s inclusion first and then afterward you reduce some of it, I assume, right? That’s the opinion that the latter general term is decisive, and the other opinion… that’s the rationale behind it: take that, and then see how much you can reduce from it. Yes, but I can say the same rationale in the opposite direction too. I don’t know why he chose this; I don’t know. But that’s the first direction. Now notice in terms of number of sides: the thing located here—in how many sides is it similar to what’s written in the verse? One. In one side, right? This is called similarity in one side. Meaning the result, if it says—we can already begin summarizing—the result of particular and general is a radius of inclusion of one side. That is the radius of inclusion, right? You add all the sides: anything that resembles the list of items written in the verse in one side, the law also applies to that. Maximum inclusion. That is called one side.

Good. Now what does general and particular and general do? One side is the most minimal. Meaning two sides—two sides, right? What is something similar in two sides? That’s everything located inside this, because everything located inside this—say for example an item appearing here, birds—in which two sides is it similar to what’s written here? It’s product from a product, right? Because it is included in the broader radius. And it is also something that grows from the ground. But it is not offspring, offspring of the earth; in that respect it is not similar to what’s inside. So it is similar only in two sides. Everything found in this band is similar in two sides. Everything found in this band—and of course also what’s inside—is similar in at least one side. There is no necessity specifically for three sides, not here. In principle no, but we’ll get to that later. We’ll get to it, but the canonical case is three sides. There are sugyot from which it seems we even deliberately tend to establish three sides, but let’s leave that for later. I’ll talk about it, but for now I’m presenting this sugya because it’s simple; I don’t want to get into all the complications from other sugyot.

Okay, so we’ve found these two. Now this is the opinion that the latter general term is decisive. This approach basically tells me: one additional side. Particular and general gives one side, but because in the structure there are three components, it becomes two sides. So the one who says we also include birds holds that the latter general term is decisive. That’s the root of the dispute: how to interpret general and particular and general. Do we assume “the latter general term is decisive,” or—now I’ll explain the other side—“the first general term is decisive.” How does “the first general term is decisive” work? We start with general and particular. And Rashi tells us: general and particular comes to exclude. In general and particular and general—the first general… wait—“and the one who excludes birds holds that wherever there is general and particular, the first general term is decisive, and the general includes only what is in the particular.” What does it mean that the general includes only what is in the particular? That it’s only one, as if only the middle circle. Seemingly that’s three sides, right? Everything fully similar, right? Everything here looks like three if I’m not—just what is fully similar. Don’t write it that way; it’s not precise. In a moment it will be three sides and not “fully similar.” No, that’s still not precise, I think. In a moment I’ll explain; I think it’s three sides. Yes, it’s not three sides—soon we’ll see.

So this is how it starts. Now, when we add another general term at the end, we include something more, right? Rashi tells us what should have happened. We include something more, so what should be here? Also birds. Two sides. Then we’d return to the same place. So what is the dispute between “the first general term is decisive” and “the latter general term is decisive”? For you it’s obvious that this can’t be right. If there are more—no, but here we’re dealing with three sides. There are three here. Therefore it’s obvious this isn’t right. And this is the reason they want to aim for three sides, because we have—wait, don’t jump ahead of me, I’ll get tangled later. General and particular is four sides, not three. When I say four sides, that’s just a mathematical expression. There aren’t literally four sides here. Four sides means only the things written in the verse, not even what resembles them in all sides. After all, there are other things that could resemble those four things in all their sides. No—only what is written in the verse. And the medieval authorities explain: this follows from the question why we need the rules of general and particular, and also the rule of binyan av. The medieval authorities on the baraita of the rules explain that the purpose of the rule of general and particular—why do we need it at all?—is so that we not make a binyan av from the particular. Okay? To tell us: only the particular, nothing beyond it. Meaning that general and particular prevents even the kind of generalization of binyan av, which in a moment we’ll see is actually a fairly small generalization. No—only the items written in the verse. So on the mathematical level I call that four sides, meaning more than three. Three sides is already a generalization. So basically it’s not sides, it’s those specific details. Exactly. I call it “four sides” only for completeness, just to make it easier to handle. Okay?

Then if a general term is added at the end, you reduce it to three. With three sides, where are we? That’s what is similar in three sides, right? So this is the dispute: are the birds inside or outside? In particular and general you have nothing—you call it four sides so people won’t make a binyan av out of it and say it doesn’t include anything and so on. Right.

So what does this mean, basically? That the dispute whether we include birds or not is really a dispute whether the radius of inclusion is here or here, meaning whether we work by similarity in three sides or similarity in two sides. And what is the root dispute? How we handle this triple instance of general and particular and general. If we say the latter general term is decisive, then particular and general takes me to one side, and this general term lowers me to two sides. So “the latter general term is decisive” gives me this result: similarity in two sides. That’s the latter one being decisive, and generally it’s broader. “The first general term is decisive”—the first, of course, is more restrictive, so it’s narrower. Okay? “The first general term is decisive” means: general and particular gives four sides, and this general term adds one side, because a general term at the end includes, while a general term at the beginning excludes. Okay? So it returns to three sides. And then we arrive here.

So the dispute between the two baraitot—not between Abaye and Ravina; that comes later, whether it’s birds or fish—the dispute between the two baraitot is whether it’s here or here. It doesn’t matter right now whether this means birds or fish. Is “the latter general term is decisive,” or is “the first general term is decisive”? That is really the dispute.

And now we basically know everything about the rule of general and particular. Because now we can write a whole table saying this: we have general and particular, we have general and particular and general, and we have particular and general. Okay? Now, this is “the latter general term is decisive” and this is “the first general term is decisive.” This table is built in a way no other sugya manages. Once we cracked this sugya, we understood the whole issue. All the other sugyot are a terrible mess.

So general and particular, we said, is four sides according to both; there is no dispute about that. Their dispute, by the way, is only in a triple form. On those two there is no dispute, right? This is one side. How many enter this table? How many? Three by four? Four rows by three columns. Here—“the latter general term is decisive”—we start from particular and general. Particular and general is one, then we go down to two, so here it is three. Okay?

Now we still have two questions left. One question: I’m still missing another rule. What about particular and general and particular? It’s obvious that can’t exist, because you… Why? According to what we said there. Why? What about it? It doesn’t appear in this sugya, but in principle? We have no idea what a particular does to something that already has general and particular on it. Why? We do have a very good idea. A particular at the end excludes—we know that. A particular at the beginning includes—exactly the mirror image. What’s the difference? If we had particular and general and particular, what would come out? We’ll see in a moment. We’ll see. But first the question is what happens with it.

Now you might say: who says such a form exists in the Torah? Maybe we don’t need that rule because there is no verse built in that way. But there is a sugya in Nazir that does make such an interpretation; there is such a verse. More than that, it also has to exist, because I have another difficulty. What does the Holy One, blessed be He, do if He wants to instruct us to include in three sides according to the approach that the latter general term is decisive, or to include in two sides according to particular and general and particular according to the approach that the first general term is decisive? After all, each approach needs to explain to us what the full toolbox is. The Holy One, blessed be He, has to build a logical language capable of defining any radius of inclusion He wants. If He wants us to include by one side, He writes it in one form. If He wants us to include by two sides, in another form. Three sides, four sides, and so on. And each of the approaches—whether the latter general term is decisive or the first general term is decisive—has to describe to me a complete toolbox, otherwise something is missing from the language. The language cannot express the instruction “make a generalization of two sides” or “of three sides.”

Now of course these two questions answer each other. Because let’s do the calculation of what happens with particular and general and particular. It comes out to the same thing. It’s exactly the complementary case. Let’s see. You’ll see that it completes exactly what is missing. It comes out two and three. Right? Three and two. Let’s see.

According to the approach that the latter general term is decisive, yes? We start from general and particular. Right? General and particular is four. And a particular at the beginning? Three. No, three. A particular at the beginning includes, and therefore it’s fewer sides. A general at the beginning excludes; a particular at the beginning includes, because particular and general is the maximal inclusion. A particular at the beginning is something that leverages inclusion. Okay? So that gives three.

What happens according to “the first general term is decisive”? We start from particular and general. What is particular and general? One. And a particular… wait, yes, a particular at the end narrows again. A particular at the end always narrows. General and particular is narrowing. Therefore, more sides means the set is narrower. Notice what happened here. Exactly the rule missing from this sugya, which we didn’t know what to do with, is what completes the toolbox. Meaning, according to the approach that the latter general term is decisive, this rule is exactly what enables the Torah to instruct us to include by three sides. And according to the first-general-term approach, this is the rule that helps us include by two sides. And that is the complete structure of the rules of general and particular. Okay?

And this sugya is the only one we found that presents a wholly coherent, orderly, precise, defined structure—really even didactic. I wouldn’t be surprised if this is a sugya they actually built this way in order to teach this whole idea. Even though, again, when you first read it, it seems like a pile of incomprehensible stuff. But I think that if we explain it this way, everything flows perfectly—like a knife through butter. And it fits here exactly into the missing holes.

That doesn’t appear in the sugya. So here I’m completing it based on the logic I learned from the sugya. The logic I learned from the sugya is the logic of the top three rows. Now I ask myself two questions: so what do we do with particular and general and particular? I already know the logic of “the latter general term is decisive” and “the first general term is decisive,” and I also ask myself: who performs the inclusion by three sides and by two sides according to each approach, since that is currently missing? And suddenly I see that it lines up exactly. So it’s clear to me that there is another rule here. If I were writing a baraita of the interpretive rules today, I’d make it fourteen. In Rabbi Yishmael’s time they hadn’t yet conceptualized it. What they did conceptualize, though, was particular and general and particular. They conceptualized it intuitively? They didn’t conceptualize it intuitively? Yes. Or maybe they simply didn’t feel a need, because they said that the three-side method is included under general and particular and general. Of course. What I’m saying is: this is the process I described in previous sessions too. The process is that all the rules always existed; over time, more and more of them split off, got formulated, and became independent rules. With Hillel the Elder, if you remember, there was only one rule of general and particular. One. Then Rabbi Yishmael has three general-and-particular rules. Why? Did they invent two more in the meantime? No. What Hillel called the rule of general and particular is this whole table. The rule of general and particular means: what do you do when the verse shifts from particular language to general language, in a broad sense? Three, two—it doesn’t matter in what order. It’s a whole collection of rules with the same idea: that the move from particular wording to general wording tells me to determine the radius of inclusion.

Now in a later generation they conceptualized it. And now I already have mathematical tools that tell me, based on the formulation of the verse, how to determine the radius of inclusion—how many sides I include. And then by means of that framework I can determine exactly what will be included from this verse and what will not be included from that verse. Therefore Rabbi Yishmael already writes three rules. He didn’t invent two; he broke down the rule of general and particular, the principle of general and particular, into three sub-rules. And now he has three. In light of the sugya in Nazir, I would make it four. And now he has three. In light of the sugya in Nazir I would make it four, and then you’d have fourteen interpretive rules. There are more—it doesn’t matter—you can keep producing them, and in fact they already made more than seventy interpretive rules in Rav Sherira Gaon and later works, and the Rash of Kinon in Sefer HaKeritut made many more rules. Because this really keeps developing over the generations. But it isn’t invented; it’s just becoming more and more finely articulated—what they always did. They always did this; they just didn’t yet give it a precise formulation or divide it into two separate rules. They said: look, when it’s general and particular, understand intuitively that it comes to generalize. How to generalize? I understand intuitively how to generalize on the basis of the rules. When we lost that intuition—no, when they lost the intuition of how to do it—then you have to produce mathematics. There’s no choice. But before that mathematics existed, the Sages apparently had some kind of intuition: when they see a certain kind of wording in a verse, they understand how far it needs to be generalized. Therefore the rules of general and particular, in a broad sense, were for Hillel the Elder just one such rule. It’s a rule that says: please generalize the particulars appearing in the verse according to how it is written—and they did it intuitively. And once we lost that intuitive understanding, suddenly the Talmud reconstructed it and built mathematical rules out of it. And those are these. Okay?

Good, did you want to say something? No, no, no. Okay, so that’s it.