The Voice of Prophecy, Lesson 35

Table of Contents

• Sight and hearing as metaphors for grasping the external and the internal
• The holy tongue: speech and letters as the thing itself
• Reading a book: sight functioning as hearing
• Gezerah shavah: a second logic, receiving from a rabbi, and hints from the Torah
• Expound and receive reward: the value of the tool beyond the halakhic result
• Mah matzinu, binyan av, and the distinction between analogy and induction
• Disputes over the definition of binyan av and mah matzinu, and the scope of the rules
• The principle of unifying causality and simplicity: the philosophical lesson of binyan av

Summary

General overview

The text argues that sight has a kind of sharpness, clarity, and unambiguity that grasps the outside, while hearing is somewhat indirect but also capable of penetrating inward; on that basis it explains why the Nazir chooses the metaphors of sight, hearing, and a barrier in order to distinguish between grasping form and grasping matter. The text argues that according to the Nazir, in the holy tongue, speech and letters are not an arbitrary representation but the thing itself, and therefore hearing the letters and grasping the name are understood as an immediate grasp of essence, whereas sight is understood as an intellectual image dependent on the senses. It then presents gezerah shavah as a tool that represents a kind of intuitive, analogical “second logic” meant for uniquely gifted individuals, and analyzes the tension between that and the rule that “a person may not derive a gezerah shavah on his own,” along with the way the Torah leaves hints and gaps in order to train this capacity. Finally, it explains mah matzinu, binyan av, and reasoning by similarity as a distinction between analogy and induction, and concludes that binyan av assumes a philosophical principle of unifying causality and genuine simplicity that makes generalization possible, similar to “Occam’s razor.”

Sight and hearing as metaphors for grasping the external and the internal

The text presents sight as stronger in the sense that it is sharp, clear, and unambiguous, and therefore experienced as grasping the thing itself rather than a representation of it. It presents hearing as less confined and as able to operate “behind a wall,” and therefore as more connected to the inside and interior of the thing than sight, which does not pass through a barrier. The text clarifies that the differences in physical capacity between sight and hearing are ultimately quantitative matters, but the metaphors are not a physical description; they are a language chosen to indicate an essential relation between grasping form and grasping matter. The text asks why the Nazir uses precisely a barrier and visual imagery in order to describe the grasp of representations, and answers that the choice is connected to the fact that sight is understood as grasping externality, whereas hearing is understood as a grasp that reaches the inside.

The holy tongue: speech and letters as the thing itself

The text argues that according to the Nazir, in the holy tongue the linguistic relation points to an essential relation, to the point that speech is the thing and the letters in a thing’s name are components of the thing itself rather than external representations. The text states that the intellectual image is an indirect grasp through the intellect and through the eyes, whereas hearing is a grasp of the thing itself; therefore grasping the letters and the word in the holy tongue is a grasp of the matter and the essence. The text illustrates this by saying that seeing a table is not objective, because changing the instruments of perception changes color, shape, and description, and so all of these are representations; by contrast, the letters that spell “table” are presented as the very essence of the table itself. The text gives an example from “I have set the Lord always before me,” and argues that the Tetragrammaton is divinity itself, while all philosophical ideas and images are indirect representations; it even connects this to the statement that “the entire world of Atzilut is the Tetragrammaton.”

Reading a book: sight functioning as hearing

The text states that when you read a book, you use your eyes, but the action is not “sight” in the metaphorical sense but “hearing,” because the reader does not see the thing itself but representations that he translates into concepts and an imagined picture. The text concludes that the concepts of sight and hearing here are not sensory concepts but metaphors for the question whether one grasps the thing itself or its representations. The text argues that it is possible to establish contact with the thing even without being able to describe it, because every description belongs to form and not to the essence that is being grasped.

Gezerah shavah: a second logic, receiving from a rabbi, and hints from the Torah

The text presents the thirteen hermeneutic principles in the Nazir’s thought as philosophical principles that teach us about the world, and emphasizes that gezerah shavah teaches both about the meaning of the holy tongue and the letters, and about specific contents in each particular gezerah shavah. The text distinguishes between a gezerah shavah that is mufneh and one that is not mufneh, and states that a gezerah shavah that is not mufneh appears more like verse interpretation and therefore refutations are relevant to it, whereas in the mufneh case an immediate grasp of similarity is created that cannot be refuted. The text raises a difficulty from the rule that “a person may not derive a gezerah shavah on his own” against the claim that this is a tool for uniquely gifted individuals, and brings from the Jerusalem Talmud, Pesachim, the reasoning that if one were to derive it on his own he could reach absurdities such as “making a creeping thing impart impurity in a tent and a corpse impart impurity like a lentil” through the exposition of “garment, garment.” The text offers an answer that sometimes “the locations were transmitted but not the words, and sometimes the words but not the locations, and it was left to the sages to determine which they are,” and interprets this as a deliberate design in which the Torah gives hints in order to train and sharpen the cognitive capacity involved in gezerah shavah, and not merely to produce a legal ruling.

Expound and receive reward: the value of the tool beyond the halakhic result

The text argues that if gezerah shavah were a mechanical axiomatic game, it would have been better simply to state the laws explicitly, and therefore the very fact that the structure is allusive and requires exertion points to value in developing the faculty itself. The text interprets “Expound and receive reward” as “Expound and improve yourself,” as growth in cognitive capacity, and explains that in this way it becomes understandable that one can learn from a gezerah shavah and then go back and learn from somewhere else, because the goal is not only the legal outcome but also the process. The text brings Ralbag, who argues that the laws are “pre-sold,” so to speak, and that one can derive through the thirteen hermeneutic principles any law one wants, and therefore the principles are not a creative source of laws; it presents this as the antithesis of the Nazir’s position, which attributes essential significance to the tool itself. The text adds that according to Maimonides in the Laws of Rebels, a religious court can overturn laws derived through the thirteen hermeneutic principles, and raises the possibility that in the approach of Kinat Sofrim, “a person” means a private individual, whereas the Great Sanhedrin does derive on its own.

Mah matzinu, binyan av, and the distinction between analogy and induction

The text defines “mah matzinu” as an inference by similarity between two particulars in the form “just as we find in one, so too in the second,” and presents it as an analogy that is not explicitly counted among the thirteen hermeneutic principles and is sometimes included together with gezerah shavah. The text defines “binyan av” as learning a rule from particulars through the formulation “this is not like that… the common side… so too anything similar,” and identifies it as search inference, that is, induction. The text explains that in binyan av the refutations and the “let the two cases prove it” are meant to isolate the relevant parameter that justifies the generalization, and therefore “the two cases prove it” proves regarding case A what the relevant causal factor is, rather than proving directly regarding case C. The text reinterprets why binyan av is “one from two,” and argues that the term “binyan av” reflects the construction of a parent-rule from the children, whereas “one from one” is an analogy called mah matzinu.

Disputes over the definition of binyan av and mah matzinu, and the scope of the rules

The text notes that in Halikhot Olam there are those who say that mah matzinu is included in binyan av from one verse, and that binyan av is also called both “one from one” and “one from two”; it also cites another view that does not call “one from one” binyan av, but rather mah matzinu. The text presents the Nazir’s approach as fitting comfortably with the view of Rabbi Shmuel, according to which even “binyan av from one verse” can in practice really be from two elements found within one verse, whereas mah matzinu remains a tool of analogy from one particular to another. The text also adds examples in which “binyan av” refers to learning from a single example when what is learned is a general rule, such as “a sheep in its first year” and “and he shall offer that which is for the first sin-offering.”

The principle of unifying causality and simplicity: the philosophical lesson of binyan av

The text states that in the common-side argument one cannot go on refuting by claiming that the two teaching cases each have two different reasons for the same law, because there is an underlying assumption that each law has one reason and not two separate reasons. The text illustrates this with “and you shall not stray after your hearts and after your eyes,” as an explanation that two different cases are specifications of one principle—following impulse rather than rationality—and therefore they are one prohibition and not two prohibitions. The text compares this principle to “Occam’s razor” and concludes that the Torah teaches that this is not just an aesthetic rule of the game but a truth about the structure of the world, and therefore one simple theory that resolves many difficulties is truer than a multiplicity of separate answers. The text concludes that the very ability to generalize is itself philosophical content encoded in the principle of binyan av, and therefore induction appears among the thirteen hermeneutic principles as a principle that teaches a correct perception of the world and not merely a formal tool for deriving laws.

And continuing, we said that therefore, to a certain extent, sight is something stronger than hearing. He goes on there at length, bringing all kinds of opinions that sight is preferable to hearing, sight is greater than hearing. And we discussed that there’s an aspect like this and an aspect like that. We said that sight is more unambiguous, sharper, clearer, but on the other hand it is less deep. In the sense that it is sharper and clearer, somehow that implies that it grasps the thing itself and not a representation of it. You see—you see, and that’s it. It’s not some kind of representation. In hearing, it is perceived as something more indirect. It’s not the thing itself; it’s something that comes out of it, that reaches me, some kind of relation of it to me. But on the other hand, as we said, a sound can be heard even from behind a wall, and sight cannot see through something. Meaning, what is inside the thing—you can only hear it, you can’t see it. The inside, the inner dimension of the thing, can be heard and not seen. Plus the example we gave, that hearing is harder to limit, something like that. And that is quantitative, not essential. Since I can hear through a wall, if I put up two hundred barriers then I also won’t hear. If I put up insulated concrete blocks, I won’t hear. I mean, that’s quantitative, so fine, okay. But still, it is not automatically determined that if it is behind something then it cannot be heard, as opposed to sight, where the moment it is behind something—regardless of the thickness of the thing or whatever—you can’t see it. And that makes the thing thinner. I don’t understand how that makes it thinner. What do I know? I’ll take a window—then I can see, and that blocks the hearing. A transparent window, I don’t know. A transparent window represents exactly the fact that it is a special material because it is transparent. There is one kind of thing that really is exceptional in this sense, that lets me see what is behind it, because ordinarily a partition does not let you see what is behind it. A partition against sound is not such a simple matter. Something thin and so on. So is it a matter of simplicity? Is it simpler? I don’t understand how that teaches anything. These things are only metaphors. We are not claiming, after all, that sight and hearing are two physical things and both of them are representations, as we said—that is obvious. But why does the Nazir choose the metaphor of a partition, the metaphor of sight, in order to indicate the grasp of representations, of form and not of matter? We said that the chosen metaphor—one of the reasons it is chosen—is because sight grasps the external thing, whereas hearing also grasps the internal thing. Now with physical sight and hearing, you’re right, it’s a matter of quantitative difference. But why are these the metaphors? Now when you look at the thing, and also when you hear the thing, those are representations. After all, if you hear the word that denotes the thing—which in the simple view is perceived as the most indirect representation on earth, because it is not connected to the thing at all, it’s just hearing what it’s called—it turns out that in the holy tongue, for the Nazir, it’s the opposite: it is the thing itself. Speech is the thing. This linguistic relation actually points to an essential relation. That speech is perceived as the thing itself; the letters from which the name of the thing is composed represent components of the thing itself. It’s not the same thing. A lot depends on it; there are formulations that take it to be literally the thing itself. The letters are not a representation; the letters are it. Here what you’re saying—that it represents the thing itself—is not necessary. No, but thought in speech is the thing itself. You hear the thing in the verbal name. That is free of conceptual depiction—that’s what he says. Conceptual depiction is indirect grasp. Hearing is to grasp the thing itself, not indirectly. How can it be that this… It’s not some chemical thing that represents… What matters more is that I grasp… like sight. Sight is also conceptual depiction. No, on the contrary—someone here defined it a while ago: conceptual comes from the language of eyes. In the Nazir, in several places, conceptual depiction appears with a double meaning. Conceptual depiction means visual depiction; that’s why it is also called a depiction. It’s not analysis in the sense of thinking with the intellect, although it is also that, but the source is the seeing of the eyes. Because to grasp a thing through the intellect is to grasp its representations. And to hear is to grasp it itself. Matter and form, which we already distinguished several times. To grasp the matter of the thing, the thing as it is, not through properties, not through external representations—that is to understand the letters that represent it, the word that represents it in the holy tongue. I don’t understand how that works. To grasp the thing itself is to grasp the letters that represent it? No—you say “the letters that represent it” because that’s how we speak, but the letters do not represent it; that is the thing itself. What you see is a representation. You see the table, you see what a table looks like; you do not see what the table itself is. After all, a person who had other cognitive tools—we discussed this at length once—a person who had other cognitive tools would see the table completely differently from you, and that is obvious. There is no objective appearance of the table. If I were equipped with eyes that do not transmit green light but instead turn everything like that into the sensation of red, then I would see the table as red. If it were represented by some spatial distortion along the way—we call it distortion, but it’s not distortion, it’s simply another form of perception—that turned this rectangle into a circle, then you would see the table as round. Or someone might come with some faculty or sense that isn’t one of our five senses, something entirely unfamiliar to us, and he would grasp this table as—I don’t know—something completely different from the way we grasp it. So the question is: what belongs to the table itself? What is not a representation of it? It turns out that its shape, its color, its height—everything is representation. What is the thing that belongs to the table itself regardless of who perceives it? What is the thing in itself? In Kant’s terms, right? So the Nazir says: it is the form of the letters that compose it. In form—again, a bit linguistically—the form, or also the sound of the letters, is how to grasp the thing as it is. That is also how it was created by an utterance, after all; all things were created by divine utterance. Meaning that their true, essential, inner content is the utterance, the letters. And everything else is representation. Exactly the opposite of how people usually understand it. Usually people think that a word represents arbitrarily. I choose the word “table”; I could have chosen the word “yakumfurkan.” It doesn’t matter—as long as I explain to everyone that this object is called “yakumfurkan,” then it makes no difference whether it’s “table” or “yakumfurkan,” right? It’s arbitrary. But seeing the table—that seems objective, like the thing itself. Here he says the opposite. Seeing—what is seeing? True, all of us are built with these visual means, but in principle there is nothing essential in that. If there were someone with different means of sight, he would perceive the table differently. Or without sight, with some—I don’t know exactly what—or with means of hearing, and he hears tables instead of seeing them. He isn’t sensitive at all to all these visual things; he wouldn’t see anything here. He would only hear tables. These electromagnetic waves would be translated for him into sound, not vision. So he would hear tables, not see tables, right? And there is nothing essential in the way we see a table; it is a function of our sensory apparatus, that’s all. What represents the table itself? The letters of the word “table,” t-a-b-l-e—that is the table itself, essentially. This sounds a bit detached. What do these words mean? After all, for me these words mean nothing. For that you need to learn. There are some people for whom it does already mean something. They already know a few things—for example, a verbal analogy teaches us that things that are written similarly have something in common. Do you understand? Meaning, you actually can learn things—shared roots, you can learn things about things, from the language. They always say, “I have set the Lord always before me,” so there are various books that say you should imagine the word yud-heh-vav-heh. And that always bothered me—why should I think that the Holy One is beside me and with me? No: yud-heh-vav-heh is the word; yud-heh-vav-heh is divinity itself. It’s not a representation; it is divinity itself. That is the root of the whole matter. And about this there is already a great deal written in many places. It always annoyed me—fine, so now I’ll think of this, and that’s supposed to say something to me? Letters? And everything it says to you—all the ideas, all the lofty and philosophical notions—those are all indirect representations. You see it this way; someone else can see it differently. The yud-heh-vav-heh is the thing itself. The whole world of emanation is yud-heh-vav-heh. And that itself—not its representation. That is what has to be grasped here. It’s a bit difficult; I also don’t live this way. But also hearing the letters—it seems that hearing also testifies to hearing… even hearing the letters is already sounding, hearing… When you see the letters, you also use your eyes, but you use your eyes—and we discussed this back then, we discussed hearing and sight when you read a book, for example. Then that is not sight, that is hearing. Why is that hearing? Because sight is seeing the thing. A book, when you read it, you don’t see—for example, if it says “the table is green,” you don’t see a table; you see representations and translate them, and from that you form the concept of a table, and you say that it is green; you create for yourself some imagined picture. Meaning, the information that reaches you is actually some kind of representation of the thing. The fact that you see it through your eyes is something else—that doesn’t matter. Therefore the concepts of hearing and sight here are not concepts of sensation; sensation is only a metaphor used to describe this. What are we doing? Everything we do, we do with the senses. But the question is what are we doing with the senses? Are we grasping the thing itself, or representations of it? That’s the form we have with our senses. No, but one has to understand: the fact that you have no way to describe what you absorb does not matter, because every description belongs to form. So it doesn’t matter. Meaning, in principle you make contact with the thing even if you do not understand it in the terms of your usual concepts of understanding.

So if that is the case, then we also—it seems to me we mentioned this last time—we gave an introduction about the status of the thirteen hermeneutical principles according to the Nazir. We said that the thirteen principles are philosophical principles, conceptual principles, that come to teach me about the world. So what do I learn from the principle of verbal analogy, from the principle of verbal analogy? First, we said, the significance of the holy tongue or the significance of the letters. And second, each verbal analogy on its own, of course, specifically teaches me something about the topic it deals with. One can learn from the principle of verbal analogy, and from each specific verbal analogy in the Torah, also specific content about the principle itself, about the thing itself that the verbal analogy addresses. I would also agree that here there is the element—what?—that verbal analogy itself is a general mode of learning and not necessarily… yes, but not from the verbal analogy, not from the principle of verbal analogy, but from the comparison itself. It could even be false. Although we spoke about the fact that this is not necessarily so. You can understand it as a scriptural decree and things like that. It does not necessarily follow, but it is clear that if you understand that verbal analogy itself has content, then it is much harder also to say that this particular verbal analogy does not teach me something essential. Someone who says that this tool called verbal analogy has no content at all, that it is merely an axiomatic principle—then a particular verbal analogy, the repetition of “to her” between a slave and a woman, does not necessarily teach me about a similarity between a slave and a woman, but merely some way the Torah chose to encode various laws that apply to slaves—so go look at women; what applies there applies here too. And not because there is really some essential similarity between the two things. That remains open, but at least it is open. On the other hand, I think it is fairly clear that the connection is essential. Here it also seems to me that there is room to distinguish between a verbal analogy with an available term and one without an available term. If the verbal analogy is not based on an available term—we discussed that, right?—that is, there is no extra word from which we derive the verbal analogy, then there are disputes: one available word, two available words, no available words. We mentioned this a bit last time. In a verbal analogy that is not based on an available term, in practice it looks like some kind of interpretation of the verses. If you have an available word—let’s start the other way around—when you have an available word, an extra word, then how does that teach you the law? After all, there is no connection to the law; it is an extra word. It is not that the content of the word teaches you something. It is an extra word; you have nothing to do with it, so you learn something else from it. When you find an extra word, say, if it is available on both sides, you find another available instance of the same word elsewhere, that switches on some sort of lightbulb for you and you say, okay, there is a connection here. But that has no connection to the content of the word itself. This is not interpretation of the verse, right? Meaning, I smell here—let’s call it that—some similarity between two passages, hinted to me by extra words. A verbal analogy without an available term is, simply speaking, interpretation of the verse. You learn that there is some law here, and you see that there too there is the same law because the same words are used, so apparently there is the same interpretation. We mentioned this in connection with Hillel’s verbal analogy, “in its appointed time,” “in its appointed time,” that it overrides the Sabbath. There it seems to be a verbal analogy without an available term, because “in its appointed time” itself is the meaning of the word: in its appointed time means you should always do it at its proper time, even if that falls on the Sabbath. Therefore it overrides the Sabbath. Not that the word is extra and therefore I do something with it that I merely smell out, but rather that is simply the meaning of the word. So there may be differences here regarding what we just said. If the verbal analogy is not based on an available term, then this is really interpretation of a verse. So here we are still working within the ordinary rules; this sensory element is not what is functioning here, in places where we are reading texts. Therefore in a verbal analogy that is not based on an available term there are refutations, right? In tractate Niddah 22, as we saw, the Talmud says that if the verbal analogy is not based on an available term—true, on one side this is a dispute, but let’s say not available versus available on both sides; let us deal with the extreme cases—then in the case of not available at all, according to the opinion that still does derive the verbal analogy, one may nevertheless also refute it. But if you have a refutation, then it collapses, because it is logical. Because it is logical, exactly. If you are now trying to draw conclusions by way of logic, you may be mistaken, so if you have a refutation then it falls. But a verbal analogy based on an available term—such a thing cannot be refuted. What can you refute? Either there is such a similarity or there isn’t. If I smelled it, then there is such a similarity—for someone who knows how to smell, of course. Then there is such a similarity. What sense does it make to refute it? To refute means that I am not grasping the thing itself. I infer it by logical means. So maybe the inference is right and maybe it is not. Then one can refute: maybe you are wrong. But when everything works through some sort of sixth sense like this, an intuition awakened through extra words, through available words, then the intuition says that this is similar to that—what sense is there in making refutations? It is simply that I see that this is similar. So that is immediate apprehension; there are no refutations.

If it is true that “not available” is abstracted from the verse—“not available” is also built on a mode in a specific case and is also not so abstracted from the passage—then perhaps it isn’t even verbal analogy at all. No, but why are you making a verbal analogy when the word is not available? In any case it is more interpretation than the available case. Because why are you making a verbal analogy here? Why make a verbal analogy? What does it mean, the words are similar? He says: what does it mean, the words are similar? But after all, they are needed; they are used because they are needed. So what? Rather, what do you say? You say: true, they are needed, but in the end that really is the interpretation, so what do you want? Therefore in some sense it is always in that mode—this is the interpretation of the verse. I don’t know; one would need to go through the verbal analogies that are not based on available terms. I haven’t done that research now. But it seems that in any case verbal analogies without available terms are more interpretation of a verse than verbal analogies with available terms. Verbal analogies with available terms really look like something that has nothing to do with the verse. You have nothing to do with that word; it is extra. Suddenly you identify an extra word somewhere else—boom, you connect the two things. Not because of some local interpretation here, of what role this word is playing here. So I think the logic clearly says that this is so. Now to what extent this is so—in the end one has to check every verbal analogy individually and see.

There is also a distinction among verbal analogies—they divide, and they can sometimes change the verbal analogy. Fine, that’s not… when there is a rejection, they change the verbal analogy. And they always ask: after all, this is something that came from one’s teacher, so how can you change it? Things like that. Either you received it or you didn’t receive it. So people say—I heard there is a rule saying that verbal analogy is sometimes stated regarding two matters without the… what’s it called… Why are you saying that? Let’s be precise; I’ll get to that in a moment. The very fact that you heard it from your teacher—that is a serious problem here. And he goes on with it later. “The second logic, the heavenly, upper one, is reserved for exceptional individuals, not for every person. Therefore the restriction of the principle of verbal analogy in general is that a person may not derive a verbal analogy on his own.” I’m reading the end of section 15, right? When you look at this, then of course it contradicts everything we said, basically. It starts out well: it says that this is not given to just anyone. One has to develop the second logic, the healthy intuition; one has to know how to smell similarities between things. This is not just formal play, right? If it were formal play, then anyone could do it. Mathematics—you can even get a computer to do it. But if this relies on some analogical intuition, not deductive—the computer performs deductive operations. Analogy requires some healthy intuition. What really resembles what, and what does not resemble what. So therefore it is for exceptional individuals. But it is not just for exceptional individuals—nobody does it. “A person may not derive a verbal analogy on his own” applies to everyone. It just came down from Sinai, and everyone receives it from his teacher. So if that is so, then what does it even mean? Then it says nothing at all. It really does revert to being an axiomatic game. Because if so, then what does this teach me? In any case I cannot use this tool called verbal analogy, so I cannot—even exceptional individuals cannot do anything with it. And in fact everyone receives it from his teacher, and his teacher from his teacher, all the way back to Moses our Teacher. So what have we accomplished? It knocks down the whole edifice.

There could be two possibilities. First of all, it could be that the rule that a person receives only from his teacher began from a certain stage and not literally from the very beginning. Then there was some Moses and his circle, a person, people… But in the simple understanding, the conception is that one’s teacher… even in some of the medieval authorities (Rishonim), it seems to me it is written explicitly: a person does not derive a verbal analogy on his own, only from his teacher, and his teacher from his teacher, all the way back to Moses our Teacher. But there are discussions there about this; I remember seeing somewhere a discussion of this issue. I don’t remember where. If it was like that, you could say that at some stage we lost the second ability, at least in a clear enough way that we cannot rely on it, at least not enough to innovate laws. It’s not necessarily that we lost it altogether, but we cannot rely on it to derive new laws. But the simple meaning seems to be that this really goes back to Sinai; this rule is always binding. Just as Rabbi Kook copied what was said, the verbal analogy… that is what he notes down below. So apparently there is a problem here arising from the rule that a person may not derive a verbal analogy on his own.

So below, in note 43, he says: “The reason is stated explicitly in the Jerusalem Talmud, tractate Pesachim: if a person were to derive a verbal analogy on his own, he would make a creeping thing convey impurity in a tent and make a corpse convey impurity in the amount of a lentil, by deriving ‘garment, garment.’” And if you say, then every verbal analogy is received by tradition—I’m skipping to the answer, right?—if so, what was given to us to derive by verbal analogy? These are the thirteen principles by which the Torah is expounded—so what are we doing in this matter if every verbal analogy is traditional? And the answer: “Sometimes the locations were transmitted but not the words, and sometimes the words but not the locations, and it remained for the sages to determine which they are.” Meaning, the Torah—or the Oral Torah—gives us hints. In other words, there are cases where they tell us: look, in this verse and that verse there is a verbal analogy. I’m not telling you from which word, nor other details. Some details are missing and some are present. Sometimes they gave the words but not the locations. They told you: look, there is some repetition of “to her” between a slave and a woman; I’m not telling you from which verses, you have to search for where it is extra. So this is really a kind of puzzle. Now that sounds a bit strange. Did the Holy One come to confuse us? To play games with us? Give me what you want me to do, and I’ll do it as best I can—why play around? That is exactly the point. The point is that if these were really axiomatic rules, then indeed this would sound like an unnecessary game. Why are you encoding things for me in such a complicated and confusing way? Don’t encode it—say explicitly what you want from me. But precisely because of what the Nazir says—that verbal analogy is a philosophical instrument that sharpens my capacity for thought and perception—the Torah helps me walk along that path, to learn how to sharpen that capacity of perception through verbal analogy. Therefore it says to me: look, I’m giving you hints, like a game where the Torah gives you certain clues so that this faculty, this cognitive and intellectual faculty of verbal analogy, will become sharpened in you. So sometimes they give you a hint about the locations, sometimes about the letters, the words, and you have to complete it on your own. This is in the Jerusalem Talmud, tractate Pesachim, chapter 6, halakhah 1, and also in Nimukei Yosef on tractate Bava Kamma at the beginning of chapter 8. He brings it there: when the law is already known, you may in general derive a verbal analogy on your own. That is, when you already know the law and only do not know its source, you may derive for it a verbal analogy entirely on your own, with no given words, no given locations, nothing at all—and according to everyone, in that case a person derives it on his own. So once again there are always these degrees of freedom that the Torah left, precisely as hints in order to help me sharpen this auditory capacity, because that is the whole goal. The whole goal is to help me use these tools, because they are important tools in and of themselves. Not only the resulting law learned from the verbal analogy is the goal of the matter, but the development of the ability to use verbal analogy itself is also one of the Torah’s concerns. Otherwise you really cannot understand this whole game. And therefore perhaps that is what “expound and receive reward” means. I think that is the depth of the matter. It is not games in order to receive reward. “Expound and receive reward” means: expound and improve yourself—that is what it means to receive reward, meaning become more perfected.

And that makes sense, because sometimes we see that they derive something by verbal analogy, and afterward retract from that verbal analogy and learn it from somewhere else. So if this is from a received tradition, then how does that make sense…? Yes, yes—that’s exactly… Now this really makes sense, because it may be that a person did not in fact receive this particular verbal analogy, but is now honing his skills. He received the law, or the source, or the route through which he attains the law, and now he wants… So that is exactly why all the rule-books discuss this. The Mabit here… But one can also speak of verbal analogy in general where a person has nothing at all in the law from his own reasoning, not even the hints. That almost concludes the opposite: against the Torah saying that from Sinai there descended verbal analogies at certain points, he subjectively notices agreements that there is similarity between them. But that would only give you the benefit of the similarity between the places. We said there are two benefits in verbal analogy: one benefit is to understand that there is something shared between slaves and women, but the second benefit is to take this tool of verbal analogy and know how to use it also when looking at the world, or perhaps at other places in the Torah. That is exactly the conception of verbal analogy—that it is not because of some mechanical axiomatic factor, but because something is embedded in the words themselves, right? But when everything is already given to you from Sinai… No, but if, for example, I want to know whether there is a similarity between the verb “to send” and “table,” unrelated to Torah law—just to understand the surrounding world, to understand what it means—then I need to sharpen my analogical capacity. We already said that analogy requires some human faculty; it is not a tool that a computer can perform. It is not deduction. That is the very thing the Torah comes to sharpen in me. The Torah comes to create in me this auditory logic, not only because of the legal outcomes to which I arrive, because the legal outcomes can simply be written out for me in an orderly code of Jewish law and we are done. Especially if it all comes from Sinai, then why would I need all this at all? The point is that apparently there is value in the tool itself. On the contrary—that is the proof of what the Nazir argues, that the tool itself must also have some value here, otherwise the game seems unnecessary. We saw this above on page 4 in the introduction; we saw it there.

A similar comment is made by Ralbag below. Ralbag and Maimonides understand the status of the thirteen principles differently from the Nazir. So Ralbag raises this claim. He says that in fact the laws are pre-sold, predetermined. The laws I already know; nobody ever derived a law from the thirteen principles. Why? Because I know the laws, and only afterward do I stitch the thirteen principles onto them. Why? Because if things really came out of the thirteen principles, I could derive absolutely any law on earth that I want by means of the thirteen principles. Therefore it cannot be that these thirteen principles are really used to derive laws—that is what Ralbag says. And in fact what lies behind this, as we said, is the conception that the thirteen principles are an axiomatic system. I saw someone say this also about Maimonides. Maimonides doesn’t say it—did Maimonides say it? Because some prove that Rabbi Abraham, son of Maimonides, said that his father had said this and concealed it—that Maimonides concealed it. Some pamphlet someone published, that really all the laws are… something like that. I don’t know it, but his conception in Milot HaHigayon is clearly like that. So he brings it here in the note. How can a person retract? How can a person retract? Retract with regard to practical legal implications? Regarding laws. Yes. Truly, according to that view, one shouldn’t be able to retract. But yes, they do retract. But they do retract. I don’t know. I think that conception is incorrect, but I don’t know, I don’t know what they do with it. But the Nazir says: that is not correct. So he brings it as the antithesis. Here too we apparently see the same thing in Nachmanides. But it is not exactly the same thing, because Nachmanides does not conclude that the whole thing is a rigged game. Nachmanides says: sometimes the laws are given, sometimes the locations are given, sometimes the word is given. You have hints. You cannot simply build from a vacuum, because otherwise you really could create everything. So there is something somewhat more moderate here, but still the human creative element remains part of the process. It is not just a completely rigged game, because otherwise it really sounds entirely unnecessary. If all the laws are known, then why should I care whether it comes from this verbal analogy or another verbal analogy? Who even cares? I already know the law, so what’s the problem? Clearly, what the Jerusalem Talmud means too, when it says that if the laws are given then I can make a verbal analogy on my own, is that I make a verbal analogy on my own and derive from it other conclusions. Once I have compared a slave to a woman—it is known that slaves are exempt from positive commandments dependent on time. That is a law given to me. Now I say: I don’t know from where. Fine, so I make a verbal analogy of “to her” from woman. Then why should I care now about the verbal analogy? I already know the laws. The point is that now I take this verbal analogy and continue further with it, and I say that perhaps slaves are also exempt from “do not make a bald patch,” or something like that. Whether yes or no, I’m not yet expert enough in the Jerusalem Talmud. But in principle I take this verbal analogy and keep working with it. Otherwise why should I care that there is a verbal analogy here? If the law is already known, then why am I making this verbal analogy? Therefore, according to Ralbag and these strange conceptions—which were never clear to me—why should I care? Why am I looking for derivations when the law is already known? Is it just some kind of intellectual gymnastics, some way of interpreting the Torah or something? I don’t know exactly. Maybe “receive reward” in the plain sense. It’s a little strange.

Now the Nazir’s whole move regarding these verbal analogy derivations really does become strange. It could be that anyone who understood expounded it. Who wrote it down for us as we have it today—I don’t know. The question is whether all the laws were really known from Sinai. What did slaves do until they derived the verbal analogy? I mean, I don’t understand. Slaves existed or didn’t exist until they derived that verbal analogy, or they hadn’t derived it and nevertheless observed or didn’t observe? Perhaps they didn’t. In Maimonides, after all, it is described in the laws of rebellious elders that one court derives a Torah-level law by means of the thirteen principles and another court overturns it. We spoke about this—the difference between the thirteen principles and a law given to Moses at Sinai is that the thirteen principles too were given at Sinai, understood at Sinai, as tools—but not the law. In contrast to a law given to Moses at Sinai, which is the law itself as already given. For Maimonides this is called words of the scribes when it comes to the thirteen principles. The principles themselves were given at Sinai, not the specific derivations that come out of the principles. On the contrary, Maimonides writes this explicitly: that if there is a court that derives by means of the thirteen principles a Torah-level law involving karet, stoning, whatever you want, and a court lesser than it in wisdom and number—at least in Maimonides this is how most understand it—another court, and for this there is no requirement that it be greater in wisdom and number; if another supreme court derives a different plain meaning in the Torah through the thirteen principles by which the Torah is expounded, then it can overturn a Torah-level law, permit the rival wife of one’s daughter, desecrate the Sabbath—whatever it wants by means of that. However it learns the Torah, that is what it has. Only with enactments, fences, and customs is it said that one needs a court greater in wisdom and number. So here we see some of the hints that the Torah gives us in order to sharpen in us the capacity represented by this principle of verbal analogy. The principle of verbal analogy represents an intellectual or cognitive power, and we sharpen it through Torah study. But it is a means of grasping the world; it is not an axiomatic principle for interpreting the Torah and deriving laws. On the contrary, the laws were sharpened in order to sharpen in me this capacity, which I will also use for other needs. Otherwise the laws themselves become forced.

And this is unlike those who say—I’m now reading from the note at the top of page 87—“and this is unlike those who say that according to the one who requires an available term, he does not require reception by tradition.” Yaavetz in his glosses to tractate Niddah. And the opposite in the book Sha’arei Chokhmah, page 32: there he says that according to the one who requires an available term, specifically he requires a received tradition, whereas one who does not require an available term does not require a received tradition. Like the Rokeach, who said that according to the one who does not require an available term, he derives it on his own. The dispute here seems to me to revolve around the following question: on one hand, an available term seems more clearly something one can derive, because it is an extra word. But on the other hand there is no refutation against it. Here one needs a special sense of smell, as we said before, to grasp what this extra word is saying. Therefore there is some dispute here about what to do with an available term—whether, on the contrary, specifically such a thing one can derive on one’s own because it is clearer, or no, specifically here something higher is required, some deeper faculty, some sort of sense of smell that not everyone has, and therefore not everyone can derive it on his own. That could be the dispute between the two sides here.

Beyond that, one should know that the book Kinat Soferim—you know Kinat Soferim on Maimonides, on Maimonides’ roots in Sefer HaMitzvot? There is Kinat Soferim, a commentary on Sefer HaMitzvot and on the roots. So in root 2, Kinat Soferim argues that according to Maimonides—and this is a dispute among commentators on Maimonides in the second root, but that is how he argues—that a person does derive a verbal analogy on his own; “a person may not derive a verbal analogy on his own” means a private individual, whereas the supreme court derives it on its own. “A person may not derive it on his own unless he received it from his teacher” refers to anyone who is not the supreme court. But the supreme court can derive it on its own. And in truth, otherwise Maimonides really should have written that in the continuation of the laws of rebellious elders. Because Maimonides writes there explicitly that the thirteen principles by which the Torah is expounded—every court does whatever it wants; it can nullify the words of the previous supreme court, even if that court was greater than it, and that makes no difference whatsoever. So say at least that with verbal analogy it is not so. But he does not say that. So in the straightforward reading, I think that indeed Maimonides’ language indicates that the supreme court has no such restrictions. Why? Because these really are the special people on whose second logic one can rely. And that completely solves the problem the Nazir is struggling with here. On the one hand, a person may not derive it on his own because it is for exceptional individuals. But on the other hand, I do indeed want a person to do something with it, because otherwise what good is it that I was given this tool? This tool was given to help me, which means I need to do something with it. So here you see that indeed, yes, the supreme court can work with this thing. Fine, that is a dispute in the plain reading of Maimonides’ words; not everyone agrees with that.

So much for verbal analogy. Now section 16. Where are we, what time is it now? Six? “What is found from one case” and comparison by similarity—section 16 is “what is found from one case,” and section 17 is “building a principle.” So let’s read both of them for a moment, because these are two things worth seeing side by side. “Comparison by ‘what is found from one case’ is two things equal in their matter; we compare one to the other, the obscure to the explicit, in their laws, in the formulation: ‘just as we find in one, so too in the other.’” That is the meaning of the words “what is found from one case”: just as we find in one, so also in the other. “This is a substantive comparison of one detail to one detail, one-to-one. One-to-one”—we will see what that means in the next section—“which is not explicitly counted among the thirteen principles.” “What is found from one case” is not written in the thirteen principles; there is no such thing there. “And it is called ‘what is found from one case,’ and is sometimes also termed verbal analogy, as included with it. It is comparison by similarity—analogy.” This is classical analogy. Ordinary analogy, the kind used in all areas of life, is also used in Jewish law, and therefore it seems to me that it does not appear among the thirteen principles by which the Torah is expounded, because it is an ordinary intellectual tool that everyone uses. It is obvious—you use it at every step of study. Even if they had not given the thirteen principles, you would still do it. You do not need the thirteen principles for that. Otherwise I could understand nothing in the Torah. The whole use of analogy—if it says that an ox gored a cow so one must pay, then if a dog bit a cow must one also pay? You see that at every step you are using analogy; you do not take the words of Torah in an absolutely literal way. So there is no need for a principle among the thirteen principles called analogy. Anything that is a simple intellectual tool is not found among the thirteen principles. That is a rule. Know this as a rule. That is what it would seem. We mentioned something like this also with a fortiori reasoning, and we will get to it further on. A fortiori reasoning also is not an ordinary deductive logical inference, because otherwise, as we said, there would be no need to write it among the thirteen principles. It is a principle. We’ll discuss that later. It too is an auditory tool, right? “What is found from one case”—logic is not an auditory tool? It is an auditory tool, it is an auditory tool, but it is a tool that in fact serves us in other contexts too. Only here it does not rely on a word appearing in the verses. It’s just similarity: understand that if it happened here, then it also happened there. Not because there is a shared word, not because they were written next to one another, no—there are no textual hints to the matter. Rather, it relies on understanding.

Let us read the second one for a moment and then come back again. Letter 9: “Building a principle and searching comparison. The third principle, building a principle, is learning a general rule from details that resemble each other in the common side they share.” If we were calling it… what? Right, the third principle that we are discussing, no? “Learning a general rule from details that resemble each other in the common side they share. The standard formulation is: ‘This case is not like that case, and that case is not like this case; the common side between them is such-and-such; so too anything that resembles them in that respect,’” right? “This is searching comparison—induction.” The previous one was analogy, and this is called induction. Now this too is apparently an auditory tool, right? Yes—that is what I said earlier. I stopped mid-sentence and said we would see that later. We said that both induction and analogy are auditory tools. First of all, the distinction he makes between building a principle and the various forms of “what is found from one case”—write this down, because the whole thing he does here is really illuminating. What is “building a principle”? What does the phrase mean? That there is some “father,” some underlying source, shared by all the details, right? Because at first glance, usually when we talk about building a principle, we just mean analogy. Not all the more so. In the principles of the thirteen hermeneutical rules, according to most commentators, building a principle denotes learning one thing from two others—what is called one-from-its-fellow or what was earlier called “the common side.” “One from two” means what is called “what about the common side.” I learn from A; against A there is a refutation. So B proves it. What about B—there is a refutation there too. A proves it. The common side between them applies to everything similar. That is called building a principle, specifically the common side. Usually we understand building a principle as basic analogy, and “the common side” as just some expansion of the basic analogy. But no. What is called “the common side”—building a principle is only the common side, only one from two, where there are two teaching cases and one learned case. Why is that so, really? I never grasped that. Why should that be a distinct principle? It’s just another case of analogy. What is special here? The answer is: it is not analogy, it is induction. It is induction. I found one detail where the law is such-and-such. I also found another detail where the law is such-and-such. Through the refutations I only use those as a means to clarify which parameter is the relevant one that generates the result. If in A the law is X and in B the law is also X, then I want to know what the law is in C. Is the law in C also X or not? Meaning, I am learning C from A. Fine? Now A has many properties. I do not know which relevant property I need to compare between A and C. So I say: B will prove it. What does B prove? B proves that the relevant property for the comparison is not the differing property but the common one. That is the point. Fine? Again: take the “common side” in tractate Bava Kamma, in the first Mishnah there. There are two primary categories, right? Categories of damages. “Whatever I was obligated to guard, I have thereby enabled its damage, and I am liable to pay.” The four primary categories of damages: the ox, the pit, the consuming one, and the fire. “What about the ox, since its intent is to damage? What about fire, since it goes and damages?” etc. Each has its refutations. The common side between them is that it is their way to damage and that their guarding is your responsibility. If I am not mistaken, that is exactly how the Mishnah says it there, right? This is called the common side. Fine? So how does the mechanism of the common side operate? I take one detail—an ox. And I want to learn from it that for any damaging thing, any property of monetary value that causes damage, I have to pay. Why should that be? An ox intends to damage. So who says you can learn from it? Fire proves otherwise. Fire does not intend to damage. I’m just giving an example; I don’t remember the exact refutations. Fire, which does not intend to damage. Fine? So what does that prove? It proves that also in the case of the ox, the reason one must pay is not because of its intent to damage, but because of what? Because of the shared property it has with fire. What do ox and fire share? After all, fire too has its own refutation. What nevertheless remains shared between ox and fire? That both—it is their way to damage, and their guarding is your responsibility. Meaning, the relevant parameter for learning what one must pay for is anything whose way is to damage and whose guarding is your responsibility. That is induction. You see one detail, you see a second detail, and you try to generalize. You just generalize correctly. Otherwise you could generalize that anything whose way is to damage requires payment. No, no—you generalize correctly. That is not the important parameter. The important parameter is anything whose way is to go and damage and whose guarding is your responsibility. That is the correct generalization. So in fact the whole “common side,” all these devices, serve only to determine which parameter one is permitted to generalize from. Therefore “will prove” means B proves something about A, not about C. B proves which property in A is the relevant one from which to learn for the sake of C. Fine? So what we really have here is induction. I find one case where one must pay—the pit. I find another case where one must also pay—fire. From these two details I learn inductively that what is common to them probably always requires payment. So it follows that what matters is the shared feature between them. And then that becomes induction. Afterward I learn the third detail. Fine, that is the next stage; that doesn’t interest me. The important part here is specifically the induction. Deduction is always obviously possible—that isn’t a problem.

By the way, in high school, for example, when they teach induction—if you ever noticed—at least that’s how they always taught us: check for n = 1, then check for n = 2, and then n = k and k + 1. Why do you need to check n = 2? Why not only n = 1? Why do you need to check n = 1, check n = 2, and then assume for n = k and prove for n = k + 1? In high school it’s enough to check n = 1; you don’t also need n = 2. Because if you prove progression by one each time, then from one you already get to two. That is true in principle. It just seems to me that the mistake stems from the fact that when you find a detail, it isn’t always really the right detail. So check that this really is the right detail from which you want to generalize. Check n = 2 for a moment, to see that this is indeed the property, to see whether you’re even on the right track. When you are solving textbook exercises, you know the answer is correct and you are only looking for the proof. But someone who is truly operating by induction doesn’t know the answer; he is searching. If I have a case and I want to know whether it is right to generalize it to all cases, then here don’t take just one case—always take two. Take another one as an initial check to see that you are latching onto the correct property, not onto some incidental property. Do you understand? Therefore induction is done on the basis of two cases, not one. Although theoretically one could have done it on the basis of one. It is not an essential difference, one versus two. But there is some healthy logic here that serves to mark the irrelevant properties. We said that induction presumes some relevant similarity property. In order to filter out the irrelevant properties, you examine another example. Therefore building a principle is always from two. It is from two because it is induction. I find one detail, find a second detail, and generalize to a rule. That is why it is called building a principle. What does “building a principle” mean? I take two details and ask who their father is. What is the rule of which both are children? So that is building a principle—I build the father out of the children. That is why it is called building a principle.

By contrast, “what is found from one case”—going back to the previous section—what is that? It means: just as we found it here, so too there. Do you understand? That is not induction; it is analogy. This is very clear in the terminology too. “Just as we found it here, so also we found it there”—that is analogy. “Building a principle” says from the outset that it is induction. Therefore all the rule-books say that building a principle is always one from two. It was never clear to me until I saw this Nazir here. It is really eye-opening. Otherwise, if it were from one, then clearly it would be “what is found from one case” and not building a principle. If it is only one and one from one, then I understood “the common side” as basically just pure analogy, that’s all. There was some problem with that analogy, so you fix it with another analogy. But why should that be something essentially different from ordinary building a principle? Call the whole business one thing. Why are they insistent that building a principle is always one from two? Because one from one is analogy, while one from two is induction. In one from two you are not comparing one thing to one thing; you find what is shared by the two, derive a rule, and then descend back to the particular case you care about. But in fact you are learning a rule from the two; you are not learning one detail from another detail. Therefore it is induction. So if building a principle is written as from one, the question is whether it is really called building a principle. The rule-books discuss this. Why is it called building a principle at all? Why “building a principle,” as it were? Right. I’ll try to say something about that; I hope it will come out okay. That is a good comment. In any case, it is clear that this is not deduction. Even analogy—maybe I need to qualify what I said earlier—deductions certainly are not written there. A fortiori certainly is not deduction, because deductions have no reason to be written among the thirteen principles. Analogy and induction are nonetheless things in which one can err; they are not necessary truths. So perhaps there is room to include them, but I’ll try to defend that with a somewhat more substantial argument in a moment.

Now look at note 44 under section 16. In note 44 he writes—there is a paragraph beginning “what is found from one case is not mentioned among the thirteen principles.” Do you see it there, in note 44? Yes? Do you see? “What is found from one case is not mentioned among the thirteen principles in the baraita of Rabbi Ishmael’s thirteen principles. Some say it is included in the principle of building a principle from one text.” Sefer Halikhot Olam, laws of building a principle, etc. “According to that approach, we learn that building a principle means both one from one and one from two. That is the position of Raavad, and it is primary. Therefore for the Ramchal it is called building a principle and what is found from one case. And some say that he does not call one from one ‘building a principle,’ only ‘what is found from one case.’” One from one is “what is found from one case”; only one from two is building a principle. What is the dispute here? The dispute is exactly what we said by way of introduction: what is “what is found from one case,” and what is “building a principle”? The question is whether building a principle means only one from two, or also one from one. In other words, whether induction—no, because “what is found from one case” is just a synonymous name for building a principle. But the point is why it is called building a principle—that’s the question. Not why it is called “what is found from one case”; that is not the formal term. Building a principle is the formal term. Why? Raavad holds that there is no difference between induction and analogy. We spoke about this once—that to a large extent the distinction between them is arbitrary. Induction and analogy are built on the same idea. Both of them are building a principle. How do you do “what is found from one case”? asks Raavad. How do you do it? He says, “What is this father?” But think for a moment—why do you really infer that way? Because there is something shared. Exactly—because you infer on the basis of the shared property; in fact you infer about a rule, so in fact you are doing induction. So why should it matter whether it is one from one or one from two? You are always doing induction. Therefore—just a moment—therefore it is always called building a principle. Both are called building a principle because both are induction; even analogy is induction. In Halikhot Olam, however, these are two different things. There is building a principle one from one, which is analogy, and induction is another intellectual tool. And what really underlies this? There underlies a very interesting conception, it seems to me, that says that building a principle is actually induction—what? No, no—that these are two separate things. Perhaps induction is the result of many building-principles; we’ll see in a moment, but… not building-principles, many “what is found from one case.” Analogy is some sort of perception that does not pass through generalization. I see two objects, I see that they are similar, and somehow I feel that the same law that applies to this also applies to that. We always presented it this way: what do you mean, “feel”? You really understand that their shared property is true of all objects that have that property. No—perhaps, says the author of Halikhot Olam, that is not true. It may be true in some cases, but not always. Analogy is a deeper tool. Analogy is some kind of intuitive apprehension; it does not pass through some generalization and then specification back down to the case. Rather, I sense with healthy intuition that there is similarity between this and that. That is called analogy. By contrast, induction really is extracting some more general characteristic; it is learning something more general from particulars. That is induction.

Fine. How does he define what building a principle is? Further on we will see: building a principle from one text—move to section 17. In note 46, do you see? According to this, even building a principle from one text is not learning from one, but from two that are in one text. Do you hear? Leviticus 15:4: “Every bed on which the zav lies shall be impure, and every object on which he sits shall be impure.” When the two examples appear in one verse, that is called one from one. When the two examples appear in different verses, that is one from two. But you understand that both are induction, and therefore both are called building a principle. Therefore both are called building a principle: induction. So the only difference is whether it comes from one verse or from two verses—technical matters; there is no essential difference. But analogy is called “what is found from one case.” Why? What suddenly makes that so? So what is the relation between one text and two texts—why is that… The question is: when the Torah itself—no, when the Torah lists, you see the verse I brought—the Torah lists two examples. Why does it list two examples? Here it seems that it was trying to signal to you that you should make a generalization. In two different cases, you understand on your own that in this case the law is thus and in that case the law is thus; it was not written for that purpose. You understand on your own that if here the law is this way and there the law is that way, then you make the comparison. There is some difference in the Torah’s intention. I don’t know exactly what difference it makes, but they are still two different things. Fine? But there is also building a principle from one case, as Rashbatz brings somewhere: “a female goat in its first year”—this is a building-principle, anywhere the Torah says “a female goat in its first year.” And in several other places too: “and he shall offer the one for the sin offering first”—this is a building-principle for all sin offerings, that they precede the burnt offerings brought along with them. So he says that Rabbi Meshullam brings this and says: in my opinion Rabbi Ishmael would not have called this building a principle, but rather learning the obscure from the explicit. This is not building a principle; it is really analogy. It is not building a principle; it is one-from-one. It is building a principle from one text in the sense that you asked before—simply from one thing, one example, not from two examples in one text. So why is it called building a principle? The Nazir says: no, this too is called building a principle. Why? “Although the essence of building a principle is the comparison of a general rule to one detail or to several details—‘this case is not like that case… the common side between them… so too anything similar’”—do you understand what is really being done here with “a female goat in its first year,” the building-principle we read here? We are not comparing one example to another example. We extracted a generalization from one example. So again, this still is not analogy. It is a generalization drawn from one example, but it is a generalization—we extracted a principle from it. Analogy is a different faculty, says the Nazir. What is analogy? Analogy is to apprehend intuitively, without any generalization in the middle at all, some relation between two particulars and to understand that just as in this one, so also in that one. Without going through some general rule shared by both. And because it is intuitive, it would have needed to be written explicitly among the thirteen principles. What? Then it should have been written explicitly among the thirteen principles, if it is really not an auditory tool. Yes, but on the other hand you have no guidance there as to what to do with it. After all, you simply use this intuition also in the rest of life. Are there human beings who do not use intuitive similarities? Everyone uses them. Even in non-Torah legal interpretation people make analogies between cases. Fine, I really don’t know, because then you’ll ask me about induction: why is induction written there—building a principle? So I’ll also try in a moment to say something about that.

In any event, if so, then there are several levels here. There is building a principle from two texts—that is complete induction from two places. Building a principle from one text means two examples in one verse—that too is induction. Then there is building a principle really even from one example, but if the learned case is not a particular but a general category, then it is still called building a principle. Only where it is really from one particular to another particular is it called analogy. That is the Nazir’s own position. Raavad does not go that way. That is what he says at the end of note 44: “My mind is more at ease with the opinion of Rabbi Shmuel…” meaning not like Raavad. He truly tends not to say like Raavad. Raavad holds that both are induction, as we said, right? Building a principle from one text, building a principle from two texts. This “what is found from one case” is building a principle from one text. Meaning, according to Raavad, both induction and analogy are induction. And he insists: analogy is a deeper tool than induction. Analogy is apprehension that does not pass through generalization. I understand directly some similarity between two particulars; it does not pass through generalization.

And one last point, and with this I’ll finish—what time is it now? Ten past six. Yes. Regarding “the common side,” I also heard this last year—it was going around the yeshiva here; you heard it in any case. What comes out from “the common side” is something very interesting. Suppose I have A and B as teaching cases, and C is the learned case, right? Now I learn C from A, and then I refute it: what about A, since it has some distinguishing property? Then they say: B proves it. And against B I also have another refutation: what about B, since it has some other property? Then they say: A proves it, the common side between them, etc. Apparently one could continue to refute: what about A and B, since A has this and B has that? Perhaps in each case, indeed, what causes the law is what is unique to A, and in B what causes the law is what is unique to B—but in C neither cause is present. This derivation is not closed. Why can’t one refute in that way? Because there is only one cause for a law. Exactly. There is an assumption here that every law has only one cause. There is no such thing as a law that has two causes, and this is a very far-reaching claim. In general discussions of causality in philosophy, this is highly significant—the claim that a cause is not only a sufficient condition but also a necessary condition. Or rather, pardon me: not only sufficient but also necessary. In short, there are not two causes for the same thing. Everyone agrees that a cause is a sufficient condition, but not everyone agrees that it is a necessary condition. Here we see from the Torah the philosophical principle taught by building a principle. The philosophical principle taught by building a principle is that everything has only one cause. If you see two things that seem to be causes of something, then know that they are particular manifestations of a more basic principle.

“And do not stray after your hearts and after your eyes.” The Minchat Chinukh asks, on this week’s Torah portion, about Nachmanides: why doesn’t he count this as two prohibitions? One is fantasies of transgression, and the other is fantasies of idolatry. Why doesn’t he count them as two prohibitions? He asks this about Nachmanides because Nachmanides also counts components of a commandment as separate commandments, and that is the dispute between Maimonides and Nachmanides in root 9. The answer is very simple: because these two things have something shared between them. And any prohibition that has two things on which one might apparently violate the prohibition—know that there is something common between them. There are not two separate things under one prohibition. They are two examples of an overarching principle, which is the principle the prohibition is talking about. The common thing is simply going after your impulses—meaning after your drives, not after your head; an irrational action. That is the prohibition of “do not stray.” Someone who goes after the impulse of desires, of forbidden relations, is going after impulse and not after reason. Someone who goes after idolatry also goes after impulse, not after the mind that understands that there is no truth in it. So both cases are simply cases of not being rational. Therefore there is one prohibition in this. And there is always one shared thing. Every prohibition has one definition. It is not “either this or this or this is forbidden.” There is no such thing. If it is this or this or this, these are all manifestations of one principle. And that is what we learn from the principle of building a principle.

And in truth, if you think about it, every induction is built this way. Otherwise one cannot make inductions at all. I say: this object fell to the ground not because it has mass but because it is round, and that object fell to the ground because it is square. So every object that is either round or square falls to the ground. I do not infer that because both objects have mass, therefore they fall to the ground. So if I do not accept this principle, then I cannot even make progress in life. This is what in philosophy is called Occam’s razor. Occam was a medieval Christian scholar, William of Ockham—Ockham is basically the name of his place. William of Ockham argued that one does not posit assumptions beyond what is necessary. And usually philosophers understand this as a rule of the game, not as pointing to truth. Rather, if you want to build efficient, aesthetic, sensible science, then use things in a reasonable and simple way. That is more convenient, because there is no way to know whether the truth really is the simpler theory. Maybe the complicated theory is the true one. Do you have any guarantee that nature specifically follows simpler theories? That is if you look at it from a purely scientific point of view. It seems to me that building a principle teaches us that this is not merely a rule of the game—it is true. The truth is always the simple thing. That is what Rabbi Chaim always says, after all. If I have ten difficulties, I can suggest ten answers. But if I have one answer that solves ten difficulties, that is the truth. Even though, apparently, ten answers also solve all the difficulties, so what is the problem? If I have one answer, that is the truth. Our entire capacity to generalize is built on this. Now in science, because there is no philosophical grounding for generalization, it really can be refuted. What about A, since it has this property? What about B, since it has that property? How can you know that their common side is the cause? So you say: fine, let’s adopt a rule of the game that selects the simplest theories. Why not? That’s the most sensible thing; I have no other tool to determine which theory I should choose. But we learn that the Creator of the world tells us that the world really is built this way—that the true theories are the simple ones. It is not some kind of game device. That is the lesson we learn from this principle called building a principle.

The ability to generalize contains behind it very important philosophical information, and therefore it seems to me that it is written among the thirteen principles. I told you before—you asked me why induction is written among the thirteen principles, while about analogy I said it was unnecessary. Because with induction there was at least room to say that it is only a rule of the game. I might have understood it as an axiom, as something arbitrary. The Torah comes to teach me the philosophical principle that stands behind this principle, as the Nazir says: the principles come to teach me philosophical principles. Therefore the principle of induction is written here in order to tell you that this is truth, and not some coding device. As for analogy, there too one might have said—though again, why is analogy simpler? Here it is no longer a matter of deciding whether two different causes bring about the result or whether the common thing brings about the result. Here I can simply make the analogy and that’s it. With analogy the question is only whether it is right or wrong. Rather, here there is the possibility of error in perception. So this principle of building a principle comes and teaches you what the correct perception is here, how to understand the world correctly.