2019-04-22 – Between Midrash and Logic – Lesson 7

Table of Contents

• Synthetic a priori judgments and the laws of science
• Kant’s transcendental explanation and the description of the phenomenal world
• A critique of Kant and the claim that he empties the synthetic of content
• An intermediate faculty for generalization, and the straight line as evidence
• An analogy to the world of law and a critique of philosophy of law
• The hermeneutical principles in Maimonides as an intermediate halakhic level
• The example of “it is forbidden to bring in vehicles” and an extension that is not deduction
• Deduction versus induction, and analogy as adding information
• A fortiori reasoning, refutation, and the claim that it is not deduction
• Plain meaning and midrashic interpretation, the heap paradox, and degrees of syntheticity
• The intention of the legislator, the intention of the text, and the example of Rabbi Kook
• Hint, acronymic reading, and gematria, and the boundaries in relation to plain meaning
• Midrash as synthetic a priori as opposed to interpretation and legislation

Summary

General overview

The text reviews the Kantian distinctions between analytic and synthetic, and between a priori and a posteriori, and places the laws of science in the category of synthetic a priori because they make claims about the world but are not logically derived from observations. It presents Kant’s transcendental explanation, according to which science deals with the world as it appears to us through the tools of cognition, and then criticizes that view as emptying out the synthetic and turning the law into something analytic relative to our cognitive apparatus. Instead, it argues for the possibility of an intermediate faculty that allows generalization that is not pure deduction, and compares that faculty to a parallel intermediate level in law and in Jewish law, especially in Maimonides’ concepts of derash and the hermeneutical principles. The conclusion is that the hermeneutical principles are synthetic a priori tools whose essence is analogy and induction, not deduction, and a fortiori reasoning is brought as a central example of this through the very possibility of refuting it.

Synthetic a priori judgments and the laws of science

The text states that the laws of science are synthetic a priori because they do not arise merely from the facts, but add to them a general claim about the world. It illustrates this with Newton’s second law and argues that one cannot arrive at the relation between force and acceleration through analysis of the concepts alone, and therefore it is a synthetic judgment. It explains that observations provide only isolated measurement points, whereas the general law is like drawing a straight line through five points in a way that contains more information than what was actually measured. It formulates Kant’s question as a “question with an exclamation point”: how are synthetic a priori judgments possible, not whether they are possible.

Kant’s transcendental explanation and the description of the phenomenal world

The text presents Kant’s position that science does not describe the world as it is in itself, but the world as it appears to us. It argues that phenomena are perceived only after they have already been dictated and shaped by our cognitive and sensory tools, and therefore properties such as colors, smells, sounds, heat, and cold do not exist in the world itself, but are translations produced by our conceptual system. It uses the example of “if a tree falls in the forest” to argue that there is no sound without a listener, only, at most, pressure waves in the air. It raises the possibility of different brain wiring in which a person would “hear sights” or “see sounds,” and compares this to an oscilloscope that translates an acoustic wave into an image, in order to reinforce the claim that our description depends on our tools.

A critique of Kant and the claim that he empties the synthetic of content

The text argues that the Kantian explanation is not satisfactory because in practice it turns the synthetic a priori into the analytic a priori by including the cognitive tools within the analysis itself. It presents a critical formulation according to which Kant leads to the conclusion that if, in the world itself, acceleration were different from what the law dictates, we would not even be able to see it, and it argues that this goes too far and is implausible. It focuses on the difficulty of connecting the constraints of thought with the constraints of perception, and asks why a cognitive constraint regarding the law should also limit the ability to perceive a different acceleration. It argues that at that level of speculation Kant has no advantage over simply remaining with Hume, and it demands an explanation that offers an alternative rather than merely saying, “we know, and that’s that.”

An intermediate faculty for generalization, and the straight line as evidence

The text proposes a position according to which a person has the ability, through thinking, to accumulate information about the world—not as pure thought, and not as pure empirical cognition, but as something in between. It describes scientific generalization as drawing a straight line through experimental results, an act that is not merely “intellectual processing,” but a kind of cognition in which “I simply see in the world that this is the correct general law.” It presents this proposal as recognition of facts even if it does not amount to a full explanation, and argues that no other philosophical explanation really does more than that.

An analogy to the world of law and a critique of philosophy of law

The text presents an analogy between the scientific distinction and the legal distinction between interpretation and legislation, and places “legislative interpretation” or “judicial legislation” as a parallel intermediate level to the synthetic a priori. It argues that the dichotomy that forces us to classify every act as either legislation or interpretation fails to describe the situation as it actually is. It expresses a critical view of the field called “philosophy of law,” arguing that many of those who work in it are more jurists than philosophers, and it especially criticizes the status of Aharon Barak’s writing in the field as work that lacks engagement with substantive justifications and is philosophically problematic.

The hermeneutical principles in Maimonides as an intermediate halakhic level

The text argues that the hermeneutical principles are the appearance of the synthetic a priori within the halakhic realm, and that the same questions that arise in philosophy of science and legal theory return in relation to Maimonides. It describes Maimonides’ position that derashot “expand what is written in the verse” and do not merely uncover it, and therefore the question arises whether this is rabbinic or Torah-level, especially when Maimonides calls it words of the Sages. It draws a distinction between a decree such as the prohibition of fowl cooked in milk, which is not claimed to derive from the verse, and an interpretation or a law given to Moses at Sinai such as identifying “totafot” as tefillin; and then it places derash in an intermediate state that is neither enactment nor mere uncovering. It interprets “You shall fear the Lord your God” as including Torah scholars as an expansion of the spirit of the verse that goes beyond the language of the plain meaning, yet still remains connected to the verse itself.

The example of “it is forbidden to bring in vehicles” and an extension that is not deduction

The text gives the example of a sign in a playground saying “it is forbidden to bring in vehicles” in order to illustrate the difficulty of deciding whether a generalization regarding a scooter or a tank monument is interpretation, legislation, or some intermediate level. It argues that there is a situation in which one can extend the idea of the sign according to its spirit without claiming that this is exposure of a full literal intention and without establishing a new enactment. It states that this intermediate level cannot be a “logical derivation,” because logic and deduction always merely uncover what was already latent in the premises.

Deduction versus induction, and analogy as adding information

The text defines deduction as a tool that only reveals and does not add information beyond the premises, and therefore it parallels interpretation that merely uncovers. It defines induction and analogy as tools that add information beyond what is given in observation or in the premises, and therefore they are not deductive. It returns to the example of the scientific line in order to show that the general law adds information beyond the five measurements and therefore cannot be the result of deduction. It concludes that the hermeneutical principles, insofar as they add information beyond what is explicitly written, are expected to have the character of analogy or induction rather than deduction.

A fortiori reasoning, refutation, and the claim that it is not deduction

The text argues that a fortiori reasoning is not a logical-deductive argument, and brings as a central indication of this the possibility of refuting an a fortiori argument, whereas deduction is not refuted—at most, one discovers that there was an error in the inference. It presents an a fortiori argument concerning damages caused by an ox as an inductive leap in which one generalizes from a single case in the public domain, where horn is more severe than tooth and foot, to the general conclusion that horn is more severe in every respect, and then applies that in the damaged party’s courtyard. It explains that the refutation attacks this generalization rather than the original datum, and therefore the very existence of refutation indicates that the inference is not necessary. It distinguishes between ordinary a fortiori reasoning and “if two hundred includes one hundred,” which according to the Maharsha, second edition, in Bava Kamma is deductive and is not one of the hermeneutical principles by which the Torah is expounded; and it brings an example from Chaim Perelman about a law in Belgium that forbade selling two liters of wine but permitted three liters because of the purpose of the law, in order to show that even in “if two hundred includes one hundred” a purposive refutation can appear.

Plain meaning and midrashic interpretation, the heap paradox, and degrees of syntheticity

The text argues that the distinction between plain meaning and midrashic interpretation is not sharp in reality, and that speaking in dichotomous terms creates a difficulty similar to the heap paradox. It states that there are levels of plain meaning and levels of derash, and that the “degree of syntheticity” determines to what extent an interpretation is plain meaning and to what extent it is derash. It presents “pure types” for the sake of understanding: deduction as pure logic is pure plain meaning, and anything that is not deduction is derash—while acknowledging that in practice even plain-sense interpretation includes elements that are not pure.

The intention of the legislator, the intention of the text, and the example of Rabbi Kook

The text argues that intention can be included in a text even if the legislator was not aware of it, and identifies this as the intention of the law or the idea of the law. It brings Rabbi Kook’s words about the Sochatchover, in a letter to his grandchildren or great-grandchildren, about Rabbi Eliezer who heard from his teacher things “that no ear had ever heard,” including his teacher’s own ear, in order to describe a situation in which meaning emerges from the source beyond the awareness of the one who generated it. It argues that in relation to the Holy One, blessed be He, lack of awareness is irrelevant, but emphasizes that one need not rely on the omnipotence of the Holy One, blessed be He, in order to validate derashot; it is enough that the expansion is partially included in the text and is therefore binding.

Hint, acronymic reading, and gematria, and the boundaries in relation to plain meaning

The text presents the example of reading the word “grass” as “seven” by reversing the letters, and argues that this is at most derash, or perhaps even just a hint, and not deductive plain meaning. It notes that acronymic readings and gematria appear among the thirty-two hermeneutical principles of Rabbi Eliezer son of Rabbi Yose the Galilean, and are associated mainly with the aggadic context. It brings empirical examples about “miracle seven plus two minus two” and about studies of choice in jam sales in order to show that one can test patterns in reality, but concludes that this does not turn such manipulations into plain meaning, but at most into persuasion in the realm of derash or hint.

Midrash as synthetic a priori as opposed to interpretation and legislation

The text concludes that midrash is synthetic a priori in the sense that it expands beyond what is written, yet still makes a claim about “the Torah” as an analogue to the world—unlike legislation, which is not a claim about the Torah but the creation of a new law. It places interpretation as the measurement points and the written text, and midrash as drawing the line that generalizes beyond them. It ends by stating that the hermeneutical principles, even when they are the closest to logic, such as a fortiori reasoning, remain tools that are not deduction, but rather expansive inferences with an inductive or analogical character.

Okay, I don’t completely remember anymore exactly what we did last time. We talked a bit about the Kantian distinctions, right? Between analytic and synthetic propositions, and between a priori and a posteriori propositions. And basically the conclusion was—well, I hope I finished this, I just don’t completely remember—that in order to accumulate information about the world, we have to pay—or not pay, I mean—we have to use cognition and not only thought, on the one hand. But on the other hand, it’s clear that there are certain components of the information that we accumulate by means of thought and not cognition, or by means that look like thought and not like cognition. That’s what Kant called synthetic a priori propositions. Those are basically propositions—we gave examples of this—one could say all the laws of science are like that. Meaning, every scientific generalization, on the one hand, does not emerge only from the facts; in that sense it is a priori. But on the other hand it is also synthetic. Synthetic means that it contains information about the world, or makes claims about the world, and does not merely analyze the concepts involved in it. Someone who thinks that the laws of science are analytic laws is basically eliminating the difference between mathematics and science. In other words, he turns science into a branch of mathematics. When we say that Newton’s second law, which connects acceleration with force, is a scientific law, what we are really saying is that it is not enough to analyze the concepts of force and acceleration in order to reach the conclusion that there is a direct relationship between them. That is a result that requires observation. It is not something one can arrive at merely by analyzing the concepts, and therefore it is a synthetic proposition. On the other hand, observation does not give it to us. This is the example we talked about with the straight line, right? We measure various accelerations and various forces, and we draw a straight line between several points that we measured, when that line is not the result of observation alone. The observation was only the five points, and no more. So how can it be that there is a line, or a law, that contains information and yet does not emerge from observation? That was basically the question of the synthetic a priori as Kant formulated it. Except that Kant, as I think I mentioned, asked this question with an exclamation mark and not a question mark. Meaning, he really asked: how are synthetic a priori propositions possible, and not whether synthetic a priori propositions are possible. In other words, it’s obvious that this is possible; the only question is what the explanation is. Now, the explanation he proposed—and I don’t remember anymore whether we got this far—was the transcendental considerations, meaning that it is our way of looking at the world. Did I talk about that? Kant’s explanation was that when we look at the world, we judge—the sciences do not deal with the world in itself, but with the world as it appears to us. And the world as it appears to us is already colored by colors dictated to it by our cognitive tools. We do not look at phenomena as they are in themselves; we look at phenomena as we perceive them. Right? Today we know a bit more about neuroscience, and it is certainly like that, but you don’t need to know too much neuroscience for this. It is obvious that in the world itself there are no colors and no smells and none of the properties or things that we talk about in our cognition. All of that is in our heads; none of it exists in the world itself. In the world itself, at most there are wavelengths of electromagnetic waves, and different wavelengths take on the form of colors for us. Okay? But that is only a property of ours; it is not a property of the world. There is nothing of that in the world itself—there is no color there at all. So, if we suppose—what? The whole question is: if we strip away phenomenology as something subjective, suppose that after we strip that away we still come into contact with objective things from reality—would that too be perceived as some kind of abstraction? I didn’t understand. Meaning, if we discuss—if we try to strip away everything we know about the world and claim that everything not measured in abstractions is really something that exists only in our subjective consciousness, then we enter into some kind of contact with something. Who said I’m saying that wavelengths really exist? I didn’t say that. What I said a moment ago is that wavelengths exist in the world. There is something, some abstraction, and at its final limit of course I won’t be able to formulate it in any language, because every formulation is always some kind of translation, some kind of our own perception. That is obvious. This is only a distinction, let’s call it a relative distinction. When I say that wavelengths exist in the world itself and not colors, obviously wavelengths too are a kind of language of mine, and maybe one can continue abstracting further. Do wavelengths and colors also exist in some sense? No, they do not exist in any sense. That is completely clear. I don’t think one can argue about that. The famous question, right, of whether if a tree falls in the forest, does it make a sound when there is nobody there listening? Does the tree make a sound? The answer is obviously not. Obviously it makes no sound at all, because sound is the result of acoustic waves hitting our eardrum. What exists there at most are acoustic waves. When we are not in the forest and the tree falls, acoustic waves are created there, the air moves, there are pressure waves in the air. But sound is what is created when a pressure wave strikes our eardrum, and that is created only in us. There are no sounds in the world; sounds exist only in us. These are forms of perception with which we color the phenomena that exist in the world, if they exist at all—and again, I’m not getting into the even more philosophical question now. But even if there is something in the world, it is certainly not colored in any way by the colors with which I color it. No… again, “colored” here is literal and figurative at once, maybe not the best term. I’m talking about colors, sounds, tones, whatever you want, it doesn’t matter, heat and cold—all these concepts do not exist in the world. They are concepts that are translations of phenomena existing in the world into our conceptual system. Okay? If there were someone whose visual sensory centers were connected to the auditory center in the brain, then he would hear sights; he would see sounds if the wiring were reversed. What? There’s a condition like that where the body gets confused in… That is very plausible. Even if you hadn’t told me, I would have guessed there is. Meaning, that’s very plausible, why not? It’s just a matter of wiring. Even people who have absolute pitch in music often describe the sounds they hear as colors. Okay, but this is completely obvious: what we have here is simply wiring between sensory receptors and centers in the brain. And the moment I change the wiring, if I route it from the fingers to the visual center, then I will see touch, and I won’t see contact, and I won’t see electromagnetic waves, okay? Electromagnetic waves I’ll hear, the way an oscilloscope does, right? An oscilloscope translates an acoustic wave into an image. We see sounds. What does the oscilloscope do? It just does different wiring from what we have in our heads, that’s all. There is nothing special about it. So I only say this because it strengthens this Kantian claim much more: when we describe the world with scientific laws, we are not describing the world as it is in itself. We are describing the world as we perceive it. We speak about the velocities of bodies, the temperature of bodies, all kinds of things of this sort—these are all measures, measurements, or qualities that exist in our cognition and that we impose on the world. We use these glasses to observe the world, and that’s how we describe it in that language. And therefore, says Kant, if so, we should not be so surprised by the fact that when we contemplate the world we can draw conclusions not only by observation but also in an a priori way. Why? Because when we infer those conclusions, they are not conclusions about the world itself; they are conclusions about the world as we perceive it. So if we get to know our perceptual tools really well, there is no reason why we should not be able to anticipate all kinds of things about the phenomenal world that will appear before us even without observing it. For example, I could predict that I will never be able to see one of the colors that does not exist in my own spectrum in the brain. Right? There will never be a sight colored in some color that is not one of the seven colors that exist in the different sectors in my brain. I can say that without any observation, without observing the world. Why? Because if I know my sensory tools, my cognitive tools, then from that I can infer all kinds of things, at least some things, about what will appear before my eyes from the world. Since what appears before my eyes from the world is colored by colors—again figuratively and literally—that I impose upon it. So every scientific thing we already assume in advance. In a certain sense that’s true, yes. And that is one of the problems with the Kantian explanation; that’s why I think it is not satisfactory. And I’ll formulate—yes. Here he basically agrees with him. Right, exactly. You’re asking the same question in different language. Meaning, the claim is that in fact he didn’t really solve the problem; he only acknowledged it. In other words, he basically says: look, we really cannot know the world—we cannot know the world. He turned the synthetic proposition into an analytic one. In other words, that is basically what he did. So the proposition is not synthetic a priori; it is analytic a priori, and that is certainly possible, so there is no problem. Only, when you do analysis, don’t analyze just the concepts; analyze also your cognitive tools, the concepts or the objects. But that doesn’t matter—it is still only analysis. So then of course it’s no wonder that it is a priori. So he creates the concept. What? He creates the concept in some… Yes, exactly. He empties it, he empties it of content, basically. Maybe I’ll formulate this in another language. So I’m saying that what Kant is basically saying is this: if I apply to a body whose mass is two, I apply to it a force of magnitude four, okay, then the acceleration should be two, right? F = ma. Okay? The acceleration is supposed to be two. If the result—if the real acceleration in the world itself, right, were three, I would not see it. So this is not a claim that the acceleration in the world itself is really two. The acceleration in the world itself may be three; it’s just that an acceleration of three would not be something my cognitive tools would allow me to see. All the accelerations I see will only be accelerations that are force divided by mass. Now, that claim is a very far-reaching claim—indeed, in my opinion, absurd, not only far-reaching. Because what he is doing here is linking our cognitive constraints with the constraints of perception. I mean, when there is a body accelerating at three meters per second squared, I can see it, right? If the force accords with Newton’s second law, I have no problem seeing a body moving at three meters per second squared. So now, if the force on it is a bit different—what is that? Does that now impose a different constraint on my sight? Why? I now cannot see a body moving with that same acceleration just because a different force acted on it? Force is an abstract thing anyway, which I don’t actually see at all. Somehow that force, in a mystical way, prevents me from seeing the body’s acceleration? He claims that what exists is only the constraints. What? He claims that what exists is only the constraints, and that we cannot perceive anything except them. Yes, but the question is why. I understand that I cannot think otherwise, suppose. But why can’t I see otherwise? After all, he connects them—he wants to say that the generalization actually stems from the fact that I cannot think otherwise. Why does that work? Because that very same constraint also determines that I cannot see other things. But the constraints on thought and the constraints on sight are not the same constraints. Even if the constraints on my thought, say, lead me specifically to Newton’s second law, to the conclusion that F = ma and not F = 3ma or ma squared, why does that also always fit my cognitive constraints, which tell me that given a certain value of force I will not succeed in observing a body moving with a different acceleration? Why not? But for example, like the way we observe people living in one time dimension and not in several time dimensions, maybe he is simply saying that an acceleration that works differently also operates in another dimension? But why? Why? Where does that come from? Fine, if you apply more force, then more acceleration acts. You’ll see—if we’re getting to this level of speculation, I don’t need Kant at all. I can stay with Hume and say: no problem, we simply know, that’s all, even if it is mystical and we don’t understand it. After all, that was Hume’s question: how can it be that we know this without having observed it? What’s the problem? We know, that’s all. You’re not answering, do you see? Once you don’t answer, then why develop all these theories that in any case don’t answer? Maybe they’re true, but maybe the mystical claim is also true. Meaning, maybe we do have some ability to know the world without observation, period. So then I no longer need to look for philosophical explanations. When you offer me a philosophical explanation, you are supposed to offer me an alternative. You are supposed to offer me an alternative that gives me an explanation, not something that remains at the level of maybe I have some mystical ability that I don’t understand. If that is the case, then let’s stay with Hume—forget all the… It’s less that it’s a mystical ability; it’s simply trying to explain it again through Kant’s theory, where it is given… But you have to show me—you have to show me how this happens. Why is it that I cannot manage to see an acceleration of three, but I can see an acceleration of two? How is that connected to my visual apparatus? After all, in another context I have no problem seeing an acceleration of three. So what… do you see? At that level of speculation I don’t think this is an explanation at all. It adds nothing for me beyond remaining with Hume. It seems to me—again, I’m not sure that what I propose instead is an explanation—but it is at least an acknowledgment of the facts, and it seems that no other explanation does more than that. And what I am basically claiming is that we do have the possibility, by means of thought, to accumulate information about the world. We have some ability—you can call it cognitive or intellectual, it doesn’t matter—something in the middle that allows us to generalize the results of experiments. I measured, in five experiments, right, accelerations relative to force, I found five results. I drew the straight line between them, and the claim is that that straight line is not the result of intellectual processing but the result of some kind of cognition. I simply see in the world that this is the correct general law. I have some ability to draw conclusions not through purely intellectual means or purely cognitive means, but something in between. Now, it seems to me I already said all this, as far as I remember. And I also said that there is a certain analogy here to the legal world—that in the legal world too there is a distinction between interpretation and legislation, and there too interpretive legislation, or legislative interpretation, is really that same intermediate level as the synthetic a priori in the scientific sphere. What I really want to say is that the hermeneutic principles, as Maimonides described them—when we discuss our understanding of derash as an alternative to interpretation, as something between interpretation and legislation—it too is basically the same thing. So the hermeneutic principles are nothing but the appearance of the synthetic a priori in the halakhic sphere. And there too, all the questions that are asked about Maimonides stem from the same difficulties that exist in philosophy of science or in philosophy of law, in legal theory. Okay? “Philosophy of law” is a somewhat problematic term, I think. I’m not sure there is such a thing. For some reason, lawyers deal with it, and that ruins the whole field. Algra…? What? Is that the philosopher like Algra…? I’ve heard of him. Fine. There are many who call parts of legal theory “philosophy of law,” but it seems to me that most of the well-known figures in this field—I don’t know Algra’s work so well—most of the famous figures in this field, yes, Dworkin and Raz and people like that, are more jurists than philosophers, and what’s missing here is a genuinely philosophical hand in the legal world, in my opinion. Look and see—the books in legal theory written by Aharon Barak, who is not a philosopher at all, has no philosophical understanding whatsoever, are considered almost like Bibles in fields some of which are really legal theory. And that’s not—it’s phenomenology for pennies, there’s no descent there to the substantive justifications, to the philosophical problematic. Anyway, a different issue, never mind. In any case, in the halakhic context too, this dichotomous outlook that distinguishes between legislation and interpretation and tries to assign everything either here or there suffers from the same problem. There too we are really asking Humean questions—either observation or thought, but how can it be that thought, meaning something subjective that happens in me, determines truths about the Torah itself? After all, Maimonides told us that derashot expand what is written in the verse; they do not expose what is written in the verse. So if they expand what is written in the verse, then everyone immediately asks Maimonides: “So is it rabbinic? Is it something that is your own product? You didn’t find it in the verse? So it’s rabbinic? It’s not Torah-level?” Maimonides himself calls it the words of the Sages. On the other hand, what is the alternative? That it reveals? If it reveals, then it is ordinary Torah-level law—it is just interpretation. So what is this intermediate state that we called midrash or the hermeneutic principles, which stands between legislation and interpretation? It is some kind of expansion that emerges from the verse, that broadens what is written in the verse in some fashion, not merely exposing what is inside it—but it is not an enactment. It is not something that comes from the reasoning of the Sages and that’s all. No, it is something connected to the verse itself. Yes, if we go back to those examples: when the Sages determine that it is forbidden to eat poultry with milk, that is an enactment or a decree. It is a rabbinic decree. Why? Because they are not claiming that they derived it from the verse. It came from their own reasoning; we need to heed their voice. But it came from their own reasoning—that is legislation. Okay? When the Sages determine that what is written, “And they shall be as frontlets between your eyes,” means phylacteries of such-and-such a type, that is interpretation—or really, in this case, a law given to Moses at Sinai, not important. So a law given to Moses at Sinai that is interpretive. In that case, of course, it is a Torah-level rule. Why? Because the act of the Sages merely exposes what is written in the verse itself. So they are interpreters. Once I understand that interpretation, I understand that this is what is written in the verse. That verse is Torah-level. Derash, says Maimonides, is something in between. “The Lord your God shall you fear”—to include Torah scholars—does not reveal to me that fear of God already includes fear of Torah scholars. Because if it did, it would be peshat, not derash. And it is also not an enactment saying that because, by our reasoning, one should fear Torah scholars, therefore we say one should fear Torah scholars, because then it would be a rabbinic law. There is a derash here. Derash means that we claim that the spirit of the verse, or the expansion of what is written in the verse, ought to lead from fear of God to fear of Torah scholars. Which is something beyond what is written in the verse. The classic example that is always brought, also in the legal context—this is also something Albert… used, this one I do know—the example of “vehicle,” of bringing vehicles into a public park. Hart, I think, is the father of this example. Bringing vehicles into a public park, a children’s playground. There is a sign: “No vehicles allowed.” Now what is a vehicle? Does “vehicle” also include a scooter? Is it only a motor vehicle? What happens if they place there a monument of a tank that is already disabled—memorial to the bravery of our soldiers, I don’t know when. Is that also “bringing a vehicle” into the playground? And then all kinds of discussions begin: exactly what are we doing here when we determine that it means only a motor vehicle, say, and not a scooter—is that interpretation? Is that legislation? Is that legislative interpretation? What exactly is it? The question is whether this merely exposes the content of the sign, or whether it adds additional layers beyond the literal interpretation of what is written on the sign. Sometimes this is called purposive interpretation; never mind the terminology for now, there are all kinds of terms for it. But the basic question surrounding the issue is exactly this one: are you exposing what the writer of the sign intended, or what is written in the sign—without getting into those hermeneutic issues right now—or are you expanding beyond what is written in the sign and determining additional things according to the spirit of the sign, or are you establishing a new enactment beyond what the writer of the sign established, and so on. And I am saying that there is an intermediate state: you can expand the idea written on the sign and say that in some sense the writer of the sign intended this too—but not really intended it, because otherwise this would be exposure; then you would merely have exposed what he intended, and that is interpretation. Rather, I am saying that it is clear that from the idea he wrote in this sign, it is fitting to forbid this too. Maybe with a lighter prohibition, maybe halfway—he half intended this, not fully. But it is something at an intermediate level. What? Must it necessarily be a logical deduction? No, on the contrary—it necessarily cannot be a logical deduction. If it were a logical deduction, it would be exposure. By “logical” I mean deduction, yes? Then it would be exposure. Certainly. Logic by its very nature always exposes. Even though it was not said explicitly. What? Even though it was always said explicitly. After you carry out a logical process, you see that it was said explicitly. When you say that all human beings are mortal and Socrates is a human being, therefore Socrates is mortal—was the conclusion that Socrates is mortal not explicitly stated in the premises? Of course it was explicitly stated. After all, it says there that all human beings are mortal, and Socrates is one of them. You explicitly said that he is mortal; you just do not always notice it, so the logical argument helps sharpen things that were already hidden in the premises. Okay? But a logical argument by its nature exposes, and I’ll get to that in a moment. And what about an a fortiori argument? No, an a fortiori argument is not a logical argument. Why? Because if there is an inclusion regarding a prohibition—say, the positive commandment of “The Lord your God shall you fear,” to include Torah scholars—then the question is what would happen if the same thing were also with regard to a prohibition. Would you say that this is not the spirit of the verse, or would you say that it is only the spirit and not the body of the prohibition? There would be no lashes for it. A prohibition derived from derash—yes, certainly. There would be no lashes for it? No, Maimonides writes this explicitly. The idea that this does not stem from specifically divine Torah writing? No, I don’t think so. No. In any text one can do this. This intermediate level? Yes. I think this explanation is correct also for legal theory, not only for Torah. It is something universal. We have some kind of ability. Or yes, but here there is some special privilege, because we can always say what? That the writer—which you don’t have in a human text—even if we don’t prove it from the text, oh, if the writer intended it, then again you are exposing. That the writer intended this intermediate level. That is what we can do. What difference does it make? That the legislator did not intend the intermediate level, but it is there. It doesn’t matter. Again, I don’t need that for this. Here I can go out and say that the legislator gave—there is peshat and there is derash, meaning that the legislator gave us to understand what is written. It doesn’t matter. But again, if derash really stems from peshat, but stems from it in a weaker way, not hermetically, then even if the legislator did not intend it, it is not important. Even then, I claim, it is still another layer… found within the peshat in a partial sense, within the written language in a partial way. So I am therefore partially obligated by it, even if he did not intend it. The fact that in this case the Holy One, blessed be He, may also have intended it—maybe that is true, but I do not need that in order to build this claim. Which means that even if one can argue about this in an ordinary text, here we have some difficulty. If you argue about it in an ordinary text, you gain nothing here either—that is what I’m saying. You gain nothing. Because if you argue in an ordinary text, then what you are basically saying is this: the hermeneutic expansion is not really exposing something connected to the verse itself, it is not an expansion of the verse—it is an invention. Either an invention or interpretation, one of the two. But there is no intermediate level. Once there is no intermediate level, then even if the Holy One, blessed be He, intended it, that is not interesting. Because if the Holy One, blessed be He, intended it, that means that you exposed it, you didn’t interpret it homiletically. So it is Torah-level. Why? But there is no intermediate level. You are saying there is no such thing as an intermediate level. You deny its existence in the logical sense. Therefore I say it makes no difference whether the legislator intended it or did not intend it. The question is whether you are prepared, at the logical level, to accept the existence of such an intermediate level. If yes, then even if the legislator did not intend it, if it emerges from his words in some such way, then it is also binding. No, I don’t see any difference at all. What is the difficulty in understanding it as such an intermediate level? I have no difficulty. I don’t know. Whoever has difficulty should say what the difficulty is. I don’t know. The difficulty is being locked into dichotomous thinking. What we talked about with the sorites paradox, right? That is the example of people being locked into dichotomous thinking. Fine, it is a kind of lock. The difficulty is a real difficulty because the question is what I am looking for. If I am looking for what was said—again, that is exactly the point. You’re throwing out the baby with the bathwater. Because if you do not recognize the existence of an intermediate level on the ordinary human plane, then when you now go to a text written by the Holy One, blessed be He, what you are really saying here is that you are exposing, not expanding. You are exposing His intention, because the Holy One, blessed be He, intended it from the outset. I am claiming that even if the Holy One, blessed be He, did not intend it from the outset, I am still bound by the derashot. The fact that He also happens to be omnipotent and knew that I would make this derash is not interesting. That is not why I am obligated. Do you see? That is the point. Of course, of commentators. Why only of the Sages? Every commentator in every field—it’s not only the Sages. I’m saying: take all the mysticism out of here. I don’t think it’s needed. A commentator exposes. No, no, a commentator also does derash, not only peshat. But when he does derash, then he is closer to the Sages and to enactments. So he is between legislation and interpretation. Right. But this is done everywhere. Everywhere it’s called something else. Here it is called the synthetic a priori, and here it is called judicial legislation, and there it is called whatever you want. It is all the same thing. Let’s talk about the legal world. Go ahead. It’s not really in the middle. Of course it’s in the middle. It is completely in the middle. There is use of… It is basically a new enactment that uses the earlier text. Not at all. Not at all. A judge has no authority to enact regulations. What do you mean? Right, he uses this tool. But really… What tool? But what is the tool? What is this tool? It’s not really in the middle. But what is the tool? You say there is no such tool. So what is the tool? He is not allowed to legislate. If you understand this as legislation, then he exceeded his authority. You have to say that there is something here that has some affinity to the written law or to precedent, it doesn’t matter right now what he is relating to. And true, the affinity is not hermetic, otherwise it would be straightforward interpretation. But certainly there is some affinity. This is not legislation. Legislation is the domain of the Knesset, not of the judge. The question is whether this is really a legitimate thing. There is no—you can’t do without it. First of all, what is called a justification of necessity—you simply can’t do otherwise. There is no interpretation that does not involve homiletic components, what I called here—others would call them subjective. There is no such thing. You cannot. If you remain attached only to what is written, you can abolish the concept of the judge. Every case would have to go to the Knesset. But the example of the constitutional…? is not of a judge or commentator. It is interpretation of the legal system, not of the particular statute. Dworkin is already talking about the principles in the background of a legal system, where that background is not always in the Knesset. Sometimes it is in the society to which this law was addressed. But in that way it is simply a kind of interpretation. Yes, it is a kind of… No, again, either interpretation or derash—I don’t care. But it will be something that is not legislation. That is what I mean. It will not be legislation. And it will be derash-interpretation. I don’t know. Depends on what… depends how you… what you do. Sometimes, if you prove it with signs and wonders from the words of the legislator, then it will be interpretation. If you make some looser consideration, not rigid, not pure logic, then it will be derash. And that is the difference between derash and interpretation. In the legal context, the difference is not sharp. In the philosophical context, the difference lies in the question whether you are doing deduction or not doing deduction. That’s it. Meaning, deduction is interpretation; everything that is not deduction is derash. Now in the legal world there are expansions that seem so self-evident that they are treated as interpretation, not as derash, not as analogy. It is obvious that this is what is meant. You see? Because there you cannot force a living world into logic. In Torah too it is like this, by the way. Meaning, even what Maimonides calls plain interpretation, not derash—what he calls Torah-level laws—even there certain subjective components enter. I am not claiming, not trying to claim, that this distinction is as sharp as it is in the logical world. In the logical world the difference is whether this is derash or whether it is deduction. Is it deduction or not? A clear-cut distinction. Meaning there is no… the difference is clear. If it is deduction, it exposes, because deduction by its nature always exposes what is in the premises, and therefore it is valid. And if it is not deduction, then it is derash. What I am claiming, however, is that the fundamental character of the hermeneutic principles is basically that they are principles whose essence is analogy or induction, and not deduction. That is basically the conclusion. What are you saying? If I look in Genesis, chapter 1, it says that God said, “Behold, I have given you every herb.” If I take “herb” and reverse it, it also gives “seven.” Okay? So now if I come and say: a person has a memory of seven—seven wonders of the world, seven… our whole world is built around seven. Yes. Can I then make… the Holy One, blessed be He, said that He gave us all the herb, right? And if I look at the world and I see that everything around me is seven, can I reach the conclusion that the Holy One, blessed be He, intended it to be seven? He wrote “herb.” That doesn’t convince me, but okay—if it convinces you, then maybe yes. That is certainly not deduction, meaning it is certainly not exposure; it cannot be peshat. But can I make such a manipulation? It may be that this is derash, or in this case perhaps even a hint. Hints are acronymic readings and gematria and things of that sort. Yes, okay, this is a hint, not even a derash. So if you… the question is what is the source of the hint, where does it come from? In the principles of Rabbi Eliezer son of Rabbi Yose the Galilean—the thirty-two principles—some of them are hints. Acronyms and gematria appear there. Fine. So at least in the aggadic context the Sages did make use of that. Because afterward, as a scientist, I want to test it. Suppose in ’56 Miller checked people’s memory, how much they remember. So they reached the conclusion that there is the magical seven, plus two minus two, right? So they saw that people remember seven items, plus two or minus two. And empirically they did this and saw it. So what does that mean? It means that what… that I lock onto seven and then go and test it in people’s behavior. Again, let’s return and focus for a moment on the point of peshat. If I make observations, then maybe that convinced you that seven is related to “herb.” Fine. So you were convinced there is such a derash or such a hint. Others were not convinced, but that certainly is not interpretation. No, so now suppose I came—say Walmart, right?—they want to sell jams. Jams? Jam. What is Walmart? Walmart is an American supermarket company. Ah, Walmart. Walmart, yes. Now they have in the United States two hundred and thirty-two kinds of jam. The 232 paths of wisdom. Yes. They wanted to let people choose the jams. Sales dropped. Right? They came and asked: how many jams should people be offered to choose from? And they concluded—they made observations and very, very careful research—and they came to the conclusion that supermarket sales are best when the options are within seven. Fine, okay, seven. You need to make a hundred thousand observations and see how the observations are distributed among the different numbers. You just find a few things where seven comes out; I can find you another hundred thousand things where four comes out. And then you’ll say, “Yes, that’s seven minus three.” Obviously. Fine. These things are not… No, but again, where are we heading? Meaning, in relation to us. One can do induction, meaning take from the sources and test it in reality. That is a different position. If it convinces you, good; if not, leave it. That’s not what I’m talking about right now. What I’m talking about right now is that assuming you were convinced by it, and that’s fine, then at most it is derash, not peshat. What I’m saying… That too is peshat. But if it says hippopotamus and I read it as rooster? No, but it’s the same letters. So what? Fine, and with hippopotamus and rooster I’ll do it in atbash. Hippopotamus starts with h, and t is h plus 17 so I immediately get to t. So you see it’s the same thing. Everything has a code. What difference does it make that it’s a letter transposition? It doesn’t matter, it doesn’t matter, it doesn’t matter. No, why do I have apriority regarding Kant’s synthetic a priori? Meaning, every derash is basically synthetic a priori? Yes. Yes. The claim is that derash is basically a synthetic a priori mechanism. But synthetic? What does that mean? It is synthetic in the sense—and that is exactly the point—legislation is not really something synthetic, because it is not making claims about the Torah. Let’s say the Torah is analogous to reality. It is not making claims about the Torah; it does not pertain to the Torah. They are inventing a new law, do you understand? And therefore I called that thought, not cognition. But it is thought, and it is a priori, and also analytic, because it is not making a claim about the world. Okay? Interpretation, of course, does make a claim about the world—it makes a claim about the Torah. Fine? But that is no great trick, because it is deduction, for the sake of discussion. So then why is derash a priori? Derash? Because it does not come out of the verse. If it came out of the verse, it would be exposure. Just like the line does not come out of the points that I measured. Even though it is based on them. I didn’t understand. No. No, it is a priori. It is a priori because it does not emerge from observation. It is synthetic a priori, not a posteriori. This is exactly what Kant said about that line, and he is right. Kant said synthetic a priori about mathematics, didn’t he? No, that’s another story. I’m talking about the line in physics. There it is more agreed upon. In mathematics I also don’t agree, but that is another discussion. To draw the line between the five points that I measured is not a posteriori. Because the points themselves I measured—that is the result of observation. But the general law that I generalized from those points—where does it come from? After all, it contains more information about reality than the pointwise information that I measured. Where does that come from? It is a priori; it does not come from observation. But on the other hand it is synthetic, because it makes claims about the world. I am claiming that in the world this will be the relationship between force and acceleration everywhere, right? So that is synthetic a priori. Now midrash too is basically synthetic a priori in this sense: legislation does not make a claim about the Torah. The Torah is the analogue of the world, right? Legislation does not make a claim about the Torah. I am doing my own thinking—it is not connected to the world, and that is all. And the Sages have authority to establish enactments that do not emerge from the Torah, are not connected to the Torah, and even that I need to heed. Interpretation is the points written on the graph. The points that I measured. But midrash is not exactly—it is not interpretation. Right, midrash is derash—it is drawing the line. Drawing the line. Midrash says: what is written is “The Lord your God shall you fear.” That is the point I measured. It is written. I saw it. I measured it. As a jurist I cannot accept this freedom of activity of stretching lines within… No, so I already said earlier that obviously this precise, sharp definition does not exist—not even in Jewish law, and not only in law generally. This definition between logic, which exposes, and everything that is not deductive logic, which expands. But I am presenting the two poles so that in the complex reality we will understand what we are talking about. You always need to speak about pure types in order to understand the idea itself. Then, in reality itself, something that is close enough to plain interpretation is called peshat. And then peshat—doesn’t our peshat also have synthetic aspects? It does have synthetic aspects, but few. They are less than in derash? Yes, less. The degree of syntheticity determines how much you are peshat and how much you are derash. Now the sharp distinction between peshat and derash is exactly the sorites paradox. That’s why I brought it. Because the concepts peshat and derash are not measured in a yes/no way—are you peshat or are you derash. There is something that is completely peshat, something that is quite peshat, something that is a bit peshat, something that is not peshat at all, and likewise with derash. I am only saying: what is this pure concept called peshat and derash? The pure concept is pure logic—that is pure peshat—and whatever is not logic is derash. But sir, in legal theory there is a case and you need to fit it to some precedent, a certain precedent, and then the question is how far it is, or a distant precedent, it doesn’t matter, and then the question is how similar or dissimilar it is, and then the question is what line you draw—but in midrash the justification is not that I have a case I cannot solve at all. No, of course it is. Of course it is. First of all, that’s not true. Factually it’s not true. When you read Maimonides in the Laws of Rebels and also in the Laws of the Sanhedrin, you can see that Maimonides speaks about midrash as a tool used by a religious court. A case comes before you and you need to decide it—even in a court of three, it doesn’t matter. You need to decide it. You can go to the Torah, make a verbal analogy and derive the law. Of course we do not do that today, and therefore we are used to the idea that derash is how they wrote our Shulchan Arukh, not something the decisor does in a particular case. And thought—the basic thought, meaning before we talk about laws at all—is not only precedents; there are also cases. No, so I’m saying—you simply got used to it because of an artifact: today we don’t do it. But every court, anywhere, can sit down, take the Torah, interpret it homiletically, and reach a conclusion. And that is like the difference between judges and learned commentators, what our cousins the jurists call them. Fine. So the scholars do not take a specific case and apply the law to it, but rather produce interpretations of the law as such, from which of course one can later draw conclusions regarding specific cases. So in this case you are talking about the scholars’ aspect, but in Jewish law there are both things. That is the difference between responsa and the Shulchan Arukh, or law codes. Responsa do what a judge does. A case comes before him and he has to decide what the law is. When you write the Shulchan Arukh, you are not talking about specific cases; you are writing the laws that are binding in every situation. A good example, because the structure and mode of thought of responsa is so different from the methodology of a legal code. All the responsa you know are from the period when they no longer made derashot. Fine. So what? But the responsa of Rabbi Akiva were derashot; they are written in the Talmud. A jurist too, when he comes, does not use at all the same tools that a darshan uses in any kind of legal context. Not at all—what are you talking about? Of course he does. He constantly uses those tools. He makes verbal analogies, he makes a fortiori arguments, he makes paradigm constructions from one text, from two texts. He does many things there. Two texts that contradict one another—many of the things appear there. Not everything. General and particular—I’m not familiar with that being done, maybe it is, I don’t know the field well enough, but I don’t think so. Although in the halakhic world I already mentioned that general and particular are also applied to non-biblical texts, even to responsa. Yes. That is Kant’s justification for the commentator’s right to do what he does. He claims that the commentator, when he does what is really judicial legislation—you ask what his authority is, after all only the Knesset can legislate, how can the judge do judicial legislation? So he says that all interpretation is basically a kind of legislation, since you are not dealing with the law itself; you are dealing with the law as you perceive it. Right. Kant won’t say that this is something conventional, right? What? Kant won’t say it is something conventional. He doesn’t say it, but that is basically what lies behind his words. But in interpretation it is obvious that it changes; it is obvious that everything is conventional, everything is a kind of postmodernism. No one stands behind the law. I’m saying: Kant is considered the opposite—no one can sing and interpret the law… No, that’s not true—that’s exactly the point. Kant came to confront that claim. Kant is addressing exactly that skeptical claim. Kant wants, on the contrary, to save dogmatism, to deal with skepticism and say: not true. There is a right way and a wrong way. Why? Because for him the laws are necessary. What? Because for him it is something necessary. Exactly. But basically, as you say, behind what he says, he did not really deal with the problem. Exactly. I agree. That’s what I also wrote in the book. What is the difference between the intention of the legislator and the text? Why separate them? Who said they need to be separated? Not the intention of the legislator—the idea of the text, the idea of the law. The idea of the law, not of the legislator. The legislator’s intention is not necessarily connected to these hermeneutic distinctions. When you speak about the intention of the text, I also mean in some sense the intention of the legislator, only the problem is that the intention was not always conscious to him. Suppose there were a conventional legislator who established “The Lord your God shall you fear.” If my claim is that within the command to fear the Lord your God there also lies the command to fear Torah scholars—lies there, again, not fully logically, but the spirit of the matter lies within it because it is an expansion, yet it still has an affinity to the original command—then for me that is the legislator’s intention. Do you understand? Even if you had asked the legislator, he would not have known. That doesn’t matter. It is there. I think I mentioned Rabbi Kook about the Sochatchover, who said in a letter he sent to his descendants to comfort them—or grandchildren—that they said about Rabbi Eliezer that he never said anything he had not heard from his teacher, yet in one place it says that he said things no ear had ever heard. So he heard from his teacher things that no ear had ever heard, including his teacher’s own ear. Even his teacher had not heard it. There are… But that is not a mere rhetorical flourish; it is true. There are sometimes situations in which the student can hear from his teacher something that even the teacher himself, had you asked him, would not have known, but it came out of him. So is that not the legislator’s intention? Exactly. Now decide whether you call that the legislator’s intention or not—that is already a matter of definition. It is the legislator’s intention in some sense. It is not his conscious intention. You will not find it in his writings, in his personal diary, if you look there to see what he intended to achieve by means of this law. But it is found within the law he enacted, and implicitly it was indeed his intention, because it really is there. And that is the point. Do you understand what I’m saying? Exactly. He just didn’t—his own grasp did not reach that far. And therefore I say that with the Holy One, blessed be He, that does not happen. But that is not important—that is exactly the point. That is why I say it does not matter that with the Holy One, blessed be He, that does not happen, because the Holy One, blessed be He, is omnipotent. So He thinks of everything included in the law He gave us, whereas an ordinary legislator does not. But that is not important; it is still included there. And once it is included there, it binds me. Okay? Not because of the omnipotence of the Holy One, blessed be He—we don’t need to get to that. Fine. So basically the conclusion is that if I now continue this point a bit, then I say this: in the mathematical definition of things, exposing interpretation is only logic. We talked about the hot-air balloon, right? That logic always begs the question. Meaning, logic basically always exposes what is contained in the premises. Logic by its nature is an exposing tool. What is in the premises—that is at most what you can expect in the conclusion. There will never be information in the conclusion beyond what was in the premises if the move from premises to conclusion is made by logical tools, deductive logical tools. Okay? Therefore deduction is by its nature a system of exposing tools. By contrast, analogy and induction are tools that add information beyond what is in the premises, right? If I make the induction of that scientific line from the five measurements, the complete line contains much more information than the five particular measurements. It added a great deal of information. Precisely for that reason it is not derived from those five measurements by logical tools. Because otherwise it could not contain more information than exists in the five measurements. If it adds more information, that necessarily means that the tool by which I derived the line was not deductive. So what was it? Induction, of course—it was a generalization. Right? And the same with analogy. When I make an analogy—this lectern is brown, therefore the lectern in the classroom next door is also brown. What is called a paradigm construction in another language, or analogy, right? When I make that analogy, did I add information or not? Of course I did, right? Because my premise was that this lectern is brown—that is what I know from observation, that I know for certain. The conclusion that the second lectern in the second room is also brown contains some information that was not present in the information that was in my premises, in the empirical information. I added more information. So that necessarily means that the process by which I added the information was not deduction. In this case it was analogy. Okay? So analogy or induction are tools for adding information; deduction is a tool that exposes existing information. So now, if we gather together everything I have said until now, the necessary conclusion is that in the hermeneutic principles we should expect them to have the character of analogy or induction, and never deduction. That is basically the conclusion. And someone mentioned earlier the a fortiori argument—that is the best example, because there are those who mistakenly think that a fortiori is deduction, and there is no greater mistake than that. A fortiori is not deduction. And the simplest indication of that is that it can be refuted. Deduction cannot be refuted. You cannot refute a mathematical proposition; there is no such thing. At most it was never correct in the first place, and then it is not that the inference is correct but I have a refutation; rather, there was a mistake in the inference. But in an a fortiori argument I am not refuting the inference in that sense—the inference is certainly not necessary. If I have three data points, the conclusion is… what? A premise you can refute. Yes, a premise you can refute, but the refutation does not refute the premise; it refutes the inference. Because the inference is not necessary. The inference saying that this is more severe than that is not correct—look, in this respect that one is more severe than this one. So you refute the inference. What does that mean? That the inference is not necessary. If there are refutations against it, that means it is not deduction. And all this not according to Maimonides? Why not according to Maimonides? Because if what you said is that in Maimonides this is Maimonides’ view—synthetic a priori—then it is not analogy. Why? Synthetic—analogy too is synthetic a priori. On the contrary, that is the view of Maimonides that I brought. Analogy is a priori. Analogy and induction are by definition a priori. Analogy and induction—and again you return to the same point. One has to distinguish between two things. In my opinion science is a priori in this sense. It is not a posteriori. It is synthetic a priori, unlike mathematics, which is analytic. Science is synthetic a priori in this sense. The observations that I saw are of course a posteriori—that I saw. But when you arrive at the general law, it is always a priori because it does not emerge from the observation. It is a generalization that you make. Do you understand? And in that sense here too it is the same thing: synthetic a priori. Every activity that is not pure logic or mathematics is synthetic activity, and it is almost always a priori. When it is interesting, it is a priori. When something you saw—you know it is true—that is not interesting. When you do something somewhat speculative, where there is generalization, where you arrive at some more general insight, whenever it is interesting then it adds some information for you, and therefore by definition it is not deduction; and on the other hand it can be a priori. In fact it must be a priori. So a fortiori is not deductive? What? A fortiori is not deductive? Certainly not. A fortiori is not deductive. You have to prove that something is more severe than the severe one in order to… But how do you prove it? That proof is not deductive. Say—we will still get to a fortiori, but let’s already get ahead of ourselves since we’re talking about it. Tooth and foot are exempt in the public domain, and horn is liable. Let’s ignore half-damages for the moment; let’s say it is liable for full damages in the public domain, okay? In the injured party’s courtyard, tooth and foot are liable. Now the question is: what is the law of horn in the injured party’s courtyard? Okay? So what do you say? Let’s look at the public domain. In the public domain we see that horn is liable and tooth and foot are exempt. So from this, horn is more severe than tooth and foot. Now let us apply this to the injured party’s courtyard: if tooth and foot, which are lighter, are liable in the injured party’s courtyard, then horn, which is more severe, will certainly be liable in the injured party’s courtyard. That is an a fortiori inference, right? There is an Olympic leap in the middle. We saw one example in the public domain where horn is more severe than tooth and foot, and suddenly you turn that into a general law that horn is in every respect more severe than tooth and foot. And now you apply it to the injured party’s courtyard. That is an international leap; that is induction. You are basically saying that from one datum in which I saw that horn is more severe than tooth and foot, I make an induction and say that it is more severe in every respect. And the refutation always attacks that very point. So how is it that they really use it in every respect and not only at that point? Exactly. Obviously. Otherwise it really would be deduction. An a fortiori included within a larger amount—for example—the Maharsha writes in his second edition on Bava Kamma that an a fortiori argument of the “included within a larger amount” type cannot be refuted, and he claims that one can derive punishments from law in an a fortiori of that sort. Why? Because that really is deduction; it is not an a fortiori argument. It is not one of the principles by which the Torah is interpreted. It is simply deduction. If one is liable for tearing, then for opening all the more so? Because when you open, then you… when you tear, then you also open. What is that? It’s obvious. It is included within the larger amount. Here there is no synthetic aspect at all; it is completely analytic. His daughter and his daughter’s daughter? The same thing. There is in tractate Makkot that a fortiori with the law of… no, his sister—his daughter and daughter’s daughter are not certain, actually. The daughter of his father or the daughter of his mother, as you say, then in particular she is also the daughter of his father alone. Meaning, that is included within the larger amount. His daughter and his daughter’s daughter is not necessarily the same, because you are only making a claim by reasoning that his daughter is more his daughter than his daughter’s daughter. But it is not really an “included within the larger amount” case. It is not that granddaughterhood is contained within daughterhood. Do you understand? So it is not exactly the same thing. It depends on… in any particular case the question really is how you define that group or that concept. Fine. Okay. No, so really, I mean, really a large part of a fortiori is perhaps part of the synthesis of the concept, where the concept itself—what are you, when you… But that will always be only in the simpler type of a fortiori, where there is one datum and you infer one conclusion. There? Say that “If her father had but spit in her face, would she not be ashamed seven days?” Right? If her father spat in her face then she would be ashamed seven days, so if the Holy One, blessed be He, spat in her face, she should be ashamed fourteen days, or at least seven days too. Right? There there are not three data points. But in an a fortiori argument based on three data points, like tooth and foot and horn, there it will never be like that. There it is never a question of defining the concept. No, no—there it is pure induction, that is obvious. One cannot argue that it is induction. In the “included within the larger amount” type, you are right. More than that—I think I brought in Nitzotzot an example of an “included within the larger amount” a fortiori that does have a refutation. This is from Chaim Perelman, also a Belgian philosopher of law. He mentions the Vandervelde law that said there was a law in Belgium forbidding the sale of two liters of wine. So we would say: fine, and what about three liters? Obviously forbidden—it is included within the larger amount. If two are forbidden, then three liters is also selling two plus one, right? Included within the larger amount. But no, it turns out that three liters were permitted. Why? Because selling two liters was forbidden because they were afraid the laborer would spend his weekly wages on drink… on liquor. But three liters cost more than a laborer’s weekly wages. So they did not make the decree there. Like partial admission? Huh? That partial admission also says it is included within the larger amount? Maybe. That depends on how Rabbi Chiyya’s first a fortiori works there… we won’t get into that now. But the refutation… huh? Doesn’t that weaken the strength of the…? That is a refutation! But that is a refutation! That is exactly what a refutation does. A refutation basically says that three liters do not really contain two liters, because from this perspective of concern for the laborer’s wages, it is not true that three liters contain two liters. It is exactly like a refutation of an ordinary a fortiori. A refutation of an ordinary a fortiori also does not refute the fact that horn is more severe than tooth and foot in the public domain. It refutes the generalization you are making, when you say that it is more severe in every respect. That is not correct—look, I’ll show you a case in which it is not more severe. Okay? Therefore, when there is a refutation, that is an indication that there is some dimension here that is not deductive, not analytic, but rather synthetic a priori. Therefore a fortiori, which is the principle closest to logic, is also not really a logical principle. Maybe just one last sentence—okay.