2019-04-22 – Between Midrash and Logic – Lesson 8

Table of Contents

• An intermediate category: the synthetic a priori and the hermeneutic principles
• The critique of the hermeneutic principles and the Orthodox response
• Three types of inference: deduction, induction, and analogy
• Analogy as composed of induction followed by deduction
• Unpacking hidden assumptions, halakhic midrash, and Paley’s example
• Gezerah shavah, binyan av, and the status of the “given” as opposed to reasoning
• John Stuart Mill, the problem of deduction, and the claim that information cannot be accumulated with certainty
• Reliability instead of certainty, Hume’s problem, and control mechanisms for non-deductive inferences
• The Nazir Rabbi and the hermeneutic principles as a controlled inductive-analogical logic
• The context of discovery and the context of justification in Hans Reichenbach
• A classification of the hermeneutic principles: logical vs. textual, and the concept of pirkha

Summary

General Overview

The text presents the problem of an intermediate category between deduction and free legislation through the Kantian concept of the synthetic a priori, and places the hermeneutic principles as an instance of this intermediate category in halakhic interpretation. Derash is described as drawing conclusions from verses in a way that is neither deductive nor an invention detached from the text, but rather an extension based on the “spirit of the verse” through analogical and inductive inferences. A debate is presented between the critique of Ralbag, who sees the hermeneutic principles as invention, and Orthodox responses that try to describe them as a lost deductive logic, and the conclusion is that both sides are mistaken because they assume a dichotomy instead of recognizing intermediate states. The text then lays out the concepts of deduction, induction, and analogy, argues that analogy conceals an induction followed by a deduction, and cites John Stuart Mill’s critique according to which even deduction ultimately rests on induction and therefore does not add certain information. The discussion then moves to the question of reliability instead of certainty and to the attempt to develop control mechanisms for non-deductive inferences, with the Nazir Rabbi presented as claiming that the hermeneutic principles are such a control system. Finally, the hermeneutic principles are divided into logical principles and textual principles, and their connection to pirkha and to the rule of an unfocused gezerah shavah is explained.

An Intermediate Category: the Synthetic a Priori and the Hermeneutic Principles

The text states that at the end of the discussion of the analytic and synthetic in Kant, a category is needed that lies between thought and knowledge, between logic and invention, and between interpretation and legislation, and that all these pairs are equivalent. The claim is that the hermeneutic principles are the appearance of this intermediate category in the context of halakhic interpretation, and that this is what is called derash. Derash is defined as drawing conclusions from the verses in a way that is not deductive and not simple interpretation, but also not legislation or a new invention, rather an extension of the verse from the “spirit of the verse.” The text explains that therefore the logical character of the hermeneutic principles is that of analogy or induction, because they must stand between deduction and free creation.

The Critique of the Hermeneutic Principles and the Orthodox Response

The text presents a critique of the use of the hermeneutic principles, especially the critique of Ralbag, according to which derashot are inventions and therefore unacceptable. From this comes the demand that all derashot be merely supportive derashot, so that they not be inventions unrelated to the text. In response, Orthodox answers are presented claiming that if one understands the system all the way through, it contains logic and mathematics—that is, a code of rules by which someone who knows how to use it can derive conclusions from the verses deductively, except that the ability or the information has been lost to us. The text identifies this debate as parallel to debates in philosophy of science, philosophy of law, and other contexts. The main claim is that the mistake on both sides is the assumption of an “either-or” dichotomy, while in reality there are intermediate states.

Three Types of Inference: Deduction, Induction, and Analogy

The text divides inferences into three types: deduction as movement from the general to the particular, with the example “all human beings are mortal… Socrates…”; induction as movement from the particular to the general; and analogy as movement from particular to particular or from general to general between things that do not stand in a relation of particular and general. The text states that deduction is a necessary inference because it does not add information beyond what is already contained in the premises, and therefore anyone who accepts the premises must accept the conclusion. The text raises the question of “which is more secure” between induction and analogy, and shows that “stronger” can mean either more information or more certainty, emphasizing that the more information is included, the less certainty there is. The text presents an argument in favor of analogy as “less speculative” because it adds one particular fact, whereas induction makes a very broad general claim and is therefore liable to error if there is even one exception.

Analogy as Composed of Induction Followed by Deduction

The text argues that it is difficult to distinguish between induction and analogy because many analogies are simplistic inductions, and it offers the example of a frog and horses in order to highlight an analogy between different domains. It then argues that the claim that induction is stronger because the particular is a “sample” is incorrect, because analogy always “has an induction hidden behind it.” The text shows that in an analogy such as “a frog is mortal, therefore horses are mortal,” there is implicitly a generalization such as “all four-legged creatures are mortal” (induction), followed by a descent to the desired case (deduction). The text concludes that in fact the movement from particular to particular is made in two steps: generalization and then specification, and therefore analogy is a chain of induction and deduction. The text emphasizes that analogy and induction are not necessary inferences and that one can arrive through them at nonsense, unlike deduction.

Unpacking Hidden Assumptions, Halakhic Midrash, and Paley’s Example

The text states that analogical arguments “sit inside rules that haven’t been unpacked,” and that one can “unpack” the hidden generalization. It gives an example from halakhic midrash: from “if one man’s ox gores the ox of another” liability is derived also for a dog that bites, where the hidden generalization is that anything that is one’s property and causes damage creates liability for payment. The Mishnah is then ultimately formulated as “the common side… that they are your property and their guarding is upon you….” The text argues that when the Sages made an analogy and we do not know how to unpack the generalization, that does not mean they had no generalization. Paley’s watch is presented as an example of a bad analogical argument, and the text shows how unpacking the generalization turns the dispute into a question about the induction behind the analogy. The text states that the problem with analogy is not that it is analogy, but that the dispute is really about the induction at its base, and it adds that the need to define things explicitly is not a condition for understanding, because every language rests on a conceptual system that is never fully defined.

Gezerah Shavah, Binyan Av, and the Status of the “Given” as Opposed to Reasoning

The text distinguishes between binyan av as analogy “in the ordinary sense” and gezerah shavah, which is not a simple analogy because it does not rest on relevant similarity discovered through reasoning. The text explains that in gezerah shavah the similarity is “given” through a halakhah to Moses from Sinai and through the hermeneutic principle, such as “lah lah from woman,” and therefore there is no induction of the interpreter here, but rather a similarity that was given in advance. The freedom is narrowed to the question of what to derive from it by means of rules such as “derive from it and from itself” and “set it in its own place.” The text notes the rule that “a person does not expound unless he received it from his teachers” regarding gezerah shavah, even if there are disputes in the traditions. It then argues that if a gezerah shavah is not focused, “there is room to refute it,” because when it is not focused it is at most a hint of similarity, and then the comparison is made by force of analogy and is called binyan av rather than a formal gezerah shavah.

John Stuart Mill, the Problem of Deduction, and the Claim That Information Cannot Be Accumulated with Certainty

The text presents John Stuart Mill’s challenge to deduction, according to which the necessity of the conclusion is only relative to the premises, while the general premise itself (“all human beings are mortal”) is known by induction and is therefore not certain. The text states that from this it follows that the deductive conclusion cannot receive a higher value than the premises on which it is built. The text distinguishes between the necessity of derivation from the premises and the impossibility of arriving at a factual claim about the world by purely deductive means. The text sums up that information cannot be accumulated by deductive means, and that someone who is content with deduction “will die with the same information he was born with,” because adding information requires analogy or induction. The text brings this back to the problem of the synthetic a priori and asks how information can be accumulated reliably if not with certainty.

Reliability Instead of Certainty, Hume’s Problem, and Control Mechanisms for Non-Deductive Inferences

The text states that there is no accumulation of information in a certain way, because certainty exists only in deduction, and deduction does not add information. The text presents Hume’s question about the justification of induction and analogy, and the circularity involved in trying to justify induction by means of induction (“until now it has worked”). The text argues that Hume’s problem of induction cannot really be answered, and that what one can hope for is to develop control mechanisms that will regulate non-deductive inferences. The text defines the goal as finding a substitute for certainty in the form of reliability and partial logical justification that will prevent arbitrariness and the drawing of absurd conclusions.

The Nazir Rabbi and the Hermeneutic Principles as a Controlled Inductive-Analogical Logic

The text attributes to the Nazir Rabbi the claim that the hermeneutic principles are a systematic control mechanism for halakhic midrash, that is, a “logic for the accumulation of halakhic information.” The text argues that such a system cannot be deductive, because then it would not expand information and would not allow halakhic control over the broad domain of life. The text formulates the need for a system of rules that permits expansion through analogy and induction but with control, and presents this as an effort toward a “quasi-logic” based, as far as possible, on minimal agreed-upon assumptions. The text raises the apparently paradoxical difficulty of logically controlling processes that are not logical in their essence, but concludes that good control rules can be reached even though some element of assumption will always remain.

The Context of Discovery and the Context of Justification in Hans Reichenbach

The text presents Hans Reichenbach’s distinction between the context of discovery and the context of justification. It states that the emergence of a scientific theory is a wild and uncontrolled process, and that there is no point in, and no possibility of, rejecting a theory because of the source from which it emerged—even if it came from a dream or from Elijah the Prophet—because what matters is testing it afterward. The text states that science is concerned with the context of justification: how a theory is tested, how theories are sorted, and how one chooses among them. The text sharpens the point that in building a theory there can be infinitely many possible constructions from the same data, and that there are philosophers of science who say that the question “which construction is the correct one” is meaningless. In the course of the discussion there appears a sharp rejection of positions identified with “Kuhn and his gang,” with the claim that they can be shown statistically to be wrong.

A Classification of the Hermeneutic Principles: Logical vs. Textual, and the Concept of Pirkha

The text notes that only a very small minority of the Sages’ derashot systematically use hermeneutic principles, and it prefers to focus on Rabbi Ishmael’s thirteen hermeneutic principles as a familiar framework. The text divides the principles into two kinds: logical hermeneutic principles such as kal va-homer, binyan av (from one verse and from two verses), and two verses that contradict one another until a third verse comes and decides between them; as opposed to textual principles, where the trigger is linguistic-textual, such as gezerah shavah and general and particular. The text states that in textual principles the generalization or comparison is made not because the interpreter thinks it is correct on the basis of reasoning, but because the Torah “instructed” that it should be done by means of the formulation of the verse or an identical word. The text argues that therefore, regarding general and particular, “there will never be a pirkha” in the literature of the Sages, because pirkha belongs to reasonings that examine similarity and stringency, whereas here the textual instruction bypasses the requirement of similarity. The text explains that textual principles are needed precisely where the logical principles get “stuck” because of pirkha, and therefore pirkha is an essential concept for understanding the role of the textual principles, including the rule that if a gezerah shavah is not focused, “there is room to refute it,” because in that situation it goes back to functioning as an analogical comparison rather than as a formal gezerah shavah.

I finished dealing with Kant’s analytic and synthetic categories, and in the end the claim was that there’s supposed to be some kind of category in between. We called it the synthetic a priori, between thinking and cognition, between logic and invention, let’s put it that way, or between interpretation and legislation. Right, all those pairs—we saw that they’re basically equivalent, and in every context where this appears, what comes up is that there has to be some kind of intermediate category. And the claim was that the hermeneutic principles are the appearance of this intermediate category in the context of halakhic interpretation. And that’s what is called derash. Derash means drawing conclusions from the verses in a way that on the one hand is not deductive, and this is not interpretation in the simple sense of the word, but it’s also not legislation, not a new invention. Rather, there’s something here that takes the spirit of the verse, somehow expands it in a certain way, and that is basically the hermeneutic principles. So it’s not surprising to discover that the character of the hermeneutic principles, their logical character, is not deduction but analogy or induction or things at least of that type. Because it has to be something between deduction and free creation or invention. The criticism of using these principles—for example, the criticism of Gersonides—is a criticism that basically says: this is just invention. So it can’t be. Clearly all the principles, all the derashot, are supporting derashot, because otherwise what does it mean—just some invention unconnected to the text? You can’t take that seriously. On the other hand, the Orthodox answers to that criticism hang on the claim that if we understand this all the way through, then in the end this is just logic, mathematics. In other words, we have certain rules, a certain code, and someone who knows how to use it can derive conclusions from the verses in some deductive way. We just lost the ability to use it; we lost that information. But on the principled level this is deduction. That’s basically the argument between the two sides regarding the hermeneutic principles, and it is exactly the same argument as between the two sides in philosophy of science and philosophy of law and in all the contexts I spoke about. And in all those places it seems to me that both sides make the same mistake: they assume there is a dichotomy, that it has to be either this or that, when in fact there are intermediate situations too.

To define this a little more, I’d say—we talked a bit about deduction, induction, and analogy? I don’t remember anymore. Yes? That is, analogy is basically built out of induction and then deduction. I’ll go over that briefly now. Usually in the philosophical or logical tradition it’s customary to distinguish between three types of inference. One is called deduction, which is going from the general to the particular. Right: all human beings are mortal, Socrates is a human being, Socrates is mortal. Analogy is going from particular to particular, or from general to general—that is, between two things neither of which includes the other. If this frog is green, then apparently that frog is green too; that’s some kind of analogy. And induction is going from the particular to the general. That means I know one particular or several particulars, and from them I infer some more general conclusion about the group that contains those particulars, the whole group that contains them. That is going from the particular to the general. In principle there are no other possibilities. Either you go from the general to the particular, or from the particular to the general, or between two things where there is no relation of particular and general. It could be, for example, if I say: if this frog is alive, then apparently all horses are alive too. What is that? Analogy, right? Even though I’m going from a particular to some generality, I’m going to a generality that doesn’t contain this particular. Induction is always going from a particular to a more general group that contains the particular. That’s called induction. In other words, seeing the particular as some kind of representative sample of the whole group. But when I go from something to something that does not contain it, even if one is general in character and the other is particular in character, that’s analogy. Okay? That should be clear.

Apparently these are the three possible modes of inference. There aren’t any more. General to particular, particular to general, or neither this nor that. And those are the three possibilities. Deduction? Deduction is from the general to the particular. And of course deduction is a necessary inference. We already talked about the fact that its necessity comes from the fact that it doesn’t give us new information, it doesn’t add new information beyond what is in the premises. That is, anyone who accepts the premises must necessarily accept the conclusion as well. Because the conclusion is already contained within the premises. If you don’t accept the conclusion, then in fact there was already some problem in your premises. When I say that all human beings are mortal, and Socrates is a human being, anyone who won’t accept the conclusion that Socrates is mortal also has some problem with the premise that all human beings are mortal. It’s not true that he accepted the premises. He didn’t accept the premises, because the conclusion was somehow already there in their content. Okay? Therefore this is basically a necessary argument.

What about the relation between the other two arguments, analogy and induction? Which of them is stronger, which is weaker? What do you say? Induction is stronger? Do you agree? Why? Stronger, more convincing, more likely to be correct. You say analogy. Try to explain. Now I understand the question. “Stronger” can be understood in two ways. Stronger meaning it gives me more information, or stronger meaning more certain—which of course are two opposite things, as I’ve been saying all along, that the more information there is, the less certain it is. So sorry for the careless wording. I mean: which is more certain? Deduction? No, deduction is the most certain. Between the other two? Analogy. He’s asking in Hume’s terms: analogy—and Hume himself, even though he didn’t raise this in the Treatise of Human Nature, in The Natural History of Religion he does reject it. Why? Why is it better? Because when you move from the particular to the general, you always rely on some assumption; the question is what makes it a law rather than an accidental generalization, what makes these particulars non-accidental. But when you make an analogy, that basically means there’s no secure line you can build—you’re suspended between two lines or three lines or something like that.

Look, there are considerations on both sides. A consideration in favor of… it’s a bit hard to understand the difference between induction and analogy, because after all analogy—when I say this frog is green so that frog is green too—I just made a kind of simplistic induction and said: there are two frogs, one is green, so the other is green too. So let’s talk about a frog and horses, okay? If the frog is alive, then apparently horses are alive too. But what is that? Analogy? Between two different things. Fine, analogy between two different things—I’m making an analogy between two different things. I’m saying there are considerations in both directions. The consideration in favor of analogy is much simpler. Analogy is less speculative, right? You take less risk. In other words, the claim, the information you add by means of analogy, is one particular fact. Either you’re right or you’re not, but the risk is a small risk. When you infer a conclusion about an entire aggregate, you infer a conclusion that all horses are mortal—you’ve said something very strong. Strong in the sense that it contains a great deal of information. Once it contains a great deal of information, apparently there’s a greater chance you’ll be wrong. It’s enough for there to be one horse that isn’t mortal and you’re wrong. Right? So apparently the inductive argument takes a greater risk. That is, it contains more information and therefore it is less certain. And again this is the principle of the tradeoff between the amount of information we accumulate and the degree of confidence we have in that information. The more information we accumulate, the less confidence we have that this information is correct. The less speculative the inference is—that is, the fewer claims it makes, or the less general its claims are—the more confidence I have in it. It takes fewer risks. Okay? That’s one side.

On the other hand, as you said in Hume’s name, in induction there is something that connects the particular to the general, unlike analogies. When I say this frog is mortal, therefore all horses are mortal—the frog is not a particular from within the group of horses. Yes, but in analogy too there was some connecting line there; we didn’t say tables are mortal. Okay, so in just a second I’ll get to that—you’re right. In analogy too you find some connecting line. Right. So in just a second. I’m simply repeating what you said in Hume’s name earlier. The claim is that when I say a frog is mortal and therefore all horses are mortal, there is something very weak here because the frog is not a particular from within the group of horses. In contrast, if I infer conclusions about all frogs, for example, that’s stronger because the frog is a sample of the group; it belongs to the group. But that argument isn’t right. That argument isn’t right because when you look at analogy a little more sensitively, you see that analogy is always hiding an induction behind it. Always. Right? When I say—what you remarked earlier—when I say this frog is mortal and therefore all horses are mortal, implicitly what I actually did was some kind of generalization about, say, all animals, or all four-legged creatures if you want, it doesn’t matter, right, that they are mortal. And then of course I say that horses are mortal too because they belong to that group of four-legged creatures. Right? So actually there is some induction here too. I start from the frog and say: then all four-legged creatures are mortal, and now I go back down to horses and say: then horses are mortal too. What is that downward move? Deduction, right? It’s simply taking “all animals” or “all four-legged creatures are mortal,” and specifically horses are four-legged, so horses are mortal, right?

So the conclusion is that analogy is nothing more than induction followed by deduction. Right? Basically analogy is a combination, a chaining together: first induction and then deduction. When I say this frog is green, therefore that frog is green too, what did I actually say? There’s nothing special about this frog or that one; my assumption is about all frogs—or at least that’s what I assume. Maybe I’m mistaken and it is specific, but just a second—the assumption of the inference is that there’s nothing special about these particular frogs, but rather that if this frog is green then apparently all frogs are green—that’s induction. And after that I say: if all frogs are green, let’s do a deduction—then that frog is green too. So in fact analogy from particular to particular is a generalization of the first particular to a generality, a generality that contains both particulars, right? And then I descend by deduction from the generality to the second particular. So what comes out here is that there aren’t—just a second—really three modes of inference. There is only one, really: analogy, and analogy is merely a combination of two steps, the first of which is induction and the second deduction. If it’s from general to general, would it be the reverse? No, no—it would be induction to an even broader generality. It’s always like that. Yes, if I begin from some particular A and I want to infer property X, and there is a particular B and I also want to infer property X about it, because particular A has property X, therefore particular B has property X too. As you justly remarked earlier, I’m not doing this with just any particular; there has to be something common to these two particulars, otherwise why would I compare them? So actually there is some other hidden property here; let’s call it Y. Okay? Since this particular has property Y and property X, then apparently this particular, which also has property Y, will have property X as well. Right? But notice what this is really hiding. What it’s really hiding is that from this particular I made a generalization to all bearers of property Y, that they all have property X, and in particular this thing too, which is one of the bearers of property Y, and therefore it too has property X. So in fact the move from particular to particular is done in two steps: the first is generalization and the second specification. Okay?

So who guarantees that from something like that you won’t reach complete nonsense? Right, with analogies you can reach a lot of nonsense, and with inductions too. You see one horse that is brown, and you say all horses are brown. So then say all animals—the frog is brown—that isn’t true. Exactly, that’s the point: this is not a necessary argument. That’s the problem with analogy and induction—that unlike deduction, the conclusions are not necessarily correct, or certainly don’t necessarily follow from the premises. Yes, I said that objectively, as a matter of fact, with respect to arguments for God’s existence and in physics, we’re prepared to accept proofs that involve induction and deduction, but we aren’t prepared to accept analogical proofs, because in analogy your cards aren’t on the table, and therefore this isn’t really a logical proof in the sense that you’re making a generalization but you’re not… you can always lay them on the table. In fact analogical proofs sit within rules that simply haven’t been unpacked. That is, if we even take halakhic midrash, we know that since Scripture opened up the big generalization for us, then it remains. No, that’s obvious—but behind it there does sit some kind of generalization. Okay, so you’re saying it has to be unpacked, but after I unpack it… okay, so you’re saying it has to be unpacked, but after I unpack it, it’s the same thing. The very concept of analogy basically says: I’m not unpacking it. No, why? Do you understand what we’re talking about? Why? I make an analogy from one frog to another frog. Everyone understands what the generalization is even though I didn’t say it. When you make an analogy that says, “If one man’s ox gores the ox of his fellow,” you say that a biting dog also has to pay. Everyone understands the analogy. The analogy is that whatever is someone’s property and causes damage, I have to pay. Nobody writes out that analogy, but it’s obvious. Maybe it’s… on the contrary, the Talmud reaches—the Mishnah reaches afterward—the common denominator among all of them, that it is your property, its supervision is upon you, and when it caused damage, the damager is liable to pay from the best of his land. So in the end the Mishnah makes that general conclusion, but it was already completely obvious at the analogy stage. And that… I think that’s correct. You’re saying that where there is no induction behind the analogy, then it simply isn’t a valid analogy. Fine—not valid, valid in the sense of analogy; it’s not a good analogy. Okay, I agree. But many times we make analogies—in most cases we make analogies—when some generalization sits behind them.

Now, when the Sages made an analogy and I don’t know what generalization stands behind what they did, that doesn’t mean they didn’t have such a generalization. I don’t know how to unpack it, because I’m not the Sages; I also wouldn’t have known how to make the analogy. But if I am the one making the analogy, then behind my analogy there sits a generalization, and that generalization I can usually unpack too. So why… so why is it treated as an analogy and not simply as a generalization? I don’t know—ask the people who treat it that way. I don’t… I don’t treat it that way. For example, the watchmaker proof: if the watch is ordered, and when you see every part you see that someone arranged it, the world is ordered, so apparently there is someone who arranged it. That’s Paley—the watch of Paley. Paley’s watch. It’s poor, it’s very poor as an analogy, and it’s not… now I’ll unpack it for you. This watch is ordered, and since this watch is ordered, therefore everything on earth has to be ordered, including the earth itself. And since that is so, the earth too is ordered. There, I unpacked it. How does that help? That every single thing on earth and the earth itself are… they’re not exactly… they don’t function the same way; that is, no one is prepared to say that statement, that every single thing on earth also includes the earth itself… If it’s ordered, then it’s ordered. What’s the problem? Yes? Why is nobody prepared to say it? There—Paley said it. What, that every single thing on earth includes some form of governance…? Yes. What’s the problem? It’s meaningless. No, I’m saying again: you may disagree with the analogy because you don’t agree with the induction at its base. But the fault of the analogy is not that it’s an analogy. At its base sits an induction. What you don’t agree with is the induction. No, I’m only saying that the fact that people use this tool and not that tool is not because it saves words, but also because people… there is… it gives something or hides something that you can’t manage to… Clearly, that is no doubt true. It is much better to do things explicitly and not jump over steps and not formulate them or not attain them. But it’s not for nothing that people don’t do it that way. They don’t work by means of induction… Why do you say they don’t work? They don’t work, meaning there are analogical arguments and that’s all. No—if they are analogical and that’s all, then they’re worth nothing. They’re worth nothing. Only if an induction sits behind them. Whether you unpacked it or not—that’s more of a methodological question. But if there is no induction behind it, then what is the analogy based on? After all, an analogy has to be based on some similarity between the two things. That similarity is the group of the induction. It always defines the induction group. You can… you know how to state similarity without defining induction. That’s the point. You can’t really… No, you don’t have to define the group explicitly. No, that’s already another question. There are two ways to define things in logic. But if you can’t define the thing, then… then there’s no induction. I don’t know how to define what all the objects in the world are, but everyone understands what all the objects in the world means when I make an induction. I’m not sure anyone knows how to define what mass is, but everyone understands when I speak to him about mass, he understands what mass is. Inability to define is not… not necessarily a limitation. You always start from some system of concepts that you did not define. Every definition also uses some system of concepts, so definitions always have to begin from some conceptual system that you don’t define. It’s always like that; otherwise it would be circular. Right? Every language has to be built on some system of words that don’t need to be defined. Otherwise… otherwise you’ll simply go in circles.

Yes, the problem in analogy is the hidden third element, which really we don’t know. That is, we infer that it belongs to Y… Not the third element—the group. The group, yes. And in a gezerah shavah, where there are only two elements, I solve that problem, because really the Sages… we don’t… there aren’t other things in… there aren’t other elements in the group. It isn’t a group. It’s just these two elements. That’s it. No, obviously, but gezerah shavah isn’t analogy in the simple sense. We’ll get to that. Gezerah shavah is not analogy in the simple sense, because you’re not doing it on the basis of similarity between two things. You’re granted that there is similarity between two things; you don’t infer that there is a relevant similarity between two things. You understand? It’s something else. When you do a binyan av, a binyan av is analogy in the ordinary sense. Okay? But gezerah shavah—when you say “for her” “for her” from woman—that’s not because you saw something similar between a slave and a woman. The Torah says—yes, it is a law given to Moses at Sinai, this hermeneutic principle, gezerah shavah. So gezerah shavah is given to you and gives this to you as a datum that woman and slave are alike. In that sense there is some kind of deduction here. Because actually you didn’t insert any speculation here. You were given that there is a similarity. Given that there is a similarity, everything you derive from it is already almost deduction. Okay? The degree of freedom enters in the question of what to derive. That is, which laws are relevant and which laws are not relevant, and whether to derive it and apply it there, or derive from it and not from it, and all kinds of… there is a degree of freedom for the interpreter, but not in the very inference from the fact of similarity. That is given.

Where does the given fact that there is similarity come from? Gezerah shavah. There is a hermeneutic principle that came down from Sinai called gezerah shavah. That principle tells us that where the same word appears in two contexts, I need to compare those two contexts in their laws. So that means I did not make the comparison because I saw some similarity between the two contexts. I am given that there is similarity between the two contexts. I see no connection between a woman and a slave, but in the Torah it says “for her” here and “for her” there, so the Torah gave me the similarity. I didn’t make an induction here. The induction was already given to me. I can skip the induction. But why specifically “for her” and not somewhere else where it doesn’t say “for her”? That’s another question—that already has to do with the rules of interpretation. So really in gezerah shavah, at least in the simple sense—we’ll talk about it—but in the simple sense, a person does not derive one unless he received it from his teachers. That is, as though everything was given in the tradition, even which words to derive from. Sometimes there are disputes about it, of course; each one received differently. Right.

Basically analogy does not come to state the induction and deduction. Basically induction and deduction are taken for granted. Rather, it comes to say: I state the analogy when I want to say that the other element too is inside the group that I’m in. The example the rabbi gave—this frog is green and that frog is green too—it’s obvious that they both belong to the group of frogs. Obvious. But suppose I say this frog has bright colors and this plant has bright colors, then I’m pointing out that this plant belongs to the group of things that grow in jungles and tropical regions, and that there is some property of things that grow there, whether being green or having bright colors. Very good, but still behind this there is some kind of induction. What? Behind it there is some kind of induction. But my purpose is not to state the induction and deduction. Leave purpose aside; purpose is already a subjective matter. I’m asking what this inference contains, not what the speaker’s purpose is. The speaker’s purpose can vary depending on the speaker; that doesn’t matter to me. When I examine the argument, I want to examine what this argument contains, what its flaws are, and what its advantages are. The argument as such—your purposes, everyone can decide for himself what his purposes are. Okay?

There is an objection by John Stuart Mill to deduction. Mill claims that deduction too is basically not a necessary inference, because you can’t say that the statement “Socrates is mortal” is a statement that is necessarily true. It is necessarily true only on the basis of the premises—that all human beings are mortal and that Socrates is a human being. But how do you know the premise that all human beings are mortal? Have you seen all human beings? Even among those you’ve seen, some are still alive. Until now it worked that way. Until now it worked that way. So how do you know there isn’t a human being you haven’t seen who’s been alive for two thousand years? That’s induction. Right? Meaning that at the basis of every deduction there sits an induction. Basically every deduction begins with some major premise and minor premise. Right? All human beings are mortal—that is the major, general premise. Socrates is a human being—that is the particular premise. Conclusion: Socrates is mortal. So there always has to be some major premise, because it determines the group from which I go to the particular, the generality. But how do I know the information I have about the generality? Because you went over most of them. So that’s induction. The question is whether this is a closed or infinite group that I can go through all of. No—if you can go through all of them, then you’re right, but then it isn’t interesting. Because then you simply… you already know that information explicitly. So yes, you’re right, but it’s no longer really interesting. That’s not true—knowing explicitly isn’t right. Knowing explicitly is what’s called begging the question. That is, Abraham with the hat—we already talked about that funny example, the proof that every person has to walk around with a hat. Why is that begging the question? It’s begging the question because the conclusion appears explicitly in the premises. But if you can extract the conclusion by means of all kinds of intellectual maneuvers out of the premises through complex means, I wouldn’t call that begging the question. For example, you wouldn’t call all of geometry begging the question and pointless study, right? Even though in fact all the conclusions are hidden in the premises, since it’s hard to get them out of the premises. It’s not trivial. Even though after you see it, you understand that it was there, it’s not trivial to get it out. So in this case I say: it’s not that I knew it explicitly, the proposition in geometry. When I knew the axioms, I knew it in some implicit way. It was included within what I knew, but I didn’t know it explicitly. The function of deduction—just a second—the function of deduction is to turn implicit knowledge into explicit knowledge. But if you apply deduction to explicit knowledge, then what’s the point of doing it? It’s correct, but pointless. Okay?

According to Mill, is deduction arbitrary? What do you mean arbitrary? Why arbitrary? Because it seems to be built on something you accept as an axiom. Then on the contrary, that’s not arbitrary, it’s… because my premise is an axiom. That’s exactly what Mill is arguing. Mill is basically saying that you can’t say deduction is the most necessary inference because it itself is built on induction. In other words, what is necessary in deduction is the consequence of the conclusion from the premises. But about the conclusion as such you can’t say anything as long as you don’t know what’s going on with the premises, right? And the premises you know only by force of induction. No—not arbitrary, but not deduction; rather, by force of induction. Something that is not certain. Not certain and arbitrary are not the same thing. Something that is not certain, okay? So therefore you can’t give the conclusion of a deduction any higher standing than the premises on which it is built. If you assume that deduction comes from induction, then you’re assuming something arbitrary… No, that’s beside the point. If you assume it arbitrarily, then it’s just nonsense. When you say arbitrary things—I’m talking about information. You can create whatever you want, but then you created a fictional world, a world that doesn’t really exist. Can you base all of geometry on intuitive assumptions? Whoever wants can come along, but then it’s really arbitrary. You can do whatever you want—no problem. There are many who understand mathematics that way: that its premises are basically arbitrary, and they do not claim they are true. The point of mathematics, then, is to show what follows from this set of arbitrary premises. Fine, okay. But then it’s just an intellectual stunt and no more. When I’m talking about claims—claims about the world or information I accumulate—then obviously I can’t begin from something I just decided to assume arbitrarily. It’s something I think is true. The question is why I think it’s true. So if it’s a general proposition, it’s likely to be by force of some induction. Okay. Think or believe? Think, believe—what difference does it make? How do I assume it? I don’t know. Let everyone answer for himself how he assumes. According to the conditions of logic? There are no logical conditions here. That’s exactly the point. You present it as a premise. You arrive at premises however you arrive at them. Each person however he arrives. There are no rules for that. Deduction deals only with the consequence of the conclusion from the premises. The premises themselves each person infers however he infers them.

So what Mill is basically claiming is that it’s not correct to attribute to deduction any power beyond induction and analogy, because the conclusion I reached by deduction basically sits implicitly on induction. Now, that is true of the conclusion I reached by deduction. It is not true of the consequence itself. The consequence of the conclusion from the premises is of course necessary. There you don’t need induction or anything. But when I speak about information, meaning some claim—not an “if… then” claim, but a true claim, a factual claim, a claim that says something about some state of affairs in some world—okay? A claim of that kind, there is never a purely deductive way to arrive at it. Never. Since any inference whatsoever, if I derive it through deduction, it comes out of some more general proposition. Then I’ll ask: how do I know that more general proposition? And so on, until I get stuck and say, okay, that’s induction. In other words, you cannot accumulate information by deductive means. Which is what I already said. Okay? There’s no such thing. If someone wants to accumulate information, gather more information beyond what he had before, he has to use analogy or induction. He can’t make do with deduction alone. Someone who wants to make do with deduction alone will die with the same information he was born with. He can’t accumulate information. Okay.

So in light of this discussion, this basically means we have a problem, and this is the problem of the synthetic a priori again. So how do you in fact accumulate information reliably? Because certainly, with certainty, we already know the answer is no. You do not accumulate information with certainty. There’s no such thing as accumulating information with certainty. Certainty is only deduction. Deduction never adds information. It is impossible to accumulate information with certainty. I’m saying fine—not with certainty, but at least not arbitrarily. Let there be some logical control, some degree of reliability, for the inferences I use. Yes, all of Hume’s questions basically started from this: how do you know induction is correct, how do you know analogy is correct, causality, all kinds of things that we assume when drawing conclusions, even though they themselves have no real justification. So the big question that really troubles philosophy of science and also hermeneutics and interpretation in law and in Jewish law and anywhere there is interpretation, is really the question of reliability as a substitute for certainty. Meaning: if I now want to give up the exclusivity of deductive inference and accept non-deductive inferences too because I want tools that add information, then how do I make sure I’m not just talking nonsense—meaning, not just doing arbitrary things? Who said there’s anything real to analogy and induction at all? And as Hume himself already described, there are those who answer this question by induction. They say: until now it worked, so apparently it’s fine. But that itself is induction. When you ask a question about induction, you can’t use the principle of induction to answer it, right? Therefore they ask you: what guarantee is there that next time it will work too? That’s the same question, right? Therefore you can’t base it on induction. There is something somehow circular here.

So I’m saying: to answer Hume’s problem of induction directly, it seems to me, is impossible. Impossible. At most, what we can hope for is to try to develop control mechanisms that will monitor non-deductive inferences. Okay? When I make a non-deductive inference—if I make a deductive inference, I have control mechanisms. There is mathematics, there are very rigid mechanisms by which I can check whether I worked correctly or incorrectly. There are very rigid tools that check whether I worked properly or not. The question is what happens with induction and analogy, with the non-… with the non-deductive inferences. Are there any tools there to evaluate our inferential system?

Now, the Nazir Rabbi claims that the hermeneutic principles are such a system. The hermeneutic principles are a kind of logic for accumulating halakhic information. That is, some system of rules that gives me systematic control over midrash, over expansive interpretation in the area of Jewish law. When you derive one law from another law or from a verse by some non-deductive inference, as we said earlier, how do you know it’s correct? How do we make sure we aren’t just doing whatever comes into our heads? For that purpose we were given some kind of system of rules. But notice: these rules are not deduction, because if they were deduction, once again we’d be back where we threw the baby out with the bathwater, because then we could never accumulate information that way. We need a system of rules—like Maimonides, as we showed in Maimonides—a system of rules that expands the information we have in hand, so that if there is information in the Torah, with these rules I arrive at broader information, not just uncover what is already inside it. In other words, I need some kind of system that touches analogy and induction. But this system is fairly detailed in the world of the hermeneutic principles, and the Nazir Rabbi claims that there is some kind of schema here, some kind of system of rules that provides more systematic control over analogies and inductions.

If it isn’t a closed system, basically? Because just as you receive this one, someone else can receive another closed system. We really received this one from Sinai. Maybe I wouldn’t have thought of some of these things on my own. Okay. But isn’t it legitimate for someone else to say he accepts a different system? Why is expansion mandatory? It isn’t mandatory. But if the Holy One, blessed be He, wants us to expand, and wants us to have some kind of control so that we do it properly, then He has to give us some kind of system to help us control it—an inductive logic. What is the meaning of this expansion? Like in science—what is the meaning of expansion in science? You see, you do an experiment on one body that falls toward the earth because it has mass, and you infer that all bodies with mass fall toward the earth. That’s expansion—you added a huge amount of information in that generalization. Right. There you don’t ask what the meaning of expansion is. There, in that case, I don’t have a system within which I can derive by deductive means. Here we do have, I think, such a system—it just isn’t formulated. There have been attempts; Francis Bacon tried to sketch some outline of an inductive logic, but that usually remains at the level of words. I didn’t say… I said that in nature, in the world of science, I don’t have a system within which I can derive using deductive tools. In the world of Torah I do have a deductive system: the Torah. In the Torah there are no general principles. I can derive them by deduction all the time. Apply deduction all the time and you won’t get anywhere. I’ll arrive at the whole Torah, as many sages could tell you. You’ll get almost nowhere. No—there are almost no rules in the Torah. The Torah does not operate with some set of general principles. What? I’ll derive deductively what necessarily follows from here to here to here to here, and in the end I’ll create a system. Fine, very good. So I’m saying you’ll reach a very short range, but the Holy One, blessed be He, claims that Jewish law is supposed to govern a broad domain—a broader domain of our lives. It has to give us more instructions than you can reach that way, and therefore He found it necessary to give us tools to expand what is in the Torah. That’s the claim. Why didn’t He give us the tools to begin with? I don’t know—that’s a theological question. I’m dealing now with logic, not theology. Really, I mean, I don’t know. I have no idea. But if the assumption is that there really is some system of expansive tools here, then I understand what it is for. It is meant to control our non-deductive inferences, so we won’t infer nonsense.

But that sounds a little self-contradictory. Because what does it mean to control non-deductive thinking? Usually when we think of control, control means giving us a rigid tool that tells us yes, correct; no, incorrect. But such a tool would by definition be a deductive tool, a logical tool. Yet if we want to formulate some logic-like system that will describe our non-deductive modes of inference, that sounds a little self-contradictory. And indeed the attempts throughout history to do this have not gotten very far. That is, people said yes, check several parameters, make sure there are no irrelevant parameters. But what does relevant and irrelevant mean? There really isn’t… what? I’m not talking about the path of the result; I’m talking about the path now, not the result. The result one can seemingly check—measure and see. But I want there to be control over the path, because otherwise if I now start proposing infinitely many theories, and each such theory will have to be checked in a laboratory experiment, we’ll get nowhere. There are infinitely many theories I can propose to you about anything. I want some kind of control over the theory, over the very creation of the theory, even before I test it in the lab.

And maybe this is the place to note the distinction made by the philosopher of science Hans Reichenbach. He distinguishes between the context of discovery and the context of justification. And this is a very accepted distinction today among philosophers of science. The claim is basically that when a scientific theory comes into being, that process is one over which there is no control, can be no control, and we have no interest in how it happens. If the scientist comes and says: my grandmother appeared to me in a dream and told me that all the planetary orbits are ellipses and not circles, as the Greeks thought—fine. Then let’s test it and see. If it stands up to the test, excellent. No, no. But we have no indication, and therefore no control and no possibility of rejecting a theory simply because it came from a dream, or Elijah the Prophet, or wherever you like. That is called the context of discovery. What science—and also philosophy of science, by the way—is concerned with is only the context of justification. The context of justification means: given a theory, how do I test whether it is correct or not? What is the scientific method for checking this? I put it to the test—how do I sort between theories, how do I choose which theory to prefer—but the formation of the theory is a completely uncontrolled process. This is accepted, at least among many philosophers of science. Because really, how can you explain how the scientific generalization is formed? That’s a matter of inspiration. From a set of data, from facts, there can be infinitely many generalizations. So any such generalization could be. How was it formed? I simply chose one—what difference does it make? Now we’ll see which of them stands the laboratory test. That is called the context of justification. We need to justify the theory. To discover the theory or create it is a completely wild process that lies outside the domain of logic, of philosophy of science, and certainly of science. Okay? There are those who would call this scientific genius: to hit upon the right theory, because there are no justifications and no path and no controls and nothing here. Okay?

Is this similar to deriving research hypotheses from theory? What is a research hypothesis? Is that deduction? What is it? I don’t know—tell me what you mean by a research hypothesis. In the ordinary framework of social science research, you have a theoretical and research literature review, and then now it’s usually some kind of phenomenology. I want to examine whether this parameter affects that phenomenon. That’s phenomenology; that’s not theory at all. Theory comes after the experiment. I then ask myself: I discovered now, statistically at least, that this parameter affects that result or phenomenon. Now I ask myself why. And then I build some kind of theory, some theoretical construction from which I can show why it affects that. That is the theoretical process; that is the context of discovery. Now with respect to that context there is no way to carry it out systematically. Not with measurements, not with statistics, not with philosophy, not with logic, not with anything. Because I can build countless constructions from which this connection would emerge. And the question which is the right construction is one that many philosophers of science say is meaningless altogether. Okay?

So there is something here that appears, on the face of it, problematic, if not even paradoxical: trying to create logical controls for processes that are in essence non-logical. Okay? The question what the correct construction is is one that many philosophers of science say is meaningless altogether. Okay? So there is something here that appears, on the face of it, problematic, if not even paradoxical: trying to create logical controls for processes that are in essence non-logical. Okay? That is basically the point.

Now look, there are no miracles. I also don’t intend to perform miracles anytime soon, as far as I know. But what I want to show is how far one can nonetheless get with these controls. In the end there will always remain some dimension that is simply assumed. That is, I won’t emerge from a vacuum and arrive at conclusions. I don’t know how to do such a thing. But I do think I can show that from very, very minimal assumptions—assumptions agreed upon by almost every human being, it seems to me—you can derive very good control rules for inferences that are analogies and inductions. Okay? That is basically the goal, the framework. Within that I… it’s all built on Aristotelian principles, right? That is… No, no—on the contrary. I’m not building on Aristotelian principles, because they are responsible for deduction. And what I want to do now for analogy and induction is what Aristotle did for deduction. It has nothing to do with Aristotle at all. On the contrary, it is a completion of Aristotle’s work and in a certain sense something much more impossible. Because for Aristotle it was basically trivial; he only formulated what everyone understood. It’s not trivial to do that, but it isn’t something problematic in its essence, because everyone understands it. Isn’t logic based on those primary notions of Aristotle? Yes, logic is. But not what I’m about to do. This isn’t logic, at least not in the accepted sense. Okay?

So what I’m going to try to do now and onward—we’ll do this over some time—but from here on, what I want to do is really develop something that is logic-like. We’ll need to think afterward about exactly where the non-deductive facets enter here, because I got tangled up in that quite a bit. That is, why exactly is what I’m going to present to you not a completely rigid logic? But it isn’t a completely rigid logic. We’ll see that later and try to think afterward why. But it’s very important to me that you understand what I just said. That is, what the role of this matter is, how we conceive it, what its goal is, and how it should be evaluated. What it gave us and what it cannot give us. Okay?

I just don’t know what you want to call it, but at least what I think is that the branch that is a large part of philosophy of science from Hume to Kuhn has given many examples that even the stage of justification is a stage that can’t… that isn’t right, because you never know which data… Right, you can add ad hoc assumptions and you can make a million corrections… and they bring millions of examples where both are full of experiments that failed and succeeded, and in both they would find the same solution, the same… Right. I agree. I’m not entering those nuances because they’re too fine. No, but I mean—if one really wants to open it all the way up, then one reaches the conclusion that even so, science and all our forms of life are always an assumption that is based… No, I don’t agree at all. I really do not accept that sweeping conclusion of Kuhn’s. Not Kuhn—I didn’t only say Kuhn, also Duhem and… Doesn’t matter, what difference does it make? Kuhn and company. But okay, it’s at least an opinion within philosophy of science, and no less central—namely that you never… It is a no less central opinion, but an even more erroneous one. Obviously mistaken, in my opinion. I showed that, I think, in one of the previous classes with the graph, with the graph argument. It is simply mistaken. One can prove it is mistaken. Prove it mathematically, statistically—it’s not a philosophical question at all. It’s a scientific question. I don’t know why it’s a scientific question… maybe we’ll talk about it. But the claim whether Kuhn is right or not is a scientific question. I can prove scientifically that he is mistaken. It’s not a philosophical question. It’s a question in statistics. And therefore many philosophers hold that position, but they are simply wrong. Fine, okay.

All right, okay, so maybe before I really enter the thick of it, still a few words about the hermeneutic principles. What I’m really going to try to do now—well, before what I’m going to try to do now, I’ll give those few words, and then what I’ll try. The hermeneutic principles, as we said earlier, have to be inductive tools or tools for controlling inductive and analogical thinking. That is basically their purpose. They are divided into several principal types. Let’s talk about the thirteen principles of Rabbi Yishmael for the sake of discussion. Okay? Those are the main principles where there are principles. By the way, when you examine the Sages’ derashot in general, you’ll see that only a very small minority of them are derashot that use hermeneutic principles at all. Most derashot are all kinds of—I don’t even know what—but it isn’t a systematic use of hermeneutic principles. But in order to begin thinking more systematically, I prefer to go down the path that the Sages already paved. They already defined some system of rules, so I’m trying to understand it. One just has to remember in the background of the discussion that from the totality of the derashot we find in rabbinic literature, in my opinion not even five percent are derashot that make use of one of the hermeneutic principles—the thirteen principles or any explicit principle. Most derashot simply interpret, that’s all. They don’t formulate which hermeneutic principle they are using. Some of them use one but don’t formulate it, and in some I can’t even understand whether they are using a hermeneutic principle at all, or whether it’s something else, or perhaps another hermeneutic principle not written down—I don’t know. Okay? But we’ll focus on the thirteen hermeneutic principles of Rabbi Yishmael, because there at least one is proceeding on somewhat safer ground. Rabbi Yishmael told us there are such principles, so this isn’t just my speculation. So I prefer, when beginning the investigation, to go with something relatively known and from there try to expand, rather than starting in the less familiar corners.

These thirteen principles are basically divided, broadly speaking—you can divide them into two types. There are the logical hermeneutic principles, which include an a fortiori inference, the two forms of binyan av, from one verse and from two verses, and perhaps two verses that contradict one another until a third verse comes and decides between them. It seems to me that these four can be called the logical principles. The rest of the principles—let’s call them for the sake of discussion textual principles. Textual principles are principles where the inference is not built on reasoning but on a textual trigger. For example, gezerah shavah was mentioned earlier. Gezerah shavah—“for her” “for her” from woman—we compare a slave to a woman. That is not built on my seeing by my own reasoning that there is something similar between a slave and a woman. It is built on a textual trigger. Meaning: what prompts the derashah is an identical word that appears in these two biblical contexts. But then you apply reasoning. Afterwards, afterwards I ask what to infer from this similarity. We’ll get to that. But the trigger for the derashah is not a logical trigger but the text. Okay?

The same goes for general and particular. The three principles of general and particular—the same thing. When the Torah formulates itself in general-particular language and then returns to general language, then there is a hermeneutic principle called general and particular and general, and as a result I make some kind of generalization. But that generalization does not stem from what we usually call induction. Induction is when I understand that this frog represents all four-legged creatures, so I generalize to all four-legged creatures. That is built on reasoning. Here I make a generalization not because of my own reasoning, but because, in quotation marks, the Torah instructed me to make a generalization. How did it instruct me? It formulated the verse in a way that moves from plural language to singular language—general and particular and general, or particular and general, or general and particular, whatever it may be—and therefore I make a generalization not because I think this example is representative of something, not because I think this generalization is really true, but because the Torah instructed me to make a generalization. Where would the difference be? What? Also with regard to the Torah. No, that is certainly true, but even in the Torah itself. On general and particular and general there will never be a refutation. You will not find anywhere in all of rabbinic literature a refutation of general and particular. There isn’t one. What’s different about it? No, that’s something else—there are different traditions—but there is no refutation of general and particular. Why is there no refutation? Because what refutation are you going to make? Will you say, what about this case, which has such-and-such a property? Okay, so what? The Torah told me to make the generalization despite the lack of similarity. After all, if there really were similarity—if there were no refutation—I would make the generalization myself; that’s called binyan av. Right? I would make the generalization myself if there were no refutation, if there weren’t… Therefore, for example, when I make a comparison through binyan av or a fortiori inference, refutations can arise. Why? Because refutations show me that frog A and horse B are not similar. This is a horse and that is a frog. So what are you comparing? Therefore you can’t compare them. You thought they were similar; I bring you data showing they are not similar. But in the generalization—what? No, the opposite. They prove that your assumption that there ought to be an a fortiori inference here is simply incorrect. You were mistaken; it isn’t more severe than the other. There, I’ll prove to you that it isn’t more severe than the other.

But in a generalization that stems from general and particular, or in gezerah shavah, there are never refutations. There are no refutations because what will you say? About a woman, who perhaps has, I don’t know, different biological signs than a slave—so what? The Torah told me to compare a slave to a woman not because I decided they are similar. So even if you show me they are not similar, you have not refuted the gezerah shavah. The gezerah shavah is not built on their similarity. It is built on an instruction of the text to make a comparison, not because I really think there is a comparison. Or in general and particular. Regarding general and particular, the Torah tells me: generalize around these particulars to a broader group. We’ll still see exactly how, and how broad, and how exactly it works. But in principle, that is what the Torah is saying.

Now I have generalized to a broader group, and now someone comes and says: but there is a refutation. Not true—who said the general group resembles the particular in this respect? But here the Torah itself told me that I have to go to the general group. Not because it seems similar to me. The Torah itself said: move to the general group. So now even if I find a refutation, what difference does it make? The Torah gave me an instruction. Refutation is always directed against reasoning. When I proceed by force of some reasoning, in order to be responsible I have to check it. If I think horn damage is always more severe than tooth and foot damage, let’s see. Does that hold also on the moon, also in the public domain, in a karmelit, in I don’t know, every domain you want? Yes or no? One has to check, because that’s a hypothesis. If I checked and it works, I make an a fortiori inference or an analogy, a binyan av, something like that. If I checked and it doesn’t work, then it turns out that the comparison I wanted to make is apparently incorrect. I shouldn’t make it. But if I make the comparison not because I thought they were similar, but because the Torah said: make a comparison between slave and woman, then a refutation will not refute it. The refutation shows they are not similar—so what? I never assumed they were. Therefore by definition, principles whose basis is textual have no refutations.

Regarding particular and general—before the Torah’s generalization, it is clear to me, but logically speaking, just as you generalize from particulars, what kind of approach is that, to generalize from particulars? It’s an approach we use. From particulars you generalize. Right. So why shouldn’t it be the same before the Torah told me? No—there we have to understand exactly because of refutations. Right, we’ll see that later, exactly because of refutations. That’s why I’m giving this introduction. I’ll already tell you now what you raised. Look, the usual question is why in fact we need the principles of general and particular. General and particular are principles that instruct me to make a generalization. We’ll see this later. Okay? But I make generalizations anyway. I’m constantly making generalizations. We use induction all the time. We do not need permission from the Torah in order to make inductions. We are always using generalization. So why do we need principles here that instruct us to generalize? The answer is: because we are talking about places where there is a refutation. Where there is a refutation, I will not be able to make the generalization, because I think the group resembles the particular and the refutation shows me that it doesn’t resemble it, so I may not make that generalization. Then the Torah comes and says: ah, you wouldn’t have made the generalization without my instruction? Then receive an instruction to make it. And now if I bring the refutation, what difference does it make? The Torah said to generalize. What difference does it make that there is a refutation? If you manage to prove there is no refutation, that means this general and particular is unnecessary. We’ll have to expand even further, to the first place where there is a refutation. Always keep this rule in hand: the generalization of general and particular and general always reaches up to the first point at which there is a refutation. Without a refutation you don’t need it.

But in the Mishnah, when they say “all” and use “all,” after all—“all the…” and so on—we learn that it comes to include or exclude, I don’t know what. Is that similar or not? That too is a textual trigger. It says “all”—it comes to include. Because otherwise I don’t need instructions to include; I generalize all the time. Because there is probably a refutation. Again, it’s like “You shall fear the Lord your God”—to include Torah scholars. Shimon HaAmsuni went through the whole Torah and got stuck; we’ve talked about this several times. He got stuck. Why did he get stuck? Because he couldn’t find what could be included that resembles the Holy One, blessed be He. For that you need the word “et.” Because if there were no “et,” if this were a simple analogy, then I’d do it even without the “et”: just as the Holy One, blessed be He, so too Torah scholars. Why do you need the “et”? You need the “et” because there is a refutation. I can’t make a simple analogy. That is exactly why you need a textual trigger. So the textual principles always come in places where the logical principles get stuck. That is their role. They always do some work that the logical principles can’t do. Therefore the concept of refutation is very essential for understanding the hermeneutic principles, because the concept of refutation is what defines exactly why we need textual principles, why logical principles are not enough, when the logical principles in fact also serve us in other texts.

If gezerah shavah is a textual principle and not a logical one, and therefore in textual principles there are no refutations, then why in gezerah shavah, when it is not free for derivation, can one raise a refutation, and when it is free for derivation, one cannot? Because when it is not free for derivation, it is an analogy and not a gezerah shavah. When it is not free for derivation. Right. Gezerah shavah is only gezerah shavah when it is free for derivation. The rule of gezerah shavah says: you need to compare between two contexts only where there is the same word in both contexts, and only if that word is free for derivation. That is the rule of gezerah shavah. When the word is not free for derivation, it serves at most to draw your attention to the fact that there may be a similarity between the two things. But the comparison is made on the basis of analogy. And what is that principle called? Binyan av. And it turns into binyan av? Right. It is a binyan av where you might not have noticed the similarity. The novelty here is saying that the Sages used one expression in two meanings. Because gezerah shavah means that when you have two equal words you compare the two contexts. That is called gezerah shavah. But in the formal, logical sense of the hermeneutic principles, gezerah shavah is only when the words are free for derivation. Because—that’s exactly the point, and I think it follows very clearly from what I said—when the gezerah shavah is not free for derivation, then you are doing it on the basis of two words, but what you are really doing is a binyan av. Only why did the Torah write it with the same word anyway? Because maybe it was concerned that you wouldn’t notice the similarity, that you wouldn’t make the comparison on your own, so it gives you a hint. And after all we know from other texts too that when we see a similar word in two places, that can draw attention, make us notice that perhaps there really is some similarity between the two places, perhaps the author wanted to hint at something. Maybe yes and maybe no. If there is a refutation, we’ll say: fine, then apparently not. Okay? That’s exactly the point, because it is a binyan av and not a gezerah shavah. All right. Here, okay? And return these to the office too.