Lecture dated 5 Tammuz 5777

Table of Contents

• Aspects, perfect similarity, and the radius of generalization
• The dispute between kama davka and batra davka in triangular structures
• Why the Sages work with three aspects, and the limits of formalism
• Binyan av, pirkha, and distinguishing relevant aspects
• Textual hermeneutic rules versus logical ones, and the role of the text
• Ribbuy and mi’ut as a different model
• Defining sets in law, Hart, and open texture
• The Torah as guiding interpretation through forms of wording
• Natural formulations of klal u’prat and examples like “a reasonable response time”
• Rabbi Yirmiyah, fifty cubits, and Shabtai Weissman
• Klal u’prat exegesis in responsa, enactments, and legal documents
• The uniqueness of the Torah: sharp patterns of one aspect, two, and three
• The example of Moses our Teacher, context, and the radius of generalization
• A halakhic responsum versus the Shulchan Arukh: combinatorics and Venn diagrams
• Interim summary and continuation to the topic in Chullin

Summary

General Overview

The text presents a model for understanding the hermeneutic rules of klal u’prat as a textual way of directing the “radius of generalization” of a law by counting relevant “aspects” of similarity, and it situates the disputes of kama davka and batra davka within the question of which component in the triangular structure one starts from and which element qualifies which. It argues that logic alone cannot determine where to stop a generalization, and therefore a linguistic-textual mechanism is needed to reduce interpretive arbitrariness and guide how far to extend beyond the particulars. From there it connects this to general problems of defining sets in law, inspired by Hart, presents a justification for why interpretation is not merely a matter of “having no choice” but can actually be reasonable, and shows that these textual hermeneutic rules also appear in the interpretation of legal documents and responsa, though in the Torah they crystallize into sharper patterns. Finally, it illustrates how moving from deciding individual cases to writing a “Shulchan Arukh” requires formulating sets, combinatorics, and Venn diagrams, while emphasizing the distinction between intensional and extensional definition without confusing set inclusion with the number of properties.

Aspects, perfect similarity, and the radius of generalization

The text defines “perfect similarity” as similarity in four aspects, and treats three aspects as a state that still generates generalization relative to all other contexts that are fully similar to the particulars. It states that prat uklal is the maximal generalization of one aspect, and that the fewer the number of aspects, the broader the generalization. It presents triangular structures as an intermediate tool that allows one to indicate two or three aspects, and argues that both methods have a textual device for every needed degree of generalization, including “three and a half aspects” as a term for binyan av, where even the slightest pirkha stops the extension.

The dispute between kama davka and batra davka in triangular structures

The text presents the dispute between kama davka and batra davka as an argument about the basic structure in triple appearances and about the question of what is primary and what is secondary. It explains that according to batra davka, klal uprat ukhlal rests on prat uklal as an expansion of one aspect, while the first klal qualifies it into two aspects. By contrast, according to kama davka, the base is klal uprat of four aspects, and the klal qualifies it into three. It then explains that in prat uklal uprat the relations are reversed, so that according to batra davka, klal uprat, with four aspects, is adjusted to three, whereas according to kama davka, prat uklal, with one aspect, is adjusted to two.

Why the Sages work with three aspects, and the limits of formalism

The text offers hypotheses as to why the Talmud assumes a problem of three aspects, such as a hierarchy of species within genus within super-genus, and the image of “three generations,” after which the connection is broken, as well as psychological hypotheses about the capacity to grasp a certain number of concepts at once. It emphasizes that he has no certain knowledge here, and that the question of “four dimensions” is not really an explanation but something he plans to return to. He tries to develop a formalism in which certain results remain “universal” relative to the total number of aspects, but qualifies this by saying that the Sages are not operating with rigid mathematics, and that at most one can view triangular structures as an intermediate domain, not sharply defined, between two and “n minus one.”

Binyan av, pirkha, and distinguishing relevant aspects

The text describes binyan av as a very limited tool of generalization, because even the slightest pirkha can stop it, and it interprets this as a minimal extension that is influenced even by differences that are not necessarily a relevant “aspect” but still somehow “itch” in the context. It defines the aspects as components of similarity that are relevant to the halakhic result, and illustrates this with second tithe, where the Sages determined the relevance of “offspring of the offspring of the land, fruit from fruit, and products of the soil” מתוך an understanding of the context. It cites the words of the medieval authorities (Rishonim) that adding a klal before a prat is meant to stop the extension of binyan av, and concludes that the mechanisms of klal u’prat allow the Torah to instruct us when not to generalize at all and when to generalize at different levels.

Textual hermeneutic rules versus logical ones, and the role of the text

The text divides the hermeneutic rules into two main categories: logical rules, such as kal va-chomer and the two forms of binyan av, and textual rules, such as gezerah shavah, hekkesh, and klal u’prat. It argues that the central problem is determining the radius of generalization, and that there is no logical way to stop the “slope” between full similarity and maximal generalization, because logic can at most identify aspects but cannot determine how many of them are required. It explains that this is why textual hermeneutic rules deal with guiding the boundaries of generalization, and that in practice many of these textual derivations end up converging on klal u’prat structures.

Ribbuy and mi’ut as a different model

The text distinguishes between klal u’prat and ribbuy umi’ut, and argues that ribbuy umi’ut does not work in terms of set theory but operates in a different way, as a kind of “full inclusion with one item removed” within a triangular or double structure. It states that because of this conceptual gap, he is not dealing with it in the present context.

Defining sets in law, Hart, and open texture

The text presents two ways of defining sets in ontology: extensional definition by listing members, and intensional definition by means of an essential property, and argues that in a legal system both collapse in the face of open-ended terms. It brings Hart’s example of a sign reading, “The entry of vehicles into the public garden is forbidden,” and shows how questions like what counts as a “vehicle” and what counts as “bringing in” create an endless number of borderline cases. At that point, the judge has to resort to verbal interpretation, analogies from other contexts, or purposive interpretation based on the aim of the law. It presents the criticism of “judicial legislation” alongside the claim of a lacuna, of “there’s no choice,” and adds that there is also a justification for saying that such interpretations can be reasonable and can, to some extent, reflect the legislator’s intent.

The Torah as guiding interpretation through forms of wording

The text argues that the Torah takes a step that other legal systems do not take, in that the text itself guides how to decide through linguistic patterns that indicate the breadth of generalization. It emphasizes that the Torah did not explicitly formulate “klal u’prat”; rather, the Sages identified such structures through tradition and through a linguistic intuition about human speech. But in practice, these structures narrow the interpreter’s room for maneuver. It adds that the Torah narrows interpretive freedom even further by giving several particulars rather than a single one, so that the relevant aspects emerge from what is shared by multiple examples rather than from an endless set of possible properties.

Natural formulations of klal u’prat and examples like “a reasonable response time”

The text suggests legal-style formulations such as, “It is forbidden to bring in vehicles… cars, tractors, motorcycles… and anything similar,” as a parallel to a triangular structure that signals a generalization beyond the examples. It offers another example in defining “a reasonable response time” by comparison to the response times of emergency services “according to the relevant circumstances,” in order to improve decision-making without fixing rigid numbers. It argues that numerical definitions are a “primitive approximation” compared to the power of examples within a context, and links this to the way that over the generations measures and standards become more formal, even though originally they were not.

Rabbi Yirmiyah, fifty cubits, and Shabtai Weissman

The text brings the context of “a fledgling found within fifty cubits” and the passage about Rabbi Yirmiyah being thrown out of the study hall, and presents in the name of Shabtai Weissman in The Method of the Talmud that Rabbi Yirmiyah did not mean to be provocative; rather, he was arguing that fifty cubits is derivative and that there is room to take circumstances into account. It places this between the desire not to leave everything to the judge and the desire not to turn laws into mathematics, and presents the whole move as a sophisticated mechanism that guides decisions without freezing them in an impossible way.

Klal u’prat exegesis in responsa, enactments, and legal documents

The text brings an example from Menachem Elon about a responsum of Maharam that interprets the language of Maharam of Rothenburg as having a klal-prat-klal structure, in order to conclude that “the klal adds to the prat,” even regarding something not truly similar to the earlier prat, while presenting the prat as a boundary that prevents generalization to just anything in the world. It argues that there are many examples of klal u’prat interpretation in communal enactments and responsa, and concludes that this reflects a human mode of speech in which an example followed by “and anything of that kind” directs an extension that is similar in substance. It quotes Rabbi Chaim Palachi in the responsa Chaim BeYad, who states that “permission was given to interpret the language of a legal document” by one of the thirteen hermeneutic rules, and it mentions names such as Beit Yosef, Ritva, and Rabbi Chesed LeAvraham as having interpreted the language of legal documents through the rule of klal uprat ukhlal.

The uniqueness of the Torah: sharp patterns of one aspect, two, and three

The text argues that although understanding klal u’prat as natural language is valid outside the Torah as well, the Torah and the tradition create a specificity of sharp patterns that speak in terms of “one aspect, two aspects, three aspects” in a way that almost invites the mathematization of interpretation. It emphasizes that in legal documents and judicial rulings one usually does not “count aspects” like that, and concludes that there is something unique here to the biblical text and the Oral Torah.

The example of Moses our Teacher, context, and the radius of generalization

The text demonstrates how one determines relevant aspects through context by using the example of “similar to Moses our Teacher,” and it suggests possible properties like leadership, prophecy, being a Levite, and being the son of Amram, while rejecting irrelevant properties such as his first name. It describes how klal u’prat structures would determine how many of those properties must be present in order to include a case in the set, and how that same system can decide individual cases by checking how many of the properties are present in the candidate.

A halakhic responsum versus the Shulchan Arukh: combinatorics and Venn diagrams

The text distinguishes between deciding individual cases, where it is enough to check whether the case has the appropriate number of properties, and writing a general rule in the style of the Shulchan Arukh, which requires defining the set itself. It explains that an intensional formulation such as “two aspects out of four” breaks down into many pairs of intersections, and it demonstrates a combinatorial calculation of choosing properties. It then suggests simplifying this through Venn diagrams, which make use of overlaps and inclusions in order to reduce the number of sets that need to be described. It emphasizes that this simplification relies on looking at the extension of the elements in order to identify inclusion relations between properties, but the counting of “aspects” remains intensional, because different properties are counted as two aspects even if, in terms of the scope of the set, there is no difference.

Interim summary and continuation to the topic in Chullin

The text concludes by saying that the technique depends on distinguishing between the content of the properties and the scope of the sets, and it warns against confusion when one set is contained within another but we are still dealing with two different aspects. It says that he intends to continue at home with a more detailed example and to analyze the matter in the topic in tractate Chullin, “with God’s help,” in order to see how relevant aspects and textual structures are expressed in a concrete passage.

And to say that this is a perfect similarity—I’ll put it this way—a perfect similarity of four aspects. And in fact there are three relevant aspects that characterize the particulars. “Perfect similarity” means four aspects, because similarity in three aspects is still a generalization. It’s a generalization to all the other contexts that are completely similar to the particulars, in all the relevant parameters, but there are still other such contexts. Okay? Therefore, when I speak about a situation where we don’t generalize at all, that’s four aspects. Particular and general—that’s maximal generalization, meaning only one aspect. The smaller the number of aspects, the broader the generalization. The intermediate cases are general and particular and general. We already see that we have an instruction for how to instruct one aspect, and we have how to instruct four aspects. So let’s say what we’re missing is either two or three aspects, and therefore what we have for this purpose are two more instructions: particular and general, and particular. And here there is already a dispute between the method of “the first is precise” and the method of “the last is precise.” And we saw that the method of “the last is precise” is really a method that says: we are speaking only about the triple structures, and those are the subject of the dispute. In the triple structures, the question is where to begin and which part serves as support. Which is primary and which serves as support? “The last is precise” says that in fact this general term is the primary one, and therefore the basic structure is particular and general, and the first general term qualifies the result of that particular-and-general. We said that particular and general is one aspect, maximal expansion. So if we added another general term before that, then it’s two aspects. Okay? And if we say “the first is precise,” then the basic structure is general and particular. That is four aspects, and then this general term qualifies it, of course in the opposite direction, and it comes out as three. Okay? That’s “the first,” and that’s “the last.” In particular and general and particular, the opposite happens: if I say that “the last is precise,” then the basic structure is general and particular. General and particular is four aspects, so the first particular corrects it and turns it into three. And if I say “the first is precise,” then particular and general brings me to one aspect, and that particular corrects it to two aspects. Okay? What comes out, basically, is that according to both “the first is precise” and “the last is precise,” we have a textual device for every instruction we might need: an instruction of one aspect, four aspects, two and three, or three and two. Okay? Is that because of Einstein, that there are four dimensions and maybe more dimensions? No. Actually that’s a question we’ll still come back to later. The Talmud, in the simple sense, assumes a problem of three aspects. And that’s the problem. Why exactly that is so? I only have guesses; I have no idea. But it’s clear that this is the basis the Talmud works with. Why is that? I can speculate, because when we speak about three aspects, say in the simplest cases, these are aspects contained one within another. That was also the case we spoke about in Eruvin. So in fact there is some hierarchy here of species within genus within super-genus, let’s call it that. A hierarchy of three apparently looks to the Talmud like some sort of maximum. Beyond that, it’s like father-in-law, grandfather, over the son. After three generations the connection is already severed. Things related to me through three stages somehow already lose the connection. We know there is a connection between a particular and a species, between species and genus. So we have three levels that still speak to one another. The fourth level is already something that doesn’t connect to the first level but opens a new hierarchy for it. Maybe it’s a psychological reason? Could be. If I’m not mistaken, a person of intelligence—not a genius—can grasp at once and handle four concepts in a discussion like this? Otherwise you move from one state to another to cover more. And a genius can encompass up to seven things at once in consciousness. I don’t know. In short, here these really are wild speculations, as you wish. I don’t know why. What is clear is that the basic structure for the Sages is a structure of three aspects. On top of that four aspects are defined. So then general and particular would make five, meaning the intent is not to generalize at all. In a problem that has four aspects, when I say “anything similar in four aspects,” that is certainly still a generalization, right? That includes all the things completely similar to the particulars, but there are still other things like that that are completely similar to the particulars, and therefore it will be five aspects. Particular and general will always be one aspect; that is maximal generalization. Anything similar in one characteristic, right? That’s the maximal generalization. Now, the measures in between here are already more problematic. So if we go with the formalism all the way, then general and particular and general according to “the last is precise”—we have one aspect from the general term, that comes out to two aspects, and two aspects is that same universality. It doesn’t matter how many total aspects there are; it always comes out as two aspects. By contrast, if I say “the first is precise,” then I have here general and particular, which is n plus one aspects, and the additional general term adds n. So this isn’t universal. Okay? That basically means that we have here n. Okay, this is universal because it’s one plus one? What? Because it always starts from one, that’s why the start will always start from one. Right. And here basically the same thing: particular and general is “the first / the last”—sorry, “the last is precise.” So we have general and particular. General and particular is four aspects with one deducted, that’s three aspects—sorry, five and four. Yes, exactly, this is n and here too it’s two. Okay, so in fact there is one measure here that can play and vary between different problems; the second measure is somehow fixed. My guess is that it can’t really be that exact. I mean, this isn’t actually formal mathematics. I also don’t think the Sages thought in those terms. Therefore, in my opinion, the most we can get out of this is that the triple structures are something intermediate between two and n minus one. Exactly where do you stop? And where does it cross over there? I don’t think one can get to any more fine-grained model than that. So that’s it. Meaning, I also haven’t found anyone who commented on this issue, since I also haven’t found anyone who really analyzed it in this way. Even though I think it’s almost explicit in the passage in Eruvin, so certainly I won’t find comments on it. In short, we’ll leave it for the next generation; the next generation will dare to address these things. Fine. But after doing this, after evaluating a bit how this whole business works, now we’ll return to the more general discussion of the rules of general and particular, and afterward I’ll again go to another passage to see additional implications. But I want to complete the general discussion now that we already have some example in hand that we can talk about. So where were we in the general move? In the general move we basically said that we need to define logical tools by means of which one can instruct us regarding different radii of generalization. Right? A binyan av is a basic tool of generalization, but we saw that binyan av is very limited because any pirkha—even the slightest pirkha—can stop a binyan av. That means the radius of generalization of binyan av is very narrow. Even the slightest pirkha. In other words, perfect similarity is similarity of three aspects. Perfect similarity—general and particular—no, general and particular isn’t perfect similarity. The correct definition is no generalization; that’s not perfect similarity, that’s no generalization. Perfect similarity is this. Fine. Yes. So if we have—even the aspects we’re talking about here are of course relevant things. That’s what’s called aspects. What are the relevant features of the particulars that may affect the halakhic result? When I deal with second tithe, the Sages decided that offspring of the earth, fruit from fruit, and produce of the ground—those are the relevant features by means of which one can make generalizations. There are other features of the items that appear there—wine and strong drink and ox and sheep or something like that. There are other relevant features. This one has four legs and that one has, I don’t know what. We’ll focus on them in a pirkha. The element of joy? Wine gives joy? Wine gives joy, yes. One can find many other features too. So why are we focusing only on those three? The Sages assumed those three are the relevant features. How do we know what is relevant and what isn’t relevant? Apparently from the context. That is, by understanding what second tithe is and what redemption is meant to accomplish, from the thinking behind the matter. Apparently from that we can infer which aspects are relevant and which are not. What happens in binyan av? In binyan av we said that even the slightest pirkha can exist. The slightest pirkha means even if there’s a difference in a non-relevant aspect, you already don’t extend it. Meaning it sits somewhere… If it’s not relevant, then why… what? Not every distinction is a legal distinction. Okay, obviously the distinction that this one is written with a yod and that one is written with a lamed won’t be a pirkha even in binyan av. When they speak about the slightest pirkha, understand: none of this is rigid mathematics. I’m only trying to describe things that worked intuitively. I think that “the slightest pirkha” means something that on the face of it I wouldn’t think is relevant, but it’s not something completely out of the blue. It’s some kind of thing that catches my eye. I wouldn’t put it into one of the aspects; I wouldn’t call it an aspect. But still there is something here that might nevertheless be connected to the context. And because of that, binyan av is some kind of extension—say, if we return to the problem of three aspects—then general and particular tells me four aspects, no extension at all. Okay? General and particular and general—is that obtained from binyan av? What? What is obtained from general and particular is more than all the medieval authorities (Rishonim) write. All the medieval authorities (Rishonim) write that the reason they added a general term before the particular is to stop the extension of binyan av. Otherwise you would just write the particular and that’s it. If you do only the particular with no generalizations, just write the particular—why do you need to put a general term before it? All the medieval authorities (Rishonim), explicitly in their commentary on the baraita of the hermeneutical rules, write that the preceding general term comes to stop the extension of binyan av. So that itself already tells us that binyan av is an extension a bit beyond this narrowing. So binyan av is a minimal extension. Here there is no extension at all; it’s simply only the items written in the verse. Binyan av is a minimal extension that I stop even with a non-relevant aspect. Last time I called it three and a half. Three and a half aspects is binyan av. Okay? Three aspects, which is full similarity, is general and particular and general according to “the first is precise,” or particular and general and particular according to “the last is precise.” That is exactly the number of aspects when I require similarity in all the relevant aspects. In fact, as I said earlier, that is still an extension—not that it’s an extension, it’s a bigger extension than binyan av. Right? Bigger than binyan av, because in binyan av even a non-relevant aspect stops the extension; it’s very narrow. Here only relevant aspects stop the extension. If you find a relevant aspect that doesn’t exist in the learned case but exists in the teaching case, it will no longer be absorbed. That is, the extension won’t be valid regarding it. Therefore it’s three aspects, and binyan av is three and a half aspects. Okay, and so on. So what comes out is that we have different means of making generalizations. The minimum tells me: don’t generalize at all; these particulars were written deliberately. After all, we asked: the Torah must have some device to tell me, these particulars—don’t generalize them; I mean only this case. By means of general and particular. Binyan av is the minimal generalization, and after that further generalizations. And what this basically means is that the Torah can hint to us about the radius of generalization by a textual means. That is, it can write the instruction in phrasing that begins with a general term, continues with a particular term, and ends with a general term. By doing that it told me: extend in two aspects, depending on which method we use. But in some intermediate degree, between one and three, or between one and four. Okay? Or between one and the three and a half of binyan av. The term “three and a half”—is there such a thing in the hermeneutics of the midrash? What? No, inclusion and exclusion is a completely different story. Inclusion and exclusion—whether in a triple structure or a double structure, at least in what appears in the Talmud—it’s not clear at all what the difference is between them. You make a full inclusion and remove one item. Because there is some triple structure here, it is customary to tell you: remove one item—the one that seems most reasonable to you to remove, remove it. But this doesn’t work at all in terms of set theory. It doesn’t work through sets at all. It’s something completely different, exclusion and inclusion, so we’re not dealing with that right now. Okay. So this really leads us to the difference between text and logic. Because the hermeneutical rules can be divided into two main categories. One category is the logical rules: kal va-homer, the two forms of binyan av, maybe if you want also two verses that contradict one another, which is also some kind of logical rule. There is a contradiction, so I do some kind of alignment, find some solution to the contradiction. Maybe yes, maybe no; it may depend on the specific example we’re talking about. But kal va-homer and the two forms of binyan av are certainly logical rules. What are the textual rules? Gezerah shavah, for example. The same word appears here; the Torah itself tells me to make a comparison here. I don’t decide to make a comparison because it really looks similar to me. Which is exactly what characterizes the logical rules. Because that’s what the Torah says, because it is free for interpretation. What? Because it is mufneh. The Torah tells me: make a comparison. And even if the Torah says—one does not derive a gezerah shavah on one’s own. Yes, the mufneh, the mufneh does it. No, it’s also tradition, gezerah shavah. Even if there is a similar word, you can’t derive a gezerah shavah. The rule of hekesh. I didn’t understand. There isn’t a gezerah shavah everywhere there is an identical word, where one is also allowed to make one. No, certainly there isn’t an identical word, but how can one… Hekesh. If it’s a similar word, it is mufneh. The intention is that one does not derive gezerah shavah on one’s own, only according to tradition. Obviously, but it is at least the same word or at least the same root. Not true. “The priest shall come” and “the priest comes”—that’s not the same word, but that is a gezerah shavah. Why? The Talmud brings in most cases that this is within gezerah shavah, and we said why are you emphasizing the words—it’s not important. That’s hekesh, not gezerah shavah. No, hekesh is something else, where verses are adjacent. I know. Hekesh is the plain meaning, which is what’s written. Exactly. So… That’s the strongest, what’s written. What? Hekesh cannot be refuted, while “just as we find” gets refuted every time. No, “just as we find” is basically binyan av. Hekesh is adjacency of verses, or there is a list of items within a verse, so they are compared to one another. That too was a kind of… Isn’t hekesh textual? Of course it’s textual. Right, of course it’s textual, but it isn’t gezerah shavah. It isn’t based on equal words, but on something stronger, like adjacency. It doesn’t matter right now whether stronger or not stronger; it’s a different rule. Gezerah shavah is a comparison between words. You see it isn’t a rule. What? It isn’t a rule at all. No, no, a rule—what difference does it make now whether it’s among the thirteen or not. This rule, one of the rules used to interpret the Torah. It doesn’t matter to me right now why it isn’t included among the thirteen rules; we spoke once about the fact that it’s as though it’s explicitly written, what you said here. But hekesh is not based on two equal words. It isn’t based on the fact that it’s adjacent or appears in the same verse or something like that. Gezerah shavah—the basis of the exposition is equality between words. Hekesh too is really something that starts in the text and not in logic. In contrast to binyan av, where there is no hint at all that I am supposed to learn from binyan av from “bringing to the canopy,” what we discussed in the first part of this series. Rather, I think to myself: it sounds logical to me—if this does the same job as that, why shouldn’t it do another job that the other one does? So that sounds logical to me, so I compare them. The Torah doesn’t hint anywhere that I should compare these two things; therefore this is not a textual rule, it is a logical rule. And indeed, on the logical level, the whole problem we are trying to deal with here is the problem of determining a radius of generalization. A determination of radius of generalization cannot be defined logically. Because by definition there is some sort of slippery slope here that there is no way to stop. Either you compare completely, and then it’s completely with no radius of generalization at all—only what is totally similar. Or you say: anything that is similar in even one thing—that is maximal generalization. And all the intermediate levels are in between. How can I decide, by means of logic, at what radius to stop the generalization? Here lies the groove written in the Torah: should the generalization be taken up to here, or maybe up to here, or up to here? Logic can never tell me that, because what does logic say? That there are equal aspects. Fine—but how many equal aspects? One, two, three, four? By definition that is outside logic. Logic only tells me what the aspects are. Therefore, by definition, when I want to define how many aspects of similarity there are, it must be something textual; it cannot be something logical. Therefore it is no wonder that the main textual rules are rules whose purpose is to define a radius of generalization. And those are the rules of general and particular. In fact, in all the other rules except kal va-homer and the two forms of binyan av and the verse itself—aside from that, the rules are gezerah shavah and all sorts of general-and-particular formulations, and that’s all the rules. “A matter learned from its context” and “a matter learned from its end” is also basically some kind of… well, there’s room to discuss them, and they also hardly appear. If you count how many times expositions use the rules of Rabbi Ishmael as such and in Rabbi Ishmael’s own way, most expositions do things not even defined within these conceptual tools of Rabbi Ishmael at all. And among those expositions, gezerah shavah appears quite a lot, and general and particular is almost all the rest. Meaning, those three expositions of general and particular are almost all the rest—and they’re not even balanced; one of them doesn’t appear at all, the second appears twice, the triple structure appears more. Okay? But basically almost all textual expositions are rules of general and particular. Therefore one must understand that, basically, the role of the text in the midrashic context is to define for us what logic… Logic tells me: one aspect is similar, two aspects are similar, three aspects are similar. How will I know where to stop? There is no way to do that with logical tools, therefore it must be something textual. And therefore, in fact, even if I hadn’t seen these passages, I should have expected that there would be some textual device here that would do this. And that is something required. Okay. Now I want to move a bit—so how does logic really work? That is, we are trying to define sets, a radius of generalization, or define a set by way of an example, right? There really is a problem in trying to define sets. There are basically two basic ways to define sets in ontology. One way is called the extensional way, meaning simply to enumerate all the members of the set. Okay? If I have the set of numbers up to ten, I can say: this is the set of whole numbers up to ten; I can say this is zero, one, two, three, four up to ten—simply point to them directly. That’s definition by extension, meaning what is included in this set and what is not included in this set. And there is intensional definition. Intensional definition is by the intension, by the content, by the essential definition of what characterizes the members of this set. All whole numbers less than ten. That is an intensional definition. So there are two ways to define sets, but all of that is in places like the example I took, of course extremely simple examples. When we want to define sets in a legal world, the situation is much more complicated. Both definition by extension and definition by content are very problematic. Usually we don’t manage to do it, and the one who discussed this at length was a dear fellow named Hart. Hart is a great jurist named Hart, in theories of law. And he has an example that afterward became everyone’s example; they always quote it as an example of open texture, definitions with open texture, open definitions. The example is: there’s a sign by the entrance to a public garden—entry of vehicles into the public garden is forbidden. Fine? And then you ask yourself, okay—and ever since then they’ve been torturing this definition until today. Everyone comes up with more examples, I don’t know, they pull them in all kinds of directions; there’s a lot of creativity in the legal literature there. So they begin discussing there what counts as a vehicle. Is a vehicle a tractor, a car, a truck, a bicycle, skates, a little ride-on toy for children? I don’t know, you can come up here… Then they ask what does “bring in” mean. For example, I take a tank that no longer works and want to turn it into a monument. So one of the examples—and it’s not mine; nothing here is mine; I think by now they’ve exhausted all the possibilities there—a tank I want to make into a monument in the public garden. Is it permitted to bring it in or is it forbidden to bring vehicles into the public garden? So how exactly do you define such a thing? What will you do now—list all the vehicles? Tomorrow morning they’ll invent another vehicle. You can’t do it extensionally. So what will you do intensionally? How? What defines it? All things with four wheels? You won’t succeed. There isn’t one idea that unites them all. What do you need to do? You need to do—or before that, what does the judge do in such a case when he has to decide? He interprets. The interpretation can be literal or purposive. He can, for example, make analogies from another place where the term “vehicle” appears, and see what the meaning of the concept “vehicle” is, or what the meaning of the concept “bring in” is in other contexts, in other legal contexts, and make an analogy to this case. He can of course—and I assume this is what he would do in this context—make a purposive interpretation. A purposive interpretation asks what this law was intended for, what it was trying to say. Either they think for themselves, or they look in the Knesset records, in the give-and-take when the law was passed—what explanations were given. Often they make use of those things in purposive interpretation, and based on that they decide. So, for example, someone may say that the purpose is to prevent air pollution, and then he’ll say: okay, a little ride-on toy is certainly permitted, a bicycle is no problem at all. And a tractor… It becomes very problematic. A Segway or whatever—no problem at all. And this can give us wonderful answers. Someone else will say: not at all, it isn’t air pollution, it’s the danger that the children will be run over. The children play there and you need to be careful that they not be run over. Then clearly that changes the whole picture; already completely different things will be included. It could be that bicycles are already forbidden, even though from the perspective of air pollution there is no problem with bicycles. Meaning, the purpose will basically determine what we forbid here, what the set will be. One can draw several more proposals for purposive interpretation here, and every such interpretation will yield a different list of vehicles. So now what actually happens when a judge makes this kind of interpretation? As for vehicles in a garden, I assume nobody cares very much except the person being tried before him for having entered with the vehicle. But in more problematic and more charged cases, suddenly the criticism arises. Wait a second—what do you mean? The judge is acting here as a legislator, not as an interpreter. The legislator should say this. What do you mean the judge is bringing in his own value system? He decides why the legislator prohibited bringing vehicles in, and now he’s also deriving all sorts of decrees from it. So again, with vehicles of course it isn’t all that interesting. But when it comes to ideological issues, halakhic issues, I don’t know, the case of the Sephardi girls—exactly, things of that sort—then the criticism arises: who authorized you? The legislator has to do that, not you. This doesn’t really come out of what is written in the law. The legislator didn’t do it. But the law cannot answer every such possibility. If there is a lacuna, then it is the judge’s role to fill the lacuna. That’s exactly the next stage. So the problem arises: how can it be that the judge engages in legislation, that the values of the judge decide what the outcome of the interpretation will be—and that’s not legitimate. He wasn’t chosen in order to legislate; he was chosen in order to judge. Now people come and say in response: fine, but there’s no choice. There’s no choice; there’s a lacuna, so what should we do? Every time some vehicle wants to enter the garden, are we going back to the Knesset to pass something in three readings? With coalition agreements and paying another million dollars to those who will vote for us? It isn’t realistic. So there is no choice. That is, the main consideration in this context is the consideration of no choice. There’s no choice, so what can you do? Someone has to decide, because at some point the law has to be final—someone has to put down the bottom line. So that’s the judge; that’s his role; there’s no helping it. So that is the justification of authority. It is a justification of “there is no choice,” so he does it. But the question is whether there is also a real justification here, not only a justification of authority, but a justification that perhaps these tools really do genuinely yield the intention of the legislator. That could be—I don’t know, there’s room to discuss it. Because it is entirely parallel to the problems we spoke about in the first part of the series when we discussed generalizations—the problematic nature of generalization—that for any set of data there can be many generalizations. And the fact that, at least in the scientific context, there are generalizations that seem reasonable to everyone, even though there are infinitely many other generalizations that also fit all the facts. There are generalizations that are simple, plausible, and everyone understands that this is the correct general law. By the way, we aren’t always right; sometimes we’ve fallen. But there is some agreement—it’s not a shot in the dark. Therefore I think that in the legal field too there are reasonable interpretations. That is, there is justification for such interpretation; it is not completely arbitrary. It isn’t that the only justification is “there is no choice.” No—the justification is that these interpretive methods do, with some degree of certainty, though of course not absolute certainty, reveal the intention of the legislator himself. But here—“it is not in heaven”—that is probably the point. What? Is the statement “it is not in heaven” the justification of authority, or is it… I don’t even remember what the second term was. Justification of authority and real justification, meaning a justification that it was actually right as they did it, that this is how it’s regarded. I don’t remember if there is already a legal term for it. Anyway, what happens here is something very interesting, because the Torah takes a step that no legislator, at least that I know of, takes. The text itself tells you how to decide. Meaning, when I formulate the law, I can formulate it in different ways that tell you which generalization to choose. So the generalization that the interpreter makes is no longer completely a shot in the dark. It isn’t arbitrary, and he isn’t legislating—or at least he is less legislating than he might have been. The Torah directs him. It tells him, at least on the technical level, in how many aspects he should work. How broad or narrow this generalization should be. And that is more than what usually happens in systems of law, legal systems, where they tell you what the law is and now, when you face a problem, you have to think how to interpret it. It isn’t that the Torah said there are rules like general and particular and particular and general. It’s the Sages who look at the Torah and understand. There is a tradition that started this, and that’s the whole introduction I gave. The tradition that started this says that yes, such structures lead to generalization. True, the presentation of these rules was created over the course of history. But you said a lesson or two ago that this isn’t unique to the Torah, but rather reflects something in natural language. Yes. In human language we see people say something general and then clarify themselves by examples. And we draw similar conclusions from that. Yes, but there is still something more here. There is something more here—I’m coming exactly to that in the next stage. So in fact there is something very interesting here. The Torah doesn’t suffice with saying the examples, and now you decide whether the new case before you is similar or not similar. Because then it really leaves the interpreter to be a legislator, and then the problem of judicial legislation arises, which has stirred up so much polemic among us in recent years. And here the Torah essentially prevents at least part of the problem. Because it basically directs us toward which generalizations to adopt. Of course I’m not saying it tells me the outcome, and there can still be disagreements, but they are already within a more limited framework. The text itself not only tells the examples; it also tells how far to go beyond them. How far I am allowed to generalize. Now, what about the axes of generalization? What are the relevant things, the relevant parameters? That is the interpreter’s generalization, and even that not entirely. Even that not entirely. Why? Because in most cases—not all, but most—the Torah doesn’t give one particular, it gives a list of particulars. In the example we saw in the previous lesson too, it gave four particulars. Why do we need four particulars? Because the four particulars come to tell you what the relevant aspects are. If only one particular were written here, you could generalize by an infinite number of features. There are many features; how would you know which feature the Torah intends us to use? But if four particulars are given, then we can already take the features shared by all four items, and that greatly narrows our possibilities for determining the aspects. Therefore, giving several examples too narrows the interpretive freedom we have. And it still doesn’t determine the aspects, but it narrows it significantly. And we will see that this process of taking these four items and extracting the aspects from them is a very complex process. It isn’t as simple as it appears, as I’m describing it here. So in fact our conclusion is this: the solution that the Torah basically offers to Hart’s problem—how to determine this law about vehicles that are forbidden to enter the garden—the Torah says: basically, logic… Now I’m getting closer still to the ordinary logic all human beings use. Let me give you, for example, a definition like this. It is forbidden to bring into the garden noisy vehicles or dangerous run-over vehicles, depending on the purpose the legislator intends—such as cars, tractors, motorcycles, and the like. Here you already have general and particular, right? In fact there is a general rule: it is forbidden to bring vehicles into the garden; such as a list of examples. Now look—but a list of examples still isn’t enough. Because now I can perhaps say, well, maybe that tells me how far to go around those examples; perhaps it means only those examples. So if I now make another formulation—not, that’s not general and particular and general. No, that’s general and particular. I say: it is forbidden to bring vehicles into the garden, such as cars, tractors, motorcycles, and anything similar to them. Etc., exactly. Or anything similar to them. I think that is altogether a formulation all of us would use. That is exactly the formulation of general and particular and general. It is forbidden to bring any vehicles into the garden—cars, tractors, motorcycles, and anything of that kind, anything similar to this. And if you want to be even more precise, then not “anything of that kind,” but all dangerous run-over vehicles such as these. That already really tells us what the relevant aspect is here, how to generalize. Or another example: if we want to define… Sorry a second—if you began and said it is forbidden to bring dangerous run-over vehicles into the garden, such as A, B, C, now the addition you said, “etc., and every dangerous run-over vehicle of that sort,” won’t add anything. Correct, because “such as” does it from the start. So that’s already a matter of Hebrew. So leave out the “such as.” It is forbidden to bring vehicles—tractor, car, and anything of that sort. Without “such as.” It doesn’t matter, so let’s remove the “such as”; the final general term. “Such as” is like “etc.” Yes, so it’s not important to me. So “such as” would be the final general term in this context. It doesn’t matter. By the way, that’s perhaps also an interesting point—you’ve just made a little coin drop for me. The Talmud speaks about cases where the Torah presents a structure of general-general-particular. There are several passages that deal with this: general-general-particular. And the Talmud says: cast the particular between the two general terms and expound it as general and particular and general. There is a dispute about this, but that is what Rabbi Ishmael usually does. What does that actually mean? Maybe it really is something of this sort. “Do not bring vehicles”—general. “Such as”—that is really the etc., the second general term. Motorcycle, tractor, etc.—those are the particulars. So this is really general-general-particular. And what do we do? We insert the particular between the two general terms and expound it as general and particular and general. I don’t know, that idea just occurred to me now, whether yes or no. Okay. Another example, if I want to define a reasonable response time of an institution from a legal standpoint. I want to define how quickly you have to respond. If I say a reasonable response time—what is reasonable? Whatever Aharon Barak decides is reasonable. Meaning, reasonable—what is reasonable? But if, for example, I say something like this: factor X must respond within a reasonable time, similar to the response time of the police to emergency number 100, or Magen David Adom to 101, and the fire department to 102, according to the relevant circumstances. That is already better. Again, I’m not really giving a mathematical definition, so it doesn’t give us a yes-or-no tool. But it definitely improves our ability to decide. And if I didn’t say “according to the relevant circumstances,” I would go back to the three seconds that the police or the fire department need—not that it happens, but they need—to respond. That also wouldn’t be right. I’m giving you an example, because the relevant circumstances of the police and fire and ambulance are circumstances that dictate a short response time. Somewhere else, the relevant circumstances will dictate a bit more, and still that gives you some idea where this reasonable response time can be located. It is much better to define it by examples than to define it in seconds, or define it by pointing to all possibilities, because there are many possibilities and one can’t do that. Therefore examples are an excellent way out where extensional and intensional definition have failed. That is what Shabtai Weisman wrote in his book Derekho shel Talmud. Wait, are those examples from Hartvitsky? Why define it like that? I just thought so. In England they really do respond fast. Okay. So the Talmud solves it by exact measures and quantities. No, exact measures and quantities—that’s more us, less the Talmud. No, in the Talmud, say, a foundling within fifty cubits. Fine, fifty cubits—there it’s a boundary. What is an egg-bulk? What is an olive-bulk? What is a cubit? What is that? A cubit became millimeters only in our own generation. A cubit means put your hand here and see from here to here of an average person. And the Jewish law is that if you don’t know two thousand cubits, you take your own paces. It was precisely because of this that they threw out Rabbi Yirmiyah. Yes, he brought that example there, brought the bird there? Yes, and then they threw him out and said to him: don’t confuse our minds, because leave it alone—we are not speaking here about a theoretical problem that you must solve. Right. So precisely that process is very, very indicative of what I’m talking about now: along the way we turn these definitions into something more and more formal, defined, numerical, whereas originally it cannot be numerical. Examples are the best way to define. Not a primitive approximation. They are the best way; numbers are the primitive approximation. By the way, since they mentioned that, the book by Shabtai Weisman, Derekho shel Talmud, he argues that Rabbi Yirmiyah’s intention was not to provoke or mock, but that he had a legal method that said the fifty cubits is only a derivative. But there is still room for specific discretion—what the environment is and what the air is and so on and so forth—and not necessarily a determination in advance. One just needs to understand why they threw him out. Because they thought he had come to provoke. They brought him back after they understood his intention; they brought him back. He didn’t explain himself properly. Maybe he didn’t explain exactly. As they say, there are cases where he really had… there are those who like not to explain themselves, they just throw something out. Fine. He argued that Rabbi Yirmiyah was a modern legislator, who says according to what the eyes see and according to the conditions and according to the circumstances, from which it follows that a judge, a person in advance, doesn’t know what the judge will say, like I said. No, but precisely this—we are trying to go a bit farther than leaving the judge to do everything. That is exactly what I’m trying to say here. On the one hand, you don’t want to be a mathematician—it’s foolish; one can’t establish a legal system that way. On the other hand, you also don’t want to leave the judge as the legislator. So what do you do? You find ways for the legislator himself to tell you, or at least direct you, in how you do the generalization. He won’t be able to give you an unambiguous definition, but he can direct you. And he can show you what he really meant. I think this is a very, very sophisticated solution; it isn’t primitive at all. It’s a very sophisticated solution, much better than all the mathematical solutions that could exist. Right, it also says there that this goes beyond judicial expression. And the personal judgment of each person’s norm. If you know exactly the measure, you know when the commandment of returning a lost object applies and when not, and when you may take it. It isn’t only a matter of judicial interpretation—wait, for every small issue everyone should run to the judges? No, he will also tell the person himself not to do it—the person himself, so that each and every person can decide. If you estimate that it more or less came from there, then return it, and if not then not. And if you estimate… if a cubit is the end, then they’ll go on opening doorways and burning the words of God. It gets to the point: judgment increases within all that. The judgment—fifty cubits—they’ll sue you in religious court, and the religious court will check whether your judgment was reasonable or not. That’s not the point—the point is that you should know. And therefore they fixed fifty cubits. I’m here, in a field, they found one with one foot here and one foot there. In any case, the distinction that comes up here is that now perhaps not I—there is a very famous example brought by Menachem Elon in his book, from a responsum that makes a general-and-particular exposition, a responsum of the Mahari Mi, that makes a general-and-particular exposition on a responsum of Maharam of Rothenburg. On the text of the midrash—on a responsum of Maharam of Rothenburg. Meaning not the Hebrew Bible (Tanakh), not the Torah. Not a biblical text. Meaning that this is a general textual rule. And well, I knew that already quite a long time ago. At least among people who studied Torah. No, I’m not even sure about that. For example, in communal enactments you already begin to find expositions of general and particular. That’s just how people speak; obviously that’s how people speak. And I really did a kind of search when we were working on this topic, and I found a lot. It’s not one example; there are many examples. Many examples in which they make expositions of general and particular on responsa, on communal regulations, on all sorts of things like that. I’ll give you a few examples here; I collected several examples here. So that example of the Mahari Mi says as follows: “Henceforth, my beloved ones, set your hearts on the highway that ascends to Bethel, and do not stray from the path taught by the great luminary, Maharam of Rothenburg, and that which his right and left taught and ruled, for his ways are ways of pleasantness and all his paths are peace. Behold how Maharam of Rothenburg wrote”—and now a quotation—“that one must answer all householders who pay tax. And afterward he ruled by way of a particular: and they shall go after the majority regarding the choosing of the heads of the community. And afterward he ruled by way of a general statement: in the end, all communal needs shall be done according to them, as they say. And thus a general term adds to the particular,” says the Mahari Mi, “meaning even a matter not really similar to the previous particular. And this is a rule in the Torah: particular and general, the general adds to the particular, as explained.” And you take a text of Maharam of Rothenburg and say: why is a majority needed? Where does the majority determine? In choosing the leaders. An example—that’s particular. And then they say “and all matters of that sort”—that’s general. The general adds to the particular. He didn’t take only the “all matters of that sort” and say, okay, “all matters of that sort” means everything. No. He made here an exposition of particular and general. Because apparently if you just take “all matters of that sort,” we would think the majority determines everything. But that isn’t right. For that reason an example is written here. The example is written here so that there should be a particular and general, and what does the general tell us? In essence: anything similar to the particular in one aspect. But it has to be similar to the particular in some sense. If you find something not at all similar to the particular in any relevant aspect, you won’t be able to derive from Maharam of Rothenburg that there too the majority determines. That is no longer correct. That’s the meaning of the exposition of particular and general. Meaning, the example has significance; one could not just write the general rule directly. If you had written the general rule directly, you would say the majority determines everything. No—they say a particular and everything that is like this particular. And note: this is not a biblical text. What does that mean? Apparently that this is just the way people speak. Meaning, it isn’t because the rule descended from Sinai, but because we really understand that this is how people speak. When he gives you an example and then says “everything of that sort,” he doesn’t mean to say everything whatsoever; he means all things that are at least similar, on some level, to the example he gave. Okay? That is basically the exposition of general and particular. Of course one can’t take it too far, one must be very careful not to take it too far, but still the idea here is a universal idea: that’s how people speak. So what does the general term do? What does the general term do when I speak like that? It tells you that it isn’t only in choosing the heads but also in choosing the treasurer. Does he explain why the particular? He tells you: extend beyond the particular. So now understand—he doesn’t explain; you have to understand what the explanation is, because you find the relevant aspects. He only tells you that you are allowed to rely on the relevant aspects and make extensions. Okay? Another example: Rabbi Chaim Palaggi, in Responsa Chaim BeYad. Rabbi Chaim Palaggi brings the following: “And it is known that permission was given to expound the language of a document by any of the thirteen rules by which the Torah is expounded.” And he already establishes this as a general principle: the language of a legal document is expounded by the thirteen rules. We know that one expounds ordinary language. That is written in… it is written in the Talmud. But “one expounds ordinary language” means that one is precise in ordinary language just as in the Torah if I have no other interpretation. So if I don’t have a reasonable interpretation and I find myself in an interpretive maze or interpretive fog, then there is no choice but to follow the language. The language determines, and to be precise in the language—that is called expounding ordinary language. What? Is there also a law given to Moses at Sinai to expound ordinary language? I have no idea. But that’s what the Talmud says. But here he takes the word “expound” one step further. To expound ordinary language means to use the thirteen hermeneutical rules, not merely to expound in the sense of being precise in them, but to use the hermeneutical rules. And then he continues and actually gives an exposition: “As our holy master wrote in Beit Yosef, Choshen Mishpat, section 61, new law 5, in the name of the responsum of Ritva, all of these made expositions on the language of documents. And also Rabbi Chesed LeAvraham”—I don’t know who that is—“part 1, expounded the language of the document by the rule of general and particular and general. And similarly some of the halakhic decisors made use of expounding the language of a document by whatever rule was relevant to it. If so, in our case it would seem that there is room to expound the language of the document before us by the rule of particular and general,” and then he makes some exposition. But here he isn’t merely making an exposition like the Mahari Mi; he is establishing that there is such a general principle. We know that the halakhic decisors expound the language of legal documents by the rules by which the Torah is expounded. And that is really amazing. In a certain sense he is basically claiming that all the rules by which the Torah is expounded contain some kind of… logic. You mean the textual rules. They contain some kind of logic. What, not kal va-homer too? Kal va-homer too, but that one isn’t textual. I’m talking about the textual rules, and there it is certainly true. I’m speaking about the opposite—I’m saying that even in the textual rules, for example to make a gezerah shavah: if a certain word is written in a document and I don’t know its meaning, and there are several options, then I’ll compare it to another place where the same word appears. That sounds very reasonable. It isn’t certain that it’s correct, but it is certainly a reasonable default if I have no other interpretation. Is that revealing the meaning, is it binyan av, or is it gezerah shavah? It is also revealing the meaning and also binyan av. No, in terms of gezerah shavah. “Revealing the meaning” is a gezerah shavah that reveals the meaning of a word and not a Jewish law. It isn’t revealing the meaning. The underlying assumption is that a document is something one formulates precisely and carefully, and that is already clear… that is already written in the Talmud. But here the point is that to be precise means to expound by the thirteen hermeneutical rules, not merely to be precise in the simple sense of trying to understand what is written there. There are many more places. In short, there are various additional examples here. Does this also apply to the thirty-two rules? What? It doesn’t matter. I don’t think he means specifically these thirteen. Fine. So now basically I want to go one step further, to see how we compare… both are texts, both are expounded by the same rule, but as I understand the logic of these rules in a legal document, I understand it also in the Torah. Yes, but still it seems to me that, just as in one place I even found some exactness regarding which rule to use, in most cases they don’t mean that. He said: look, if he gave an example and then generalized it, then we too should generalize. But they aren’t going to start counting aspects and say: there is general and particular and general, so that’s four aspects, remove one, that’s three aspects—and so on. I don’t think anyone would do a trick like that regarding documents. But in the Torah they do, and here I come to the point I made earlier: true, this rule may contain a kind of linguistic logic. Because that is how a person speaks, so it is reasonable to interpret him in that way. But here there is more than that. It is also a rule that is a law given to Moses at Sinai. Because the Torah also told me, and cast it into sharp, defined patterns. At least after the conceptualization, we think of these as sharp and defined patterns. And here suddenly the Torah tells me: work with mathematics. Three aspects, two aspects, one aspect. That they already do not do with documents. So it is clear that the Torah went one step farther than merely giving me another device for understanding language. There is some device here unique to the Torah text, to the biblical text. Okay? And that specificity means: to expound general and particular and general in a general sense is logical everywhere, but the specific structure—one aspect, two aspects, three aspects—that is already characteristic of… Is that the Torah or Rabbi Ishmael, or is it the conceptualization… Everything we’ve discussed until now, I think, is a conceptualization that arose, but on the basis of what had previously been done intuitively. That is the Oral Torah. Now with the development, let’s take a more concrete example to see how this whole business works with the relevant aspects. Let’s say they give me someone who is like Moses our Teacher as an example. Fine? They tell me: anyone similar to Moses our Teacher in some way. And now I need to generalize this matter. Just an example. So now the question is: what does “similar to Moses our Teacher” mean? What are the aspects we are actually looking for? Good. First of all, we are looking for what the relevant aspects of Moses our Teacher are. How will we know? There are many features. What will determine the relevant features? The context. That is, it depends for what matter we are making this generalization. If this generalization is regarding the obligation to honor him, then there is no point in saying that it means anyone named Moshe. It isn’t plausible that anyone named Moshe is a relevant aspect regarding whom one must honor. By contrast, perhaps every Levite, yes? Perhaps everyone who is a leader, yes? Perhaps everyone who is a son of Amram, I don’t know, because that’s an important family? Someone—I don’t know what. What else did I say? Prophet, leader, Levite, yes, fine. Perhaps those are relevant aspects, right? So let’s suppose we think that the relevant aspects, in light of the text, are that he is a leader, that he is a prophet, that he is a Levite, and that he is a son of Amram. Fine? Those are the relevant aspects of Moses our Teacher. And now I ask myself: okay, now how do I make the extension? Here, of course, the question is what the radius of generalization is. If the command to extend is written in the form of general and particular, then I need only those who are similar to Moses our Teacher in all these senses. In other words, only sons of Amram who were also prophets, also leaders. Aaron. What about Miriam? Aaron. What about Miriam? Fine, that’s where one can get confused. Aaron—only one similar to Moses our Teacher, if you add male then you exclude Miriam. If it’s only one similar to Moses our Teacher in all the relevant aspects, if it is general and particular. If it is general and particular and general, then it already depends whether according to “the last is precise” or “the first is precise,” and that will determine in how many aspects we generalize. But it doesn’t matter; each method knows, in each case, how far to generalize. Now how do I actually do this? Here I need to distinguish between two situations. I can ask myself a specific halakhic question, and this is the difference between someone who writes the Shulchan Arukh and someone who writes a responsum. A halakhic responsum. I think this is a wonderful illustration of the functional difference between these two genres. Because if I want to find out—say they ask me: tell me, do I also need to honor Yankele like Moses our Teacher? What exactly am I supposed to do? And let’s say the structure is general and particular and general. So let’s say I expound general and particular and general according to “the last is precise,” meaning two aspects. Fine? So what is the answer? I will check whether in Yankele there are two out of these four aspects, right? If he has at least two out of these four aspects, then he too must be honored. Okay? If it is a structure of particular and general, then one aspect is enough. If he resembles Moses our Teacher in something, one must honor him. Therefore, when I want to write a halakhic responsum, to give a ruling regarding a particular case, this is the best way to do it. List the aspects, the case-structure tells you in how many aspects one must extend, and then check, regarding the case before you, how many aspects it has. But now ask another question. I now want to write the Shulchan Arukh. Not to rule regarding a specific case before me. So what do I need to do? I need to determine who is the set regarding which we are obligated in honor, right? Because I need to determine the general principle, not decide regarding someone standing before me whether he is included in this set or not. And that is exactly parallel to extensional and intensional definition. I don’t need to decide regarding each individual whether he is in the set or not. I want to understand what characterizes the set, to give it an intensional definition. What are the properties that define the members of this set. That is what happens when one comes to write the Shulchan Arukh, right? How does one do that? To do that, we have two ways. Let’s call the properties by these letters. Basically, if I want to solve for the set that is similar in two aspects, I’ll do it like this: all the pairs, right? All the intersections of pairs. B and C, B and D, A and D, anything else? C and D. Okay. So the number of these combinations is a simple combinatorial calculation: four choose two. Which is four factorial divided by n minus m factorial times m factorial. That isn’t always correct. If I want to choose m aspects out of n aspects, then it is always n factorial divided by n minus m factorial times m factorial. And that’s how I know how many groups I need to consider, how many such unions, and that’s the Shulchan Arukh. Seems a bit complicated, this Shulchan Arukh, right? Go now tell everyone: whoever is either a leader and also a prophet, or a leader and a Levite, or a prophet and a Levite, or a prophet and a son of Amram—it’s complicated, right? So let’s do it another way. The Shulchan Arukh could not write it this way. If a specific person comes before me, I can do it this way: I’ll just list the properties and see which properties he has. If he has two properties or more, then he’s in, right? But if I want to write the Shulchan Arukh, that’s complicated. Therefore I look for another definition. Intensional definition and extensional definition. That was a definition through properties, an intensional definition, right? I’ll do an extensional definition, and what I’ll do is the following. I’ll make a Venn diagram for you. Leaders, prophets, and Levites. Fine? Now sons of Amram are this circle, right? So what does this diagram actually mean? The diagram means that the Levites, the prophets, and the leaders—none is contained wholly in the other. These are sets with partial intersections. Every two of these three have a partial intersection. Sons of Amram are of course all Levites; they do not go outside the Levite circle, but they can be prophets and can be leaders, and can also be neither. Okay, so sons of Amram are really this circle. Fine? Now I ask myself, what is two aspects? We said that I’m looking at where Moses our Teacher sits, right? He is also a son of Amram, he is also a Levite, he is also a prophet and also a leader, so he sits here. Now I ask myself who is the set around him to which I extend. If I say that I need four aspects, which is general and particular, then this is it, right? How do I do this? I simply look at how many circles it belongs to. Or if you think of these circles as sheets placed one on top of another, make a hole here and see through how many sheets it passes. If it passes through four sheets, then there are four aspects. If I now say no, the structure is specifically general and particular and general, then it’s three aspects. Fine? So three aspects, let’s see. Three aspects are of course here. What do we have here? This is three aspects, this is three aspects, and this here is also three aspects, right? So in fact this whole fan is what we have. What is missing here is exactly three aspects. So what is two aspects? Two aspects would probably expand me to here and here. On one hand it included prophet-leader… Oh, yes. And on the other hand it included all of them. Now notice what happens here. Let’s take two aspects. What is two aspects? Two aspects are really also this, and also this, and also this, and also this, right? Two aspects—three and four are always good too; that’s at least two aspects, right? Everyone who resembles in at least two aspects. Now look. The long expression I wrote before—look how much simpler it now appears. If I now write the result of this formally, I see that it’s simply everyone who is a prophet and a leader. I don’t care whether he is a son of Amram or not a son of Amram—what difference does that make? Everyone who is a prophet and a leader is included here, right? So I’ve already saved many sets. Everyone who is a prophet and a Levite, everyone who is a leader and a Levite—in fact I don’t need the whole set of Levites… Wait, no, yes I do, there is this, yes. And here there are the sets of leader and Levite, and that already also includes both of them, so I don’t need to include them—and so on. Then in fact we have—let’s see it this way. We have every intersection. Son of Amram is D, so we have A, B, and C. A intersect B, A intersect C, and B intersect C, right? That already covers me one, two, three. What is still missing is sons of Amram, right? Because all sons of Amram are included, although they are inside an additional property. That’s it. Instead of the six unions of intersections, in fact I have here only four sets. Three intersections plus one set. It’s simpler. Now here the diagram is relatively complicated. The more complicated the diagram, the less I’ll save with this technique. But if there is, for example, a diagram like this… Why? You’ll save more. What? The fewer overlaps there are… No, no, the saving comes from overlaps. Exactly. Or from disjointness, on the contrary. Meaning, two things can lead to saving. Look, let’s take this. This is the maximal saving; this is the simplest diagram, it’s concentric, as though all the circles share the same center. A concentric diagram yields the greatest saving. Let’s try to see how one writes this. A, B, and C. If I wanted to do the intersections, I would say all that I want—all that is similar in two aspects, right? The two aspects are AB and BC and AC—three intersections. Here what do I say? B, right? What is similar in two aspects is simply B. Meaning, in a concentric diagram we immediately see the saving. Someone who wants to write the Shulchan Arukh should use this method, not the detailed method. And this, basically, means that I’m looking at the elements. Here extension comes in, not only intension. That is an important point. Therefore I call this a definition through extension. How did I draw this Venn diagram? I drew this Venn diagram through familiarity with the elements appearing here. If I know that all the elements with property C also have property B, then I know it is concentric. And if I know that all those with B also have A, then that too is concentric. Meaning, I have to make this drawing through looking at the extension, at the elements. And therefore this way is the way of extension, and in this case it is simpler. What happens here? In this case we won’t save anything, right? This is A, B, and C. I want something similar in two aspects—well, no, it depends what “not save anything” means. If I want similarity in one aspect, I won’t save anything. It’s just this or this or this, exactly as I wrote in the previous method, right? But if I want similarity in two aspects, then here there will be three intersections, right? A and B, B and C, A and C. But what is the result? What is similar in two aspects? Nothing. Nothing is similar in two aspects. There is nothing that is both B and A or both B and C, right? So this also saves, actually; it depends on how many aspects we are talking about. Okay. So, in fact, an important point I want you to notice here, because it’s very confusing—we got very confused about it at first. This description, although C is included within B—everyone who is here, say, let’s go back to fruit from fruit and offspring of the earth, okay? If I say animals, offspring of the earth, okay? Then all animals are offspring of the earth, for the sake of discussion, doesn’t matter right now. So in fact it looks like similarity in one thing—just animals—because everyone who is an animal is also offspring of the earth. But no, in this technique it counts as two aspects. And one has to remember that. Even though this is one set contained within the other, it is two aspects because we are going by intension, not extension. That is, we are going by the contents. And the contents of being offspring of the earth and being an animal are different contents. Therefore all these elements have two properties in which they are similar to our particular, not one. Even though extensionally, in terms of scope, it won’t matter—it ends up defining one set, the inner set. Okay? In more complicated places we’ll see this. In the meantime, don’t get confused by it. Therefore what determines the definition of the circles and the aspects is the intension. We use the extension here to simplify the result, but basically we are going by the intension. Fine, let’s stop here. I’ll think at home about some more detailed example. Next time, God willing, we’ll see this in the passage in Hullin. We’ll take a passage in Hullin and see how this comes to expression.