2019-04-22 – Between Midrash and Logic – Lesson 6

Table of Contents

• Maimonides’ approach to derashot: between interpretation and legislation
• Pardes, sod, and metaphysics in the context of Maimonides
• A scientific analogy: cognition versus thinking
• Rationalism versus empiricism and the direction of the argument
• Judicial legislation as an intermediate category
• The difficulty of criteria: peshat and derash
• Kant: analytic/synthetic and a priori/a posteriori
• Hume, induction, and the synthetic a priori
• Intermediate categories and the parallel to derash
• Kant and the explanation of the synthetic a priori
• Authority, the Sadducees, and the claim that derash can be correct
• The goal of what follows: the logic of derash and cognitive thinking

Summary

General overview

The text presents Maimonides’ approach to derashot as an intermediate category between interpretation, which uncovers what is written in the Torah, and legislation, which creates a rabbinic law that is not drawn from the verses. It tries to establish that derash is connected to the verse, but is neither peshat nor pure legislation. It proposes an analogy from scientific cognition between cognition—interaction with reality—and thinking—an internal activity not drawn directly from the world—and argues that there too there is a parallel intermediate category. In that context, it explains through Kant and Hume the problem of generalizations and laws of nature, and suggests that the accepted dichotomies create paradoxes, whereas understanding intermediate categories makes it possible to see both derash and scientific generalization as processes with their own logic. It declares that the goal of what follows is to show how the logic of “cognitive thinking” and of derash works, against the view that this is just a game or merely a matter of formal authority.

Maimonides’ approach to derashot: between interpretation and legislation

Maimonides sees derashot as tools that expand the biblical text rather than uncovering what is already in it in the classical sense of interpretation. Interpretation in its classical sense means exposing something that is in the Torah itself after explanation, whereas legislation creates a new law that does not emerge from the biblical text, and that is what is called a rabbinic law. Maimonides argues that there are intermediate situations in which a derash is connected in some sense to a verse, yet it is neither interpretation nor legislation, and that category is called derash. The example of pure legislation is the ordinance to light Hanukkah candles, which in the simple sense is not based on verses, whereas the prohibition of labor on the Sabbath is described as a case of straightforward interpretation anchored in what is written in the Torah.

Pardes, sod, and metaphysics in the context of Maimonides

The speaker notes that he does not know how Maimonides relates to remez and sod within pardes in the halakhic context. He guesses that when Maimonides thought about sod he meant metaphysics, and therefore there is no point asking there whether something is Torah-level or rabbinic, because that question is irrelevant when one is not dealing with Jewish law. He adds that sod is connected to verses such as those in Ezekiel and the Account of the Chariot, but with respect to halakhic verses he does not think Maimonides defines anything there as sod.

A scientific analogy: cognition versus thinking

The text distinguishes between cognition as an act of interaction with the world in which facts are brought to a person’s knowledge, and thinking as an internal activity in the subject that is not drawn from reality. Cognition parallels interpretation, because both draw information from the external “given,” whether that is physical reality or a text being interpreted. Thinking parallels legislation, because both produce an outcome from within the person and not through interaction with the source, and therefore different people may produce different results without any factual contradiction arising. The speaker illustrates this with the distinction between experimental measurements, which are the result of cognition, and drawing a straight line between points as an act of generalization, which is the result of internal processing.

Rationalism versus empiricism and the direction of the argument

Rationalists believe that thinking can produce information about the world, and not merely organize data acquired by observation, whereas empiricists believe that information about the world can be drawn only through observation. The speaker argues that the distinction between thinking and cognition is usually experienced as fairly clear, but when one moves to general theories a tension emerges: the generalization is not drawn from reality, yet it still claims to say something about reality. He presents science as a process that moves from particular observations to a general law, and from here the problem arises of how a general law gains validity.

Judicial legislation as an intermediate category

In the legal world there is a phenomenon of judicial legislation, in which a judge performs an act that looks like interpretation but includes elements of legislation. In this phenomenon, the result is not the exposure of what is already in the law itself, but an addition “from the interpreter’s own resources,” so another judge could have reached a different result. The speaker maps this onto his own terms and says that this is derash, not interpretation, and that derash contains a legislative dimension and not only an interpretive one. He notes that in the legal world people usually call this combination “interpretation” as opposed to “judicial legislation,” whereas in his terms it divides into the categories of peshat and derash.

The difficulty of criteria: peshat and derash

The speaker is asked whether derash can be identified by subjectivity, and he replies that this is not a bad indication, but not necessarily a necessary one. He emphasizes that he does not have an orderly set of criteria that distinguishes when a move is derash and when it is peshat, and he attributes this to feeling and intuition. He adds that criteria of literal versus non-literal are naïve and incorrect.

Kant: analytic/synthetic and a priori/a posteriori

The text presents two divisions of propositions in Kant: a logical division between an analytic proposition and a synthetic proposition, and an epistemological division between an a priori proposition and an a posteriori proposition. An analytic proposition follows from analyzing the concepts, like “every bachelor is unmarried,” and a synthetic proposition requires the addition of information, like “this ball is heavy” or “this wall is white.” An a priori proposition does not require experience in order to recognize its truth, while an a posteriori proposition does require observation. The speaker explains that before Kant there was a tendency to identify the divisions so that the analytic overlapped with the a priori and the synthetic overlapped with the a posteriori, and from that comes the conclusion that the only way to accumulate information is observation—in other words, empiricism.

Hume, induction, and the synthetic a priori

The speaker translates Hume’s problems into a challenge to the possibility of justifying generalizations and general laws from particular observations, and formulates this as the question of how thinking can generate information about the world. He presents the laws of nature as synthetic claims that do not follow from conceptual analysis and therefore are not mathematics, but that also cannot be fully justified by observation, because observation is limited to specific cases. He explains that the problem is that science strives for general laws while observations are always particular, and that there is no decisive statistical justification, because one can build infinitely many theories that fit the same observations while differing radically in their predictions about the future. He describes two interpretations of scientific laws: one that sees the theory merely as a way of organizing facts, so it is a statement about us and not about the world, and one that sees it as a claim about the world that is “true” though not certain. He stresses that meta-philosophy asks what justifies reliance on those laws.

Intermediate categories and the parallel to derash

The text argues that dichotomous thinking—“either cognition or thinking” and “either interpretation or legislation”—leads to paradoxes, and that there are intermediate categories such as judicial legislation, cognitive thinking, and derash. It presents science as fundamentally built on derash in the sense that it rests on processes that are neither pure observation nor detached thinking, but rather a process that contains cognitive elements. It suggests that a successful generalization resembles seeing with the “eyes of the intellect,” in Maimonides’ terms at the opening of Guide of the Perplexed, so that the straight line on the graph is not merely a subjective product but something that can be “cognized.” It argues that the dichotomy leads to the position that there can be no general laws, neither in science nor in Jewish law, but only a collection of particulars, whereas accepting the intermediate category makes it possible to understand how an expansion can be correct even if it is not a disclosure.

Kant and the explanation of the synthetic a priori

The speaker confirms that the appropriate Kantian term is “synthetic a priori,” but argues that Kant explains its possibility in a way that brings the problem back. He argues that Kant turns the synthetic into the analytic by shifting the claim from reality to the human tools of perception, so that the proposition becomes analytic in relation to the tools of cognition and is no longer a claim about the world itself. He presents this as “throwing the baby out with the bathwater,” and distinguishes between Kant’s important diagnosis and the line of reasoning that he rejects.

Authority, the Sadducees, and the claim that derash can be correct

The text describes the discomfort with derash as stemming from a dichotomous outlook that classifies derash as an invention not written in the verse, and therefore at most accepted by virtue of formal authority such as ordination or the Great Sanhedrin. It presents the Sadducees as people who could not make sense of derash because they saw only two possibilities: observation-peshat, which extracts what is written from the text, or thinking-invention, which is unrelated to the text. The speaker argues that there is a possibility that derash is an expansion connected to the text and still correct in a sense that is not merely formal, and that there are also standards of correct and incorrect in expansions, not only in disclosures. He compares this to the scientific problem of choosing a theory from among infinitely many possibilities, and presents the need to understand a method that is not merely ad hoc and not based only on “I am authorized.”

The goal of what follows: the logic of derash and cognitive thinking

The speaker states that the goal of the next part is to show how the synthetic a priori logic of cognitive thinking and of derash works, and to try to bring order to inferences that look arbitrary. He says that he believes there must be a mechanism that can be transmitted and understood; otherwise the whole thing is just a game. He concludes by saying that he will argue later that the situation is not as problematic as it seems, and that examples can be presented that will make the claim much easier to accept.

Let’s see where we’re holding right now; I want to move on to the next stage. What we’ve seen up to this point is Maimonides’ approach—how Maimonides understands derashot. We saw that he views derashot as tools that expand the biblical text, not tools that uncover what is already inside it, but expand it. But as I also said last time, they sit in some kind of intermediate state that very often we find it very easy not to notice. On the one hand, it’s easy for us to see someone interpreting what is written in the Torah. Once you’ve interpreted what is written in the Torah, you’ve uncovered something—maybe it wasn’t obvious at first, but after the interpretation you’ve uncovered something that is in the Torah itself. That is interpretation in the classic sense, interpretation that reveals. The antithesis, which is also very easy to identify, is legislation. When we legislate a new law, then clearly it’s not something that emerges from the biblical text. It’s a new law; it’s neither an expansion nor a revelation and has no connection to the biblical text, and that is what’s called a rabbinic law. Legislation—the product of it—is a rabbinic law. Here what Maimonides wants to claim is that there is an intermediate state, or even several intermediate states, a state that lies between legislation and interpretation, in the sense that when you make a derashah, then yes, in some sense it is connected to the verse. It’s not like legislation; it’s not like saying: light Hanukkah candles. Lighting Hanukkah candles is a rabbinic enactment; in its plain conception at least, it has no connection to verses—pure legislation. Ordinary interpretation of not doing labor on the Sabbath—say, assuming that really is straightforward interpretation—then fine, it is forbidden to do labor on the Sabbath, because the Torah says it is forbidden to do labor on the Sabbath. That’s the other side. Maimonides claims that there is a category in the middle, something that is connected in some sense to the verses, but it is neither interpretation nor legislation—it is something in between, and that is what is called derash. And derash is precisely this middle category that stands between legislation and interpretation. To make that a bit clearer, maybe, we’ll enter into this analogy. I’m going to make an analogy. Out of the whole Pardes, he only brings this under… he doesn’t say anything about remez and sod, so I don’t know. I think that when Maimonides thought about sod, in my view—I don’t remember sources right now—but when he thought about sod, I assume he meant metaphysics. That’s what he called sod. But then that has no… it’s not connected to Jewish law. I don’t think it’s connected to the legal verses in the Torah, so there’s no point discussing whether it comes out of the legal verses in the Torah, whether it’s Torah-level or rabbinic. It isn’t measured in those terms. Sod is also connected to verses in Ezekiel, for example, the Account of the Chariot. Yes, but the question whether it’s Torah-level or rabbinic is not such a relevant question when you’re not dealing with Jewish law. With respect to legal verses, I don’t think Maimonides defines sod there. At least it doesn’t seem so to me—again, I really haven’t checked the topic in depth—but that’s how it seems to me. I’m going to make an analogy that will also accompany us a bit later on. In the scientific context too there is this kind of division into two polar aspects, opposed in a polar way, and there too it’s very easy to miss the middle. When we look at the world, we can stand before it in two positions. We can stand in the position of someone who thinks, and in the position of someone who cognizes. When we perform an act of cognition, that’s an interaction with the world itself. When I now cognize that there is a table here—I saw that there is a table here—then the fact that there is a table here was brought to my awareness in an act of cognition. I recognized that fact from the table and that’s how I brought it into myself. In that sense, cognition parallels interpretation. Because cognition basically tells me what the facts are that exist in the reality in front of me. I cognize reality, and that’s how I draw out the facts that are in it; I cognize the facts that are in it. Just as in interpretation, the facts under discussion in the interpretation are the Torah or the interpreted text, and the interpretation is basically cognition, the means of cognition of the interpreted text. Interpretation parallels cognition. What parallels legislation? What parallels legislation is thinking. Because thinking—when I stand before the world and think, it seems to me that the law of gravity is a correct law. Seemingly, what we’re talking about here, this very generalization that I make, is done entirely inside my brain—inside my intellect, not my brain. Are you drawing a distinction here between thinking and cognition? Yes. So thinking is basically something that is not done through interaction with reality. It’s an act that takes place within the subject. Inwardly. I think all kinds of things, I can generalize facts, I can just think about various ideas, whatever. But an act of thinking is an act performed without interaction with the world. It’s something that perhaps one could also say is a result of the structure of my intellect. Someone whose intellectual structure is different—the results of his thinking will be different. In contrast, the results of cognition are supposed to converge for all of us, because we cognize facts. If there’s a table here—under the optimistic assumption that our cognitive faculties are not subjective and that cognition is something connected to objective reality in a straightforward way—then all of us, if we see a table, if there is a brown table here, we will all see a brown table here. Are the tools of cognition more objective than what the intellect sees? It’s not more objective; it’s not even measured in terms of objectivity. The intellect is not—it is not, seemingly at this point at least—it’s not making claims about the world. The intellect is some kind of construction that is made within me. So what does that have to do with objectivity or non-objectivity? I’m not accusing the intellect of not being objective; it isn’t supposed to be. It’s not making claims about the world. It arranges in my head all kinds of things—maybe also facts that I’ve cognized, maybe also just ideas that I think about. But the act of thinking is an act that takes place inside me, inwardly, without any interaction with the outside. In principle, it could be that your thinking happens in a completely different way from mine, theoretically, and there’s nothing wrong with that. Since we are not making—once we make a claim about reality, then if I cognize a brown table here and you cognize a green table here, then there’s some kind of problem. This table is either brown or green; we are not both right—one of us is mistaken. But when our thinking doesn’t match, that isn’t supposed to create a problem, because thinking, at least in the picture I’m presenting now, does not make claims about the world. But the opposite thing would indeed present a problem: if a large number of people do think in the same way. Okay, no, that’s not disputed. You could maybe say that as a result of that, perhaps there is nevertheless some objective dimension in our thinking, although someone else will tell you: fine, because we all come from the same genetics, we all came from the same common ancestor, so we’re all built in the same way, and therefore our thoughts are generated in the same way. That doesn’t mean they have any connection to the world as such. Fine? You can argue about that. But on the principled level, it seems to me that the distinction between thinking and cognition is a distinction we usually live out in a pretty clear way. There are situations in which we perform cognition—we draw information from reality—and there are situations in which we think. Even if we think about reality, the thinking moves from me to reality, not from reality to me. That is, say, in the example—I think I brought here the example of the straight line, right? With the points from the experiment. We talked about that. So those points from the experiment are a result of cognition. I measured with instruments and saw that with a force like this, such-and-such acceleration is obtained, and with a force like that, such-and-such acceleration is obtained. So I cognized those particular facts, and now I’m equipped with that information that I cognized. What happens when I make a generalization? I now make a generalization, I draw the straight line through this collection of measurements. So when I made that generalization, the straight line was not drawn out of reality. The straight line is the result of an act of thought. I took those facts that I cognized and processed them. But that processing is not aided by the world. That processing is done entirely within me. And therefore this act of thinking, basically, is not supposed to make any claim about the world. It takes place within me. Even if I think it does make a claim about the world, that claim does not come from the world—it goes toward the world. That is, it emerges from my thought and perhaps, if I’m very optimistic, it also fits what happens in reality itself. But it is not drawn from reality into my intellect. The direction is the opposite. Cognition is from reality to me. Thinking happens within me, and maybe from me also toward reality. That depends on whether we are rationalists or not. Rationalists have a kind of belief that things of thought can make claims about the world. We can derive information about the world by means of thought and not only by means of cognition. As opposed to empiricists—empiricists are people who believe that information about the world can be drawn only through observation. No thinking will yield information about the world. Thinking is an ordering of things that takes place within me. Why? Because information about the world can be drawn only by activating the senses, my cognitive faculties. I look at the world and from it I draw information. After all, if I make something up in my feverish brain, why should it correspond to something that happens in the world? Thinking is a property that depends on the structure of my tools, not on what happens in the world itself. Fine? So therefore, in practice, this distinction between thinking and—say, a philosopher can think and a scientist is supposed to cognize. That’s often how people think of it, at least, though it seems to me it’s not precise in either direction—but that’s often how people think of it. And this distinction between thinking and cognition is exactly parallel to the distinction we made in the Torah context, or also in the legal context, between legislation and interpretation. It’s the same distinction. That is, interpretation is basically cognition of the facts—only not physical facts but legal, halakhic, or Torah facts. Fine? When I interpret the Torah, I start from the Torah and draw information into myself. It may be that I need to use sophisticated digging tools, but when I use those digging tools, what I ultimately uncover is something that is in the Torah, and then it reaches me. So basically interpretation is a kind of cognition, where this cognition is directed toward a text or toward a work of art, it doesn’t matter, and not toward physical facts, okay? Toward facts in the world. But it is basically an act of cognition. In contrast, legislation is an act of thought. Yes, just as thinking in the scientific context is not drawn from the world but is done entirely inside my head. It is not connected to the facts—on the contrary, perhaps I impose the results of my thinking on the facts, but it is not drawn from the facts; it is done within me. Legislation is the same. When the Sages determine that Hanukkah candles must be lit, they do not do so by interpreting some verse or by a midrash on some verse, but by deciding something that seems right to them. In that sense this is an act of thought, an act that takes place inwardly within them, not by means of interaction between them and the Torah sources, with the Torah, okay? Or the tools of derash, and so on. Fine? Rather it is something that takes place inwardly within them. “Whatever the Rabbis enacted, they enacted in the pattern of Torah law.” Fine, yes, in one sense or another. But it is a rabbinic enactment; the Rabbis do it themselves, it is not drawn from the Torah—otherwise it would be Torah law. Fine? This distinction we discussed earlier in the interpretive context—that there is basically an intermediate state between legislation and interpretation, and that is derash—the same thing also exists in the scientific context, or in cognition of reality, not cognition of texts, right? Or works of art, but cognition of reality. There too, I think, there is some kind of intermediate state between thinking and cognition. Cognitive thinking, call it that, or something like that. What? Cognizing thought. Cognizing thought, yes. In the legal context you can see this phenomenon when you look at what is called judicial legislation. Judicial legislation is basically a situation in which a judge as if performs an act of judicial interpretation. The judge’s role is ostensibly to interpret, not to legislate. The legislature legislates. The judge is supposed to interpret the laws and apply them to the case before him. But there are situations in which we understand that the act the judge performs also involves some components of legislation, not only interpretation. That is, there is something here that is as if interpretation, but it is clear that the product of this interpretive move did not uncover something that is in the law itself, but added something from the interpreter’s own resources. Yes, something of the interpreter’s own, from the interpreter’s own tools, and therefore there is something here that also borders on legislation; it has a legislative dimension. Another judge, say, would have done something different here. That is, the result is not an objective result; it is not an uncovering of what is written in the law book, not even by sophisticated interpretive means, but rather an addition, an expansion. In our earlier terms, I would say: this is derash. What the judge has basically done here is derash; he has not interpreted. And derash has a legislative dimension and not only an interpretive dimension. Fine? So in the legal context too, something similar happens. Is your index for checking whether something is derash whether it’s subjective? Meaning, whether every judge would have been able to derive the same thing from the… No, that’s not a bad indication; I’m not sure it’s necessary. You can always say that even with derash—even if I do derash—we would all reach the same conclusion because we are all built in the same way. Not because it really corresponds to some objective thing outside us, but because we are all built in the same way, and therefore we also make our generalizations in the same way. By the way, many people think this way—that scientific generalizations convince the scientific community even though a generalization is, after all, something completely subjective, because we are all built in similar ways and therefore we make generalizations in similar ways. That’s all. Not really because it captured something true in reality itself. Fine? Judicial legislation is something that is interpreted as if everything stems from interpretation; they give it the construction of coming out of—sorry, not derash—of interpretation. And they classify it under interpretation. What they call interpretation in the legal world actually divides into two categories: interpretation and derash, in the terms I’m using now. When you read books on interpretation in the legal world, you’ll see there elements of derash and elements of peshat. They don’t make such a distinction in terms of peshat and derash. They call it judicial legislation and interpretation. So I didn’t understand the question within us—meaning, when do we feel that something is derash and when is it… I don’t know, think about it. I don’t know any criteria for that. I know there are situations where it’s clear to me that someone added something here beyond what can be found in the verse itself, even though maybe I agree with what he did—it doesn’t matter—but it isn’t written in the verse itself; it’s an expansion. And there are situations in which it seems to me that what he did here was actually uncover another dimension hidden within the verse. When do I feel this way and when do I feel that way? I don’t know. It’s the same question as the relation between derash and peshat. Where does the line pass, when is this derash and when is it peshat? I don’t know. It’s a matter of feeling, intuition—I don’t know how to give a criterion for that. It’s clear that there are no criteria of literal and non-literal; those are naive criteria, and it’s clear that that’s not correct. So in the scientific world too, this middle state between thinking and cognition is something very, very central. The scientific world is basically founded on derash. Only on derash. And this is a point that is very important to understand, so I’ll expand on it a bit now. I’ll formulate it in Kantian terms. If we look at different propositions in language, we can propose two divisions of propositions. One division is a division on the logical plane, the division between an analytic proposition and a synthetic proposition. An analytic proposition is a proposition whose content is only an analysis of the concepts involved in it, yes? I don’t know—“the ball is round,” or “every bachelor is unmarried.” These are basically propositions where you don’t need to observe the bachelor we’re discussing. I’m really getting ahead of myself here in a way that isn’t careful. So indeed, this is something where it’s enough to analyze the concept I’m dealing with in order to know that it’s true. Okay? If I understand what a bachelor is, then it’s clear to me that every bachelor I look at will not be married. If I understand what a ball is, then I’ll understand that a ball—even if I don’t look at it—it’s clear that this ball is round. It follows from the analysis of the concept itself that I’m dealing with; that’s why it’s called an analytic proposition. A synthetic proposition is a proposition that does not follow from analysis of the concepts, but rather requires a synthesis with additional information beyond what exists in the definitions of the concepts themselves, like “this ball is heavy.” “This ball is heavy”—not every ball is heavy, so clearly analysis of the concept “ball” won’t give me this proposition that this ball is heavy. I have to synthesize some additional information here that is not embedded in the definition of the concept “ball,” and that’s why it’s called a synthetic proposition. Does a synthetic proposition have to refer to something specific? What? Does it have to refer to something specific—“this ball is heavy”—to a group or something? No, why? It can be a proposition that… “All bodies with mass are attracted to the earth,” for example. It’s pretty clear that’s a synthetic proposition. At least that’s how people usually think, unless you identify physics with mathematics. That is, even a proposition—I don’t really know Kant all that well—but you can also analyze a proposition or a concept and expand it through that analysis. So not analysis—that’s expansion, that’s synthesis. No, but you kind of took a concept where the definition of a ball is simply that it is round. To say that a ball is round is simply to restate the definition of the concept. It’s not always just restating; sometimes it’s more complex. When you derive from the axioms of geometry the proposition that the sum of the angles in a triangle is one hundred and eighty degrees, I would not call that simply restating the axioms, even though that is basically what you’re doing there. Because…? Because that’s mathematics, not physics. You don’t need to observe this triangle in order to know that the sum of its angles is one hundred and eighty degrees. It follows from the definition of lines and points and the axioms. That’s all. Fine? Now there it’s more sophisticated; not everyone will do it simply. When you say that the ball is round, everyone understands that—that’s not a sophisticated analysis. There are sometimes situations where the analysis is sophisticated, but it is still analysis. You still don’t need to add anything beyond what is embedded in the definitions and in the axioms, say in the mathematical context. Fine? So that’s one division, a division between analytic propositions and synthetic propositions, where this division is a division connected to the structure of the proposition, and it’s a logical division. Okay? There is another division, which is an epistemological division. Epistemological division—epistemology is the theory of cognition, yes? An epistemological division means: how do I know, or how do I cognize, that a certain proposition is true? So here the division is between a priori propositions and a posteriori propositions. A priori propositions are propositions that precede experience, and you don’t need experience in order to cognize them or recognize their truth. And a posteriori propositions are propositions that require observation, that require experience. Fine? This division between a priori and a posteriori is not connected to the structure of the proposition, right? The division of whether a proposition is a priori or a posteriori is not connected to the concepts involved in it, to the structure of the proposition; it is connected to the question of how I cognize that this proposition is true. Do I need observation for it or not? Therefore this division belongs in the conceptual sphere of epistemology, of the theory of cognition. Do I need observation—do I need cognition—or is it the product of thought? If we now speak in the previous terms, that’s why I’m bringing this up. Does this thing belong to cognition, or is it a product of thought? The previous distinction is a distinction connected to the structure of the proposition itself. It isn’t connected to the epistemological question of how I cognize it. What is the relation between what the proposition claims and the concepts involved in it? Is that relation one of analysis or one of synthesis? Therefore it characterizes propositions even if there were no human being in the world at all. I could characterize propositions as analytic propositions or synthetic propositions even if no one knew those propositions at all. Before the proposition that the sum of the angles of a triangle is one hundred and eighty degrees was discovered, no one knew that proposition. And still, that proposition was an analytic proposition. Even though no one knew it. It has nothing to do with the question of how I know the proposition. It has to do with the question of what kind of proposition it is. Fine? Was it formulated? Is that proposition still formulated out of what we already knew? Not because it was formulated. It’s not a question of formulation. Even if it was never formulated, that doesn’t matter. So no one had ever done it yet, but on the principled level, if you perform an analysis of the concepts, you’ll be able to extract the proposition or the claim. Fine? Seemingly, then, we basically have here one distinction that lies on the epistemological plane, between a priori and a posteriori—or on the cognitive plane, fine?—and another distinction that lies on the logical plane of the structure of the proposition, maybe even of thinking, one could say. How is this proposition structured? Fine? Kant, when he made—when he pointed to—these two divisions, these divisions existed before him as well, but before him people thought they were identical or overlapping divisions. Because on the face of it, in a simple way, these two divisions are independent, as I said earlier. One belongs to the structure of the proposition and the other belongs to the question of cognition—how do I cognize this proposition? So two independent divisions are supposed to create four kinds of propositions, right? Analytic a priori, synthetic a priori, analytic a posteriori, and synthetic a posteriori. If there is no dependence between these divisions, then all the combinations ought to be possible. Okay? But when you examine the set of propositions—just try to think of examples—then all the examples you come up with, almost all the examples you come up with, will be examples that are either analytic and a priori or synthetic and a posteriori. You won’t find examples—at least at first glance—you won’t find examples that are synthetic and a priori or analytic and a posteriori. I’ll give an example. For instance, let’s go back to the propositions I gave before, yes? “Every bachelor is unmarried.” Fine? So in the analytic/synthetic division, where does that belong? Analytic. In the division of a priori and a posteriori? It’s a priori. You don’t need observation in order to know that every bachelor is unmarried, right? Same thing with the round ball, right? There too it is analytic and a priori. Now let’s take an a posteriori proposition, say “this wall is white.” Fine? That is of course an a posteriori proposition. I don’t know it without seeing the wall; it could also have been blue. Right? Is that proposition analytic or synthetic? It’s synthetic, right? That is, an a posteriori proposition is always synthetic, and an analytic proposition is always a priori. Why is “this wall is white” synthetic? Because it doesn’t follow from analysis of the concept “wall” that it is white. I need additional information; I have to synthesize additional information here beyond the information embedded in the definition of the concept “wall.” That is, there are cases—all conditional propositions, of “if it appears this way then that way”—and that can be analysis. Right, depends on the proposition. State a proposition and then we’ll think. “If Socrates is a human being and all human beings are mortal, then Socrates is mortal.” That’s an if-then proposition that is analytic. Fine? But I can think of if-then propositions that are synthetic. “If the sky is blue, then it is beautiful,” for instance—a synthetic proposition. “If-then” does not automatically mean the proposition is analytic. Yes, obviously. But if it is conditional and analytic, then it is a posteriori. What? If it is conditional and analytic, then it is a posteriori. Why? Then it is a priori—why a posteriori? You don’t need observation because I need to discover—I need to discover which side of the condition I’m taking in order to… No, you don’t need to discover anything; you just want to verify the conditional itself. If you want one of the conditioned terms or the antecedent or consequent, that’s something else. But if you want the conditional itself, then what do you need? You don’t need to observe anything. So that’s something else; then it’s no longer an if-then proposition. So basically these examples show us something that, on second thought, really seems self-evident: that these two divisions are actually two sides of the same coin. Why? Because an analytic proposition is a proposition that can be extracted through analysis of the concepts involved in it, right? So clearly I won’t need observation in order to know it, right? Because it’s enough to analyze the concepts, and therefore it will also be a priori. An analytic proposition will be a priori, right? Now what happens with an a posteriori proposition, say a synthetic proposition? A proposition that says this wall is white, yes? If it doesn’t follow from the analysis of the concept “wall,” then where do I actually know it from? Only observation, only observation, right? So therefore it’s clear that a synthetic proposition is a posteriori. So in practice, this is how people thought until Kant at least: the idea that these two divisions are independent divisions is an illusion. It is the same division. They are two sides of the same coin. The a priori is always analytic, and the analytic is always a priori. It is true in both directions. Okay? Now as a result of that way of thinking, you run into a lot of problems. Because basically what that way of thinking says is that it is impossible to accumulate information. That is basically what it says. If we identify these two divisions with each other, that basically means that information cannot be accumulated. Why? Because a proposition that accumulates information, or an inference that accumulates information, is always synthetic, right? It is something beyond the information embedded in the definitions of the concepts. When I say that this wall is white, that proposition adds information for me beyond what I already had when I knew the concept “wall.” It is a proposition that added information for me. Right? Now if such a proposition can come to my knowledge only through observation, what does that actually mean? It basically means that the only way to accumulate information is through observation alone. Or in other words, analysis or thinking that does not involve observation can never add information for me. Right? That is basically what this assumption says. Or in other words, it means empiricism. Right? Empiricism is the view that information is added only by means of observation. As opposed to rationalism. Rationalism is a view that looks… Rationalism also looks at reality, no? Ah—but it says that not only looking at reality adds information. The intellect’s processing also is an instrument that can add information for me on the basis of observations. Fine, okay. I make generalizations, as I spoke earlier about the straight line. You observe the five discrete points, so you collected particular information by observation alone. Now you process the information you observed, and you say the straight line is the correct line. That processing is processing that you do in your head; it is not the result of observation. But if you are a rationalist, then you think that the result of this processing, the general law, is a law about the world. It contains information about the world even though it is the product of a process of thought alone, without observation. Fine? So in other words, in order to be a rationalist, you have to drive a wedge between the two divisions we talked about earlier. Between the two divisions, between the a priori/a posteriori division and the synthetic/analytic division. Because if you adopt the identity between these two divisions, that there is no wedge between them—that it’s the same division—then you can basically accumulate information only through observation. Now understand the limitation of such a conception. The limitation of such a conception—and these are all of Hume’s problems because of which Kant developed this whole conceptual system—is that Hume basically argued that no general law can be accumulated through observation. The challenge to induction. Yes, the challenge to induction, to causality. A whole series of challenges, all of which Kant translated into this language as the idea that Hume identifies the two divisions. Hume basically identified the two divisions, and therefore he ran into a whole list of problems. Yes, how do we know that—let’s try to characterize it in terms of analytic and synthetic and a priori and so on. Fine? Is it analytic or synthetic? Synthetic, right? Because clearly analysis of the concept “mass” will not give me the law of nature that mass falls to the earth. Otherwise there would have been no need for observation; physics would have been a branch of mathematics. But the analysis of the concept of gravity… Fine, there is no gravity yet; you haven’t discovered gravity yet. Gravity is what lies behind the proposition I stated, that all objects with mass fall to the earth. That’s what it means—that there is a law of gravitation. But I’m asking: how do you know that? So I’m saying it’s clear that there is some kind of generalization here, or it’s clear that you… this is not merely an analysis of the concept of mass itself. Right? Then Hume asks: if that’s so, then where do I really know it from? After all, it doesn’t come from observation, because in observation I observed some specific objects and saw that they have mass and indeed fall to the earth. But where do I know the proposition that contains so much information—that every object with mass will always fall to the earth? I have not observed all objects with mass at all times, right? I observed some of the examples and it worked. Right, it always worked. But the generalization is not the result of observation. In other words, in Kantian translation, what Hume is claiming is that the generalization is an a priori proposition. Since generalization is an act of thought, it is not an act of cognition. It is done not as a result of observation; it is processing that takes place inwardly within me. On the one hand. On the other hand, as you rightly said, the result of the generalization is a synthetic proposition. When I say that all objects with mass fall to the earth, I have stated a synthetic claim. So how can thought alone produce a proposition that makes claims about the world? How is it possible that thought adds information about the world for us? That is basically what the whole collection of Hume’s questions can be formulated as in this general way—it includes them all. And why is it a priori? After all, you saw objects fall! You saw objects fall, but you didn’t see that all objects with mass fall. How do you know that all objects with mass fall? You can’t say that you know that from observation. So what then? You know it from generalization. Right? But generalization is an act of thought, not an act of cognition. You do it within your own brain, inwardly, within your intellect. So why assume that such a thing will yield information about the world? Okay? There is something here that is a very, very problematic leap. Say it isn’t—say it isn’t attracted, then you infer that it is. I didn’t understand. If you see that things don’t fly off and detach from the earth… You see that about a few objects that you saw. What do you mean, see? The objects you observed—I see that they don’t detach from the earth. But maybe there are other objects that do detach? How do I make that generalization? The problem is always… laws of nature are always general laws, and observations are always specific observations. That’s the most basic problem of science, right? Every observation is like the beginning of The Brothers Karamazov, not… how does the quote go? That every… every happy family is alike and every unhappy family is unhappy in its own way. Anna Karenina, right, not Tolstoy. Tolstoy. So the question is how… And these are propositions that are proved mathematically? What? No. Physics. No. Physics, not mathematics. So the tragedy of physics is that observations are always observations of specific cases, while the laws people strive for and formulate are always general laws. And the fact that it works doesn’t mean that it’s true. I didn’t say it’s true. So you… do you have a solution to the tragedy? Why be sad—let’s be happy. It’s not true, after all; so why assume that it’s true? Fine, that too is some way of relating to tragedies. Okay. But still there is a certain tragedy here, fine? There is a certain tension built into the basis of the scientific process. The scientific process always goes from the particular, from the individual observation, to the general law. And here there is some problem. Hume says: how do you know? Who told you that induction is legitimate? Who told you that one may make generalizations? When Kant translates the Humean problem, he basically says: who told you that a process of thought can produce information? Who told you that there are propositions that can be synthetic on the one hand and a priori on the other? That is basically what he says. A priori means thought, right? And synthetic means that it adds information, right? How can thought add information? How can that be? Information is drawn in by observation. Information… it cannot be that information is added for me by an act that is an act of thought. What, such a thing is impossible? That is basically the question, the Humean question, yes. Aren’t we really using the same word here in two different senses? That is, when I say that information has been added to me, then in the abstract philosophical sense, information can be something logical that I am forced to say is true. But when I speak about physical things or things connected to reality, when I say that something is true I really mean something I am willing to rely on. Okay. And indeed a priori truth… But why are you willing to rely on it? You get on an airplane, right? After they designed it according to the laws of physics. Why do you get on the airplane? My observation is sufficient, even statistically, for me to rely on it. What does that mean? There is no statistics here at all. No statistics. Not one millimeter of statistics will succeed in showing me anything here. I will show you beyond all doubt a theory that is no less good statistically, and it will tell you that the plane will disintegrate one second after takeoff. And that will be a theory that fits all the facts. Regarding the proposition that objects with mass are attracted to the earth—the same thing, what difference does it make? All the objects you saw—I will characterize them, I will characterize them by all kinds of features, and I’ll tell you: fine, these types of objects that you observed, they fall to the earth—say, the round, the brown, the triangular, the green, and those that begin with the letter L. Say if that is what includes all the objects you observed. Those are the objects that fall to the earth. You think this is not a simple theory. It’s not a statistical consideration; it’s a consideration of simplicity. It has nothing to do with statistics. Yes, but he doesn’t check only a priori on the basis of observations. He doesn’t check only those objects. But every theory I propose will fit one hundred percent of the observations, otherwise it’s not a legitimate theory. But there are infinitely many possible theories, and only a tiny fraction of them will say the plane survives after takeoff. Only an infinitesimal fraction of them. Yes. Doesn’t it make sense to say that I actually don’t care whether it’s true or not true; rather, I create some generalization for myself and I ask whether this generalization works, and I don’t really care how true or untrue it is. No—what does “make sense” or “not make sense” mean? Decide. If it makes sense to you, then say it. To me it doesn’t make sense, so I don’t say it. It’s a question of what you think, not of what I think—simply whether it is useful or not useful. Let’s take… No, it’s not a question of usefulness. The question is whether, because of this, you are willing to get on an airplane. I don’t know; those experiments I prefer to do in the laboratory and let the electrons get killed. But for me to get on the airplane and run the experiment on the law of gravity, I would prefer to avoid that without approval from the Helsinki committee. I observed a number of cases, by means of this I made a generalization, and now I am convinced that my generalization is correct. Why are you convinced it is correct? If you test it in the lab. But why are you convinced it is correct? It hasn’t been refuted. It works. So what if it works? The test that works for you in the lab—there are infinitely many other generalizations that will fit what works for you in the lab. But at some point I’m already willing to say, okay, I’m willing to trust it. You’re willing to say—on what basis? After all, that’s what Hume asked. We all know that we are willing to say it. What a philosopher asks is why we are willing to say it. That all of us are willing to say it—that’s known. The only question is why, and that’s a good question. And after all, I can offer you infinitely many alternatives in which it won’t work. Why do you choose the optimistic alternative—and are even willing to stake your life on it? That is the question he asks. Obviously factually we all get on airplanes, almost all of us, except people who have a special fear, so they get on scooters, never mind. Fine, but we all rely on these scientific laws. What Hume asks is a philosophical question. What is the justification for this? Seemingly there is no justification for it. So indeed, when Kant translates Hume’s questions, he reverses the direction. He doesn’t ask whether it is true; he asks how it can be true. That is, he assumes that it is true—the whole question is only… But in fact Hume is right: how can such a thing be? So he makes the distinction we made between thinking and cognition, basically. Yes, yes—he makes the… I’ll get to that in a moment. Yes. Meaning, the theory that says there is scientific truth—that there is scientific truth which is true until they prove it wrong and then they change it—the question is what people mean when they say that. It can mean at least two things. It can mean that it’s reasonable; as long as it hasn’t been proved otherwise, I adopt it even though I don’t regard it as certain, but I still see it as a claim about reality. Yes. People were sure that the world was flat, until they proved it was round, and they were sure of it in… Okay, you don’t need to convince me that scientific truths are not certain. That seems clear to everyone. The question is how you relate to that lack of certainty. Do you infer from this that scientific truths—or scientific laws—do not make claims about the world at all, but are merely my way of organizing the material? What I know about the world is the set of specific facts, okay, that I observed. The theory is my own responsibility alone, and the theory is a statement about me, not about the world. That is one possible way to formulate it. Another way to formulate it—and one can say in the same words you said, both possibilities. The other possibility is to say: the theory is not certain, this is not mathematics, but it is very plausible; I think it is true. In principle it is possible that there will be a future experiment that refutes it, and then I’ll look for another theory. But as long as no such experiment has occurred, I think it is true. Not that I say, “Okay, this is my way of arranging things; I’m not claiming this is a claim about the world.” You understand? Those are two completely different statements. Okay? So what emerges from Hume’s problems is the first formulation. The formulation that says, basically, this is a claim about us, not about the world. Not sure Hume himself actually took that step, but that is what ought to emerge from Hume’s problematic. But in practice the world doesn’t operate that way, because there’s more than—take the airplane as an example—there are lots of things we do, and all kinds of laws of physics, things like that, that… Again—how did laws of physics arise? They checked a hundred, two hundred, three hundred cases, but they didn’t check the… There are philosophers of science who actually claim, according to the first interpretation, that the laws of physics do not describe anything true in reality. They are only an efficient way to organize the set of particulars that I observed. That’s all. There is no law of nature that really says all objects with mass fall to the earth; that is only a mode of expression. All objects with mass that I have observed until now fell to the earth. As long as I don’t find another object, then I will formulate it in a completely general way. If tomorrow you find an object that does not fall to the earth, nothing has fallen, nothing has changed as far as the scientific law is concerned, because from the outset the scientific law also said nothing about the world. Rather, now I can no longer use it to organize the facts. But they change it—I haven’t studied much physics—but they do change it, they do relate to it as a law. How physicists relate to it, speaking innocently, is not evidence. Metaphilosophers come and ask what the justification is for that relation. You’re right that physicists usually adopt the second interpretation: that the laws are correct laws. Not that they are correct—again, “correct” doesn’t mean certain, it’s not the same thing. Correct, but for now I think they are correct. If I had to bet, I would not bet fifty-fifty, whether they are correct or not. It doesn’t have to be fifty-fifty; it has to be zero against one. Because if you are in a completely random state, then the chance that it is correct is of course zero, not half, because the chance that it is not correct includes infinitely many other theories. Fine? It’s not fifty-fifty. But in short, I would bet not zero against one, but I don’t know, maybe two to one, depending on how much confidence I have in that theory. Fine? So on the one hand it is not certain, but I do say that it is a claim about the world. If you asked me what I bet will come out in the next experiment, I claim the theory will work. I am willing to bet two to one that the theory will work. Someone who adopts the first interpretation, by contrast, ought to bet zero against one. There is no chance the theory will work in the next experiment. If by chance it does happen, fine, that can happen with zero probability—but that’s a bizarre case. Fine? It’s completely accidental. That’s the million-dollar question one has to ask them. I don’t know. Maybe they’ll tell you they’re not sure they got on the airplane either. Who knows? It seems to you that they got on the airplane—fine, if the plane doesn’t crash, then it will turn out they really got on it. If it crashes, then it may turn out they didn’t get on it. Fine, Schrödinger’s philosophical cat. In any case, if I return to our discussion, we see here the importance of driving a wedge between thinking and cognition. Because if we remain with this identification of the conceptual division and the cognitive division, then we are basically unwilling to accept an intermediate category. For us there is no possibility of collecting or accumulating information by means of thought. Only observation. And what Kant argued is that all of science—if you want to relate to it at least as something that makes claims about reality—basically says that Hume is wrong. Science tells us that there are intellectual means of accumulating information. Which is exactly like judicial legislation, or like derash in the halakhic context, or in the legal context—which is basically some kind of intermediate state between an act that is pure thought and an act that is pure observation. It is some kind of thought-observation or something like that. Because thought that is completely detached—it really is hard to see how it adds information about the world for us. So apparently what we call thought is something that contains within it some elements of cognition. And therefore it actually yields information about the world for us. When we look at those five points that we measured on the graph, in some sense we actually see that a straight line passes through them. Not that we process the information and make generalizations in our head, but rather this is an act that has a cognitive dimension. Not cognition with the eyes, but cognition with the eyes of the intellect, what Maimonides calls at the beginning of Guide for the Perplexed. Yes? That in some sense we can cognize—we can cognize the fact or see the fact that the straight line is the correct scientific law. Fine, this is not a generalization made in our head, because otherwise there is no reason to assume it will really fit the way reality itself behaves. Rather it is something—it is a kind of cognition. We see, basically, that all along the way, in every field we deal with, there is ostensibly an option to present things dichotomously, to distinguish either thought or cognition, either legislation or interpretation, either observation or intellectual generalizations. And this dichotomous thinking always leads us to paradoxes. It leads us to paradoxes because when we see phenomena before our eyes that are complex phenomena, and we try to map them and ask ourselves: is this thought or cognition? Is this legislation or interpretation? Yes? Is this observation, is this synthetic, or is this a priori? It can’t go together, right? The problem is always that we think about it in a dichotomous way, and it is not correct to think about it in a dichotomous way. There are intermediate categories. There is something called judicial legislation, there is something called cognizing thought, and there is something called derash. Which is the same thing—on the logical level of these three processes, it is the same logic. It is the same logical phenomenon, appearing once in Jewish law, once in the legal world, and once in the scientific world. But as a logical phenomenon, it is exactly the same logical phenomenon. Try to formulate it in Kantian terms as synthetic a priori? Synthetic a priori, yes. It’s Kant’s synthetic a priori, except that when Kant offers an explanation for it, he throws the baby out with the bathwater. Yes, because when he claims that synthetic a priori is possible, he basically turns the synthetic into the analytic. And that’s how he explains that it is possible, that it is a priori. Because he basically says: you’re not making claims about reality; you’re making claims about your perception of reality. Once you are making claims about your perception of reality, analyze your tools of perception or cognition, and then you’ll arrive at the synthetic a priori proposition because it isn’t really synthetic; it is analytic if you also take your tools of perception into account. So that’s called throwing the baby out with the bathwater, and I think he’s wrong. That is, the conceptual distinction is very important to me, to understand that there is such a thing as synthetic a priori. His reasoning for why synthetic a priori is indeed possible, in my opinion, brings the problem back in full force. I think his reasoning is the problem, not the diagnosis. The diagnosis is an excellent diagnosis. Now, why am I prefacing all of this? Because basically the goal of the next part of this series is to try to show how the synthetic-a-priori logic of cognizing thought works—or of derash. We said, after all, that it’s basically the same logical phenomenon. And here the question really arises whether these phenomena are logical phenomena at all. Because in the way we often look at them, we always judge them through dichotomous glasses, and then we say to ourselves: wait a second, this is the preacher’s invention. What do you mean? This isn’t really written in the verse. It’s his invention. Fine, so maybe he has authority, because he had ordination, or he was in the Great Court, whatever—so I have to accept what he said. He has the mandate. But not that he really managed to put his finger on something that is somehow actually there in the Torah, or connected somehow to the Torah—uncovering or expanding. Yes, it may be expansion, but even expansion can be a correct expansion, despite being an expansion. There are criteria of correct and incorrect for expansions too, not only for revelations. Yes, that is basically the claim. And the perplexity in the face of these phenomena always stems from the dichotomous perception that says either this is thought, in which case there is a very clear logic—the logic we are familiar with basically deals with processes of thought, with how we make intellectual inferences, right?—and observation is the other side. If we see, we believe what we see. Why? There are also those who will challenge that, but never mind, we won’t deal with that now. As a standard, let’s accept it as obvious. What we see is certainly true. So if the Torah says something that the Sadducees also agree to, yes, something like—not eating pork—then that is something the Sadducees also agree to. There is no subjective element of the interpreter here. The interpreter is simply bringing me what is written in the Torah itself. So that is a fact, that is observation, that is the result of observation—there is no problem with it, I can handle it. It is something that the Sadducees could also handle, because it is pure observation. The Sadducees couldn’t handle derash. The Sadducees couldn’t handle derash because they thought dichotomously. They thought either you are observing or you are thinking—but if you are thinking, then that’s you, not the text. And that is basically the point. And they did not recognize this category, that there is thought that succeeds in extracting things from the text or expanding the spirit of the Jewish law that is in the text, while still remaining connected to the text. It’s not thought in the detached sense. There is an intermediate level. And the same dilemma applies to science. These views that say that scientific theory is a statement about us and not about reality, not about the world—they too basically assume that the synthetic a priori has no logic. The synthetic a priori is basically thought and not cognition, and therefore it is a statement about you and not about the world. Because thought cannot contain information about the world, cannot add information about the world for me. There is no way to accumulate information by means of thought—only by direct observation. But of course direct observation is only knowing the specific fact that I observed. That’s what direct observation means. In other words, I can never have general information about the world. That is basically what emerges from this dichotomous conception. I can never have general information about the world—or in other words, I cannot have general halakhic laws. What I can have is what is written in the Torah. If examples are written there—“if one man’s ox gores another’s ox”—then I know that when an ox gores, one must pay. How do you know that when a dog bites, one must pay? That’s your theory; you made a generalization. What is that? Your invention. So again, I can perhaps accept it—the parallel to the scientific interpretation also in the halakhic field—that says: okay, true, this is the interpreter’s invention, but that is his authority. He had ordination, he was the Great Court, he has authority, or that everything was given at Sinai—there are people who want to say that too, and that also solves the problem for them. Therefore you can accept it, no problem. They are not willing to accept the fact that here there is someone who made a derashah—it was not given at Sinai. He made this derashah himself. He expanded what is written in the verse—it is not what is written in the verse. And still, what he is doing is correct in some sense. It isn’t just authority in the formal sense, but rather he hit on what is correct. But the problem is that there are no interpretive tools that are sufficiently orderly; it’s not like generalization and things like that. After all, you could say about every single thing and its opposite. You can say that “ox” comes to include everything, and you can say that “ox” comes to exclude everything. But that is exactly the same question you can ask about the scientific example. Those five points can be stitched together with a straight line and they can be stitched together with some sine curve. But let’s assume there is some method that is accepted for doing these things. A method, yes—but who said it’s correct? We choose the simpler theory. That’s the method. But generally do they do the same thing every time? If they don’t always do the same thing, so what? Who said that’s correct? Still, you’re built in such a way that you always draw straight lines, and therefore you always draw straight lines—but who said the straight line is the right one? But that’s exactly the important question. If, say—fine, I don’t know whether it’s right or not—but if in the Torah I were to say a principle like this, that every time the Torah says “ox,” say, it always comes to include all things, and I followed it consistently, then you could say: fine, I don’t know if it’s right or not, but okay, at least you have some tool that you’re using. But because sometimes it includes, and if that tool is complicated? Then you have a complicated tool that you use—so what? Why does the tool have to be simple for you to believe in it? But sometimes they say one thing and sometimes the opposite. Right, so I’ll tell you that I have—I’ll define the tool in a more complicated way, so that there it comes out one way and here it comes out the other way. So if the tool is complicated, you can’t accept it? What’s the problem? Give a definition, then at least there will be a definition. But I’ll give you an ad hoc definition; I can suggest a definition for anything. Why, who said you can? Maybe you can’t? Why is that a demand you can make and I can’t? The question is because I’m authorized, I have ordination. That is exactly the point. The authority is formal authority; it’s not because I’m right. In that conception, I do it because I’m authorized, not because I’m right. No, this is a conception that says he is also right in the derashah, not that he is just saying something. Okay, yes. So the claim is that there really is a mechanism here that I can also transmit to you. There is a mechanism? Yes, yes, I claim there is. I claim there is. There has to be, I say—I claim this a priori, not because I know it. There has to be, otherwise this whole business is a game. Okay, so I’m saying: right now when we look, it seems very problematic. Part of what I’m going to want to show later is that it isn’t quite so problematic. That is, there are certain inferences in which one can create order. And maybe that will give us examples that will let us receive more calmly what I’m proposing here. Again, I don’t have a proof—not that I know how to explain every single case. I do think it has to be this way, otherwise it really is just a game. Otherwise it is just a game. And that’s why I’m giving this introduction, because that is basically what I’m going to want to show now going forward. Okay, fine, let’s stop here.