Mitzvot and Their Enumeration – Lesson 4

Table of Contents

• Declarative verses and imperative verses, and the division within the Torah
• Maimonides in the eighth root: commandments, decrees, and language as shaping categories
• The gap between fact and norm, and the bridging assumption
• The example of women’s testimony and change in Jewish law as a logical fallacy
• The command as constituting a norm: legislation and the prohibition against driving through a red light
• Conceptualization, the history of ideas, and the importance of definition
• The example of convexity and the law of conservation of difficulty
• Mathematical models, Popper, and clementines versus arithmetic
• Returning to the concepts of positive commandment and prohibition as a conceptualization that needs examination
• Maimonides in the ninth root: we count contents, not a multiplicity of commands
• Interest and increase: two prohibitions that are not counted as two in the enumeration of the commandments
• Love of the convert according to Pahad Yitzhak as a case of two different commandments
• The sixth root in Maimonides: one commandment with a positive commandment and a prohibition is counted twice
• Nachmanides and the Sages versus Maimonides: proof, reasoning, and the enumeration of the commandments
• Saadia Gaon and Rabbi Yerucham Fishel Perla: rejection of the sixth root and dependence on practical content
• The problem of definition: positive commandment and prohibition as a practical distinction versus duplication
• Aharon Shemesh: moving from a practical distinction to a linguistic distinction, and the criticism that he stopped halfway
• Confusing a thing with its properties: lesser sancta, ownership, and Leibniz

Summary

General overview

The text sets up a grammatical distinction between declarative verses, which describe facts, and imperative verses, which establish norms, and connects that to the division in the Torah between the halakhic part and the historical-value-oriented parts. It uses David Hume’s “is-ought gap” to explain why you can’t derive a prohibition or an obligation from facts without a “bridging assumption,” and it illustrates this with modern arguments about changing Jewish law. From there it returns to Maimonides in the eighth, ninth, and sixth roots: on the one hand, we count contents rather than multiple formulations; on the other hand, there are cases where the same content appears as a positive commandment and as a prohibition, and that gets counted as two commandments, which raises the question of how to define positive commandments and prohibitions. The discussion broadens into the question of conceptualization in general: how a definition clarifies mathematical statements but also hides the difficulty at the stage of fitting the definition to intuition, and from there to an attempt to reconceptualize the distinction between positive commandments and prohibitions, with a confrontation between Maimonides and Saadia Gaon and a critique of Aharon Shemesh’s formal-linguistic solution.

Declarative verses and imperative verses, and the division within the Torah

The text states that there are declarative verses that describe facts and imperative verses that establish commandments, and that the grammatical difference between them reflects two parts of the Torah: the halakhic part and the non-halakhic part of history, values, and similar things. The text links the connection between positive commandments and prohibitions to the fact that both are expressed in the Torah as imperative verses, in contrast to facts, which are described in declarative verses.

Maimonides in the eighth root: commandments, decrees, and language as shaping categories

In the eighth root, Maimonides presents the halakhic world as divided into positive commandments and prohibitions, and in Arabic there is no shared word for both kinds. The text states that for Maimonides, “commandments” is a term only for positive commandments, and the shared term is “decrees,” from which it follows that the connection between positive commandments and prohibitions is not trivial. The text argues that if there were not a linguistic system that already arranged the picture in advance as two subcategories under one general category, it would be easier to see a positive commandment, a prohibition, and descriptive verses as three separate categories with no common denominator.

The gap between fact and norm, and the bridging assumption

The text uses the “naturalistic fallacy,” or the “is-ought gap” according to David Hume, to argue that from the description of a fact one cannot derive a norm or an ethical-aesthetic judgment. The text presents a “bridging assumption” as the additional assumption required in order to move from facts to a normative conclusion, such as the principle “whatever causes pain is forbidden,” which allows one to conclude that hitting is forbidden. The text argues that many discussions fall into this fallacy because they present normative conclusions as though they follow from facts alone.

The example of women’s testimony and change in Jewish law as a logical fallacy

The text presents an argument according to which women should be accepted as witnesses today because they are educated and involved in public life, and defines that as a logically invalid argument, because the conclusion does not follow from the factual premises. The text states that one needs a bridging assumption according to which the disqualification of women from testimony in the past stemmed from lack of education, or a general principle that anyone uneducated is disqualified from testimony. The text argues that the real dispute is not about the facts but about the bridging assumption, and that this is why it is easy to ignore it and present the argument as though it does not require one.

The command as constituting a norm: legislation and the prohibition against driving through a red light

The text states that a commandment is derived from the command, and therefore a command is required for something to become a commandment, just as legislation is required for something to become law. The text uses the example of driving through a red light to distinguish between the fact that it is dangerous and the norm that it is forbidden, and argues that the command does not reveal the danger but gives it normative force. The text argues that legislation and command “color” the fact with a normative color and create a loaded description in which saying “dangerous” also carries within it “forbidden.”

Conceptualization, the history of ideas, and the importance of definition

The text argues that ideas are almost never created out of nothing, and attributes intellectual ownership to the person who conceptualizes and presents an idea as a system accessible for public use, just as Brisker thinking is attributed to Rabbi Chaim of Brisk. The text presents Aristotle and the Organon as an example: even if people used logical inferences earlier, Aristotle identified a general pattern and turned it into an object of study. The text states that a good definition saves confusion, and that intuition alone leads to missed points and even to the use of incorrect statements.

The example of convexity and the law of conservation of difficulty

The text presents the statement “the intersection of convex shapes is also convex” and shows that its proof becomes trivial once there is a mathematical definition of convexity: every line segment connecting two points inside the shape lies entirely within the shape. The text argues that the real difficulty is not in the proof but in arriving at the definition that represents the intuition, and that this is not proven but posited as an assumption. The text uses the “law of conservation of difficulty” to argue that mathematics does not solve the difficulty but shifts it to the stage of fitting the model to the intuitive world, and that applying mathematical results to reality rests on additional claims that are not mathematically proven.

Mathematical models, Popper, and clementines versus arithmetic

The text asks whether “two plus three equals five” is a scientific theory according to Popper, and shows that an experiment with clementines does not refute arithmetic but only the assumption that adding clementines is an appropriate model for it. The text presents a mechanical example in which two forces of five newtons in different directions do not add up to ten but to five root two, and concludes that what has been refuted is the physical assumption about the type of addition, not arithmetic. The text warns that the process of conceptualization builds an abstract model for claims about the world, and that the central problem lies in the claim that the model fits reality.

Returning to the concepts of positive commandment and prohibition as a conceptualization that needs examination

The text states that the conceptualization of positive commandments and prohibitions is not trivial despite the sense that it is self-evident, and that conceptualization is a claim that can be judged true or false. The text returns to Maimonides in the eighth root and emphasizes that language can make it easier to grasp the shared category of positive commandment and prohibition, and therefore a conscious definition is needed in order to deal with the difficulties that will emerge later.

Maimonides in the ninth root: we count contents, not a multiplicity of commands

The text quotes from the ninth root that commandments and warnings are divided into “opinions, actions, character traits, speech,” and that one should count the matters regarding which one is commanded or warned, not the multiplicity of commands repeated for reinforcement. The text brings Nachmanides’ position that repetitions are not only for reinforcement but teach an additional aspect, and notes that Maimonides agrees that when the Sages reveal that each repetition contains an added point, that must be counted appropriately. The text presents a distinction between repetition that contains no added point and cases in which the Sages teach a completely different content, such as “in plowing and in harvest you shall rest,” which is expounded as referring to the Sabbatical year and not to the Sabbath.

Interest and increase: two prohibitions that are not counted as two in the enumeration of the commandments

The text cites the Talmudic passage at the beginning of “What Is Interest,” according to which one who lends with interest violates “interest” and “increase” in order that he should violate two prohibitions, and explains in Rashi that “interest” is harm to another and “increase” is an unlawful increase of wealth. The text states that Maimonides counts in the enumeration of the commandments one prohibition of interest even though in halakhic law there are two prohibitions, because on the practical level it is the same act. The text clarifies that the lack of double counting in the enumeration of the commandments does not cancel the fact that there are two prohibitions for issues such as a positive commandment overriding a prohibition when two prohibitions are involved.

Love of the convert according to Pahad Yitzhak as a case of two different commandments

The text brings in the name of Rabbi Yitzchak Hutner in Pahad Yitzhak that the commandment to love the convert is not included within love of one’s fellow, because its fulfillment is to love a convert because he is a convert. The text states that loving a convert without knowing that he is a convert does not fulfill the commandment to love the convert, because the “because” is part of the definition of the fulfillment and not merely the reason for the commandment. The text uses this to distinguish between linguistic duplication that does not change the act of fulfillment and two different obligations that differ in the manner of fulfillment.

The sixth root in Maimonides: one commandment with a positive commandment and a prohibition is counted twice

The text quotes the sixth root of Maimonides, which states that when one commandment includes a positive commandment and a prohibition, the positive commandment is counted among the positive commandments and the prohibition among the prohibitions. The text highlights that there are two innovations here: the very fact of double counting even when there is duplication of content, and the claim that the commandment of cessation on the Sabbath is a positive commandment even though its fulfillment consists in refraining from labor. The text brings the three forms Maimonides counts: Sabbath / Jewish holiday / Sabbatical year and Yom Kippur as duplication of content, “a prohibition preceded by a positive commandment” in the case of the rapist and the slanderer, and “a prohibition transformed into a positive commandment” such as sending away the mother bird.

Nachmanides and the Sages versus Maimonides: proof, reasoning, and the enumeration of the commandments

The text argues that Maimonides brings a proof from the Sages that there is here a positive commandment and a prohibition, but the decision to count two commandments he derives from reasoning: “the matter of the command is distinct from the matter of the warning.” The text presents Nachmanides’ criticism that the Sages are not dealing with the enumeration of the commandments, and therefore one cannot bring proofs from them on that point, and suggests that Maimonides is not learning the enumeration from the Sages but rather the conceptual distinction that leads, in his view, to that enumeration.

Saadia Gaon and Rabbi Yerucham Fishel Perla: rejection of the sixth root and dependence on practical content

The text quotes Rabbi Yerucham Fishel Perla, who argues that Saadia Gaon does not accept the main principle of the sixth root, and when there is no innovation in content between the positive commandment and the prohibition, one should count only a single commandment. The text describes Saadia Gaon’s method, according to which if the commandment is “explained more clearly” in the prohibition, it is counted as a prohibition, and if it is explained more clearly in the positive commandment, it is counted as a positive commandment; and when there is no essential difference, it should not be counted twice. The text concludes that according to Saadia Gaon, writing a positive commandment and a prohibition together serves only to increase the severity of punishment for the transgressor, and has no significance for the enumeration of the commandments.

The problem of definition: positive commandment and prohibition as a practical distinction versus duplication

The text presents as an intuitive definition that the difference between a positive commandment and a prohibition is practical: a positive commandment is fulfilled through positive action, and violated through passive omission, while a prohibition is fulfilled through passive omission and violated through positive action. The text argues that if this is the definition, then the very talk of “duplication between a positive commandment and a prohibition” seems like an oxymoron, because two formulations that are logically equivalent look like duplication that cannot generate two commandments. The text brings examples in which the formulation of a prohibition requires positive action, such as “do not stand idly by your neighbor’s blood” and “do not place bloodguilt in your house,” and concludes that the practical distinction does not succeed in explaining the Sages’ division between positive commandments and prohibitions.

Aharon Shemesh: moving from a practical distinction to a linguistic distinction, and the criticism that he stopped halfway

The text cites Aharon Shemesh’s article in Tarbiz, according to which in earlier passages the distinction between positive commandments and prohibitions is practical, while in later passages it is linguistic, based on the way the Torah formulates them. The text argues that this fits the general trend of increasing abstraction in the generations of the Amoraim, but states that the linguistic criterion cannot be the cause but only the sign, because one must ask why the Torah formulated it this way rather than another way. The text criticizes Shemesh for turning a question mark into an exclamation point by making do with the claim that the difference is merely one of formulation without proposing the substance behind it, while at the same time justifying his stopping point as an academic delimitation of sticking to the facts rather than offering speculative conceptual proposals.

Confusing a thing with its properties: lesser sancta, ownership, and Leibniz

The text warns against confusing a thing with its properties or implications, and presents this through the discussion of lesser sancta as the owner’s property and the claim that one should not define the property by a practical implication such as betrothal, but the other way around. The text proposes a distinction between ownership as the state itself and rights of use as a legal consequence, and presents Leibniz’s principle of the “identity of indiscernibles” as based on the mistaken assumption that identifies an essence with a collection of properties. The text uses this to reinforce the claim that a difference in formulation in the commandments cannot serve as an essential definition, but rather points to a real difference that requires clarification, and it ends by postponing the solution to what follows.

Okay, up to this point we’ve talked about what a commandment is, about the meaning of command, about the fact that the system of commandments appears in the Torah in a grammatical form that’s different from verses that are not commandments. There are indicative verses, meaning verses that describe facts, and there are imperative verses, meaning verses that establish commandments. And that grammatical difference really reflects two parts that appear in the Torah: the halakhic part, and the non-halakhic part—other things, history, values, things like that. Within that, we talked about Maimonides in the eighth root, where Maimonides says that the halakhic world is divided into positive commandments and prohibitions, and in Arabic there is no shared word for both positive commandments and prohibitions. We call them commandments—positive commandments and prohibitions—but for Maimonides, “commandments” refers only to positive commandments; he calls the common category decrees. “Decrees” is the shared word, but in Arabic there is no shared word, and from this he tries to show that the difference—or not the difference, rather the connection—between positive commandments and prohibitions is not all that trivial. Meaning, if we didn’t have a linguistic system that had already structured this picture for us—that there are positive commandments, there are prohibitions, and both belong to the same general category called decrees—if we didn’t have language already reflecting that, it could be that it would be harder for us to notice this point, that there is something common to positive commandments and prohibitions. We would simply say these are two different things: there are positive commandments, there are prohibitions, there are descriptive verses—three different categories. Why do we take the first two and put them together, seeing them as two subcategories of one category? So I said that these two subcategories basically belong to—or are expressed in the Torah by—imperative verses, as opposed to facts, which are described by indicative verses, descriptive verses. And what do these imperative verses mean? So regarding that—I think we also talked about this—regarding indicative verses, there is what in philosophy is called the naturalistic fallacy, or the gap between “ought” and “is” according to David Hume. What does that mean? When I describe a fact, you can’t derive from it a norm or an aesthetic judgment, an ethical judgment—the proper and improper, the permitted and forbidden. A fact is by definition neutral, and therefore you can’t say “this picture is colorful, therefore it’s beautiful.” The fact that it’s colorful is a fact. The claim that it’s beautiful is a judgment. A judgment cannot be derived from facts. Or: hitting someone causes him pain—that’s a fact. You can’t derive from that that there is a prohibition against hitting someone; that’s a norm. There is a gap between the world of facts, between indicative verses, and imperative verses. If I want to create a connection between them—and very often, after all, we do say, “since it causes him pain, therefore it’s forbidden to do that”—what actually lies behind that is some additional assumption. I called it a bridging assumption. It’s an assumption whose role is to connect us, or move us, from the plane of facts to the plane of judgments or the normative plane. For example: what causes pain is forbidden to do. Okay, so if I say “hitting someone causes him pain,” first premise; second premise, “what causes pain is forbidden to do”; conclusion: it is forbidden to hit. That is already a valid argument. Here the conclusion necessarily follows from the premises, but you need to add the bridging principle. Meaning, the facts alone are not enough to ground the conclusion. I think I mentioned that in many places you can see people falling into this fallacy. Discussions about changes in Jewish law—I think that was the example I gave. If someone wants to say that women should be made eligible to testify today, even though Jewish law disqualifies women from testimony, one should make women eligible to testify because today women are educated and involved in life and in the economy and so on, present in society—that is a logically invalid argument. Not that its conclusion is necessarily wrong, but the conclusion does not follow from the premises. Because the premise is that in the past women were not educated and today they are educated. Those are facts. I assume every reasonable person would agree with those facts. But the question is whether from that I can draw the conclusion that women should be made eligible to testify today. That does not come out of those facts. You could add another premise, which would be the bridging assumption, saying that women who were once disqualified from testimony in Jewish law were disqualified because they were uneducated. Or in other words, whoever is uneducated is disqualified from testimony, and woman is just an example. But really the principle is that whoever is uneducated is disqualified from testimony. If you add that assumption, then you can say: a woman is uneducated, whoever is uneducated is disqualified from testimony, conclusion: a woman is disqualified from testimony. That’s how you move from fact to norm. And accordingly you can also conclude that if today women are educated, then there is no reason to disqualify them from testimony, because only lack of education was what disqualified them in the past. In order to say all this, you need to add the bridging assumption, the assumption that says that the reason women were disqualified from testimony was lack of education or lack of social involvement. And of course that is an assumption that, within a debate of this kind, you would have to establish, because the facts are agreed facts—that’s the easy part. The argument will revolve around the bridging assumption, and that’s much harder to establish, if at all. And therefore the easiest thing is simply to ignore it and present an argument as though that assumption isn’t needed—but it is needed. You can’t ignore that assumption. Fine, that’s just an example. So for our purposes, basically in this picture we understand the meaning of command as what constitutes commandments, and therefore “commandment” comes from the root “command.” Meaning, you need command in order for a commandment to become a commandment. I mentioned that precisely because of this, for example, if there were no law forbidding driving through a red light, and it were still dangerous to drive through a red light, it would not be forbidden. Because the fact that it is dangerous is a fact. The fact that it is forbidden is a norm. You can’t derive the norm from the fact. What do you need to do in order to turn that fact, that norm, into something valid? You need legislation, for the legislator to establish that there is a prohibition against driving through a red light, or someone acting on his behalf, establishing that there is such a prohibition. Since you need command in order to turn something into a commandment—or you need legislation in order to turn something into law—okay, therefore command, and this is another way of looking at the concept of command, does not function to tell us that driving through a red light is dangerous. I know that even without it. The role of command is to take that fact and color it with a normative color, a charged, non-neutral color. Meaning, now already when you say that driving through a red light is dangerous, it’s no longer just some description of reality, and description is always neutral, normatively transparent; rather it’s now a loaded description. Meaning, when I say something is dangerous, what is really hidden in that is the statement that it is forbidden, that one may not do it. Okay, that is basically the claim. So legislation’s role is, you could say, to turn the fact into a norm, or to give the norm its force. The same is true of command in the halakhic context: command is what does the job.

In legal theory there is a debate between two views, natural law and positivism, and one of the differences between them is that natural law understands that normative options underlie the law. What? A law in which there lies this—whether law realizes reality or law creates the… okay, I don’t know. It’s usually attributed to Aquinas, which is much later, but maybe. I once gave a lecture here at a conference on Pnei Yehoshua and talked about sparks of Brisker thinking in Pnei Yehoshua. So at the beginning I gave some introduction on the history of ideas. And I said that this field is a very problematic field. Meaning, because the moment you formulate an idea, people immediately find it in writings that predated you. I know this from myself. Every book that came out, people explained to me that it’s all already written by so-and-so and so-and-so and—and that’s true. I’m not talking about people just making things up. You really can see, at least, forms of thinking, roots. Almost nobody invents anything from nothing. I think ideas belong to the person who conceptualizes them, the one who defines them, puts them on the table, and turns them into something accessible for public use, let’s call it that. So Brisker thinking, for example, is attributed to Rabbi Chaim of Brisk, even though it’s clear that arguments of his type existed long before him. But it is still Brisker thinking, and rightly so, because he is the one who conceptualized it. Meaning, he used that approach, but he didn’t really put it on the table as a conceptual system. Yes, like what I said about Aristotle and the Organon, logic. Aristotle was the one who conceptualized logic in his book the Organon, and there too I assume that even before Aristotle people knew that if all frogs are green and this is a frog, then it too is green. Meaning, I assume people used simple logical arguments even before Aristotle. Aristotle was the first to notice that there is some fixed pattern here. He put it on the table. There is a logical law saying that if every X is Y and A is X, then A is Y. Okay? Suddenly he says there is some general law, and it can appear in all kinds of contexts—in the context of frogs, clouds, or I don’t know what, or claims in law. It doesn’t matter at all what the X is, what the Y is, and what the A is. The very structure suddenly became something lying before us. Before that, people used this form of thought, but nobody noticed that there was even some form of thought here worth pointing out and putting on the table as something that is itself a subject of research. And for that, of course, we owe him the computer and almost our entire world—this conceptualization of Aristotle. Without it, it wouldn’t have happened. For us it’s even easy to understand just how important such conceptualizations are, even if the ideas themselves existed earlier. Sometimes I have a tendency in various places to try to define concepts, and then people say, okay fine, everybody understands, what’s the problem, it’s trivial, everyone understands this. And once you advance a bit, you suddenly discover—yes, like mathematics—you suddenly discover that a good definition saves you a lot of confusion later on. Even though it seems very obvious, but no, it isn’t obvious. Meaning, when you define things really well, you’ll see that before you defined and conceptualized, you understood the concept at the intuitive level, but you couldn’t—or you could make mistakes in many things.

A nice example of this: once I saw, in a used bookstore, some kind of high-school topology book, something cute like that, presenting ideas relatively simply. So there he cites a theorem that caught my eye. He says: whenever there are shapes—and in mathematics they talk about convex shapes, in intuitive language let’s call them shapes with the belly outward. Okay? Something convex as opposed to something concave. Yes, a crescent moon is a concave shape. A ball is a convex shape. Fine? Its boundary is with the belly outward. I’m talking here with hand-waving, but that’s how we grasp it in everyday language. And there is a theorem in mathematics that says that the intersection of convex shapes is also convex. Doesn’t matter how many, but let’s speak about two. Okay? The intersection of two convex shapes is also convex. And then I ask myself: let’s try to prove that. Let’s try to prove it—maybe it’s not true, maybe there are exceptional cases. So usually if you turn to someone who isn’t a mathematician, he’ll tell you fine, it’s obvious, what is there to fuss about, it’s clear, what’s the problem. Yes, like how does that theorem go, I don’t remember anymore: if a continuous graph goes above the x-axis and reaches below the x-axis, then somewhere it crosses the x-axis. That’s a theorem mathematicians sit on for two months. The intermediate value theorem. Okay. There are several intermediate-value theorems. Anyway, mathematicians have this nagging tendency to prove things, define things, and prove everything. But it turns out this can be very useful, because someone who settles for intuitive understanding gets confused, misses things, and sometimes uses false theorems. There may be exceptions, maybe rare ones, but there are exceptions and the statements are not correct. Yes, for example this theorem about convex shapes—once we’re talking about it—if you think a little about how to prove such a thing, ordinary people will have a hard time doing it even though it feels very intuitive. But the truth is that the proof is two lines long. Very simple. Except that for this you need to define the concept convex. How would you define the concept of a convex shape, if you’re not a mathematician? Rounded—that’s a very specific case. And rounded can also mean rounded inward, not outward. So look: there is a definition, a very simple definition. A convex shape is a shape such that any two points you mark inside it—if you draw a straight line between them, the entire line is inside the shape. Right? Think of a crescent, like a banana. Why isn’t it a convex shape? Because if you take two points at its two ends and draw a straight line between them, part of the line will be outside the shape. By contrast, with a convex shape, any two points you take, draw the line—it lies entirely inside the shape, right? So now we already have a good definition of the concept convex shape. And you understand that once we define it this way, the proof of the theorem is trivial. Take two shapes and intersect them. Two convex shapes. Let’s say these two shapes here, and I want to prove that their intersection is convex. What do I do? I say there are any two points here, I draw a straight line between them, and I need to prove that it lies inside the intersection. Right? So it’s very simple. If these two points lie in the triangle and the triangle is a convex shape, then the whole line lies in the convex shape, in the triangle. Right? Now these two points also lie in the circle, because they lie in the intersection, and the line must lie in the circle too because the circle is also a convex shape. But if the line lies both in the circle and in the triangle, then it also lies in their intersection. And since this is generally true for any two points I choose in the intersection, I’ve proved that the intersection is a convex shape. How did this miracle happen, that something which at first glance seems like something hard even to know how to approach suddenly became completely trivial? Because of the definition. We simply defined, sharply and fruitfully I would say—for you can define in various ways, and there are more fruitful definitions—the concept convex shape. And from there one can derive all kinds of conclusions that others either won’t derive or will have difficulty proving, and so on.

By the way, since I’m saying this, I’ll add another sentence. Mathematics here didn’t solve any problem. You have to understand: among physicists there is what’s called the law of conservation of difficulty. Anyone who knows a bit of research in physics, and I assume also in mathematics, encounters this all the time. Right? Every time I had an idea for a breakthrough in research in physics, I ran into it somewhere else. Meaning, if there was some difficulty here that I succeeded in bypassing, I met it over there. Meaning, I don’t manage to get rid of the essential difficulty of the problem. Tricks usually don’t help. So also in this context, it seems to us that we’ve done some hocus-pocus and solved the problem, but we didn’t solve anything with the convex shapes. Think about the claim regarding shapes. You come to a person on the street and tell him, look, the intersection of two convex shapes is also convex. Okay? Now he doesn’t know how to prove it because he hasn’t properly defined for himself the concept convex shape, etc., he’s not a mathematician—but he doesn’t know how to prove it. Now you say to him, here, look, and you do for him what I did here. Okay, have we solved the problem? No, we haven’t solved the problem. Why not? Because we hid the difficulty he had in proving that claim. It is hidden here; it’s still here. Where is it? It is in the assumption that the definition of convex shape that I gave earlier—that any two points have the line between them inside the shape—really fits the intuitive concept of a convex shape that we use in our language. And who said it’s the same thing? We assume it’s the same thing; it sounds very intuitive to us. From the stage of the definition onward, the proof is simple. The difficulty was in arriving at the definition. And that you won’t manage to prove. I don’t see how one could prove such a thing, that the mathematical definition precisely reflects our intuition regarding convex shapes—what we mean when we say convex shapes. Here enters the… in effect, what mathematics does is sweep the dirt under the rug. The dirt is there. But it says, okay, let’s put everything under the rug; from the rug upward I know how to handle things cleanly. Everything’s fine. The dirt is there, under the rug. When you want to draw conclusions from mathematics to your everyday, non-mathematical world of concepts, once again you’ll run into unproven claims. And you’ll use mathematical claims, but their application to the world is not proven. How did I get to all this? The importance of conceptualization. Meaning, when you conceptualize things, define things, you have to understand that conceptualization itself is a nontrivial intellectual move. Meaning, you are building some theoretical model, mathematical, logical, however you want to call it, abstract, of claims or ways of thinking or principles drawn from everyday life, and it’s not always certain that it’s the same thing. Physicists do this all the time—building mathematical models of how things in the world behave. Okay? And very often the problem lies in the transition from one to the other. Meaning, who says the model really describes correctly what happens in physics? What happens in the model—I can do the calculations and tell you the results and maybe everything, okay? But that doesn’t mean it’s true of physics. The question is whether it correctly describes physics. And this is true of every conceptualization. Whenever we conceptualize, we need to be aware that conceptualization is some kind of claim. It’s not just a definition, in the mathematical sense. A definition in mathematics is arbitrary: define whatever you want. When we conceptualize, the conceptualization has to reflect the concept. A conceptualization can be correct or incorrect; a definition cannot. A definition can perhaps be contradictory or non-contradictory. If it is contradictory, then it has no content; it’s not a definition. But in principle it is arbitrary: you can define whatever you want however you want, as long as you remain consistent with your definition. Conceptualization is not a definition. Conceptualization is an attempt to hit upon something that exists in the world itself by means of a definition. It is not an arbitrary definition. It is an attempt to grasp, capture some idea that we understand before the definition and put it into a more precise pattern, into a definition. And therefore one should not conflate conceptualization with definition. Conceptualization is really a claim. And a claim can be judged. One can say it is right or wrong, unlike a definition, where you can define whatever you like. Very often people make a definition. In a definition you can say whatever you want; after that you derive a conclusion, everything’s fine. How can you argue that in the world this is the result? Here, I proved it to you mathematically. No. Because the assumptions of your mathematical proof assume something about the world. And that you did not show me, that it really describes the world correctly.

Once, when I was teaching mechanics here in physics, I asked the students whether the theory “two plus three equals five” is a scientific theory. Yes, according to Popper a scientific theory is one that can be put to a falsification test. Think of an experiment whose failure would refute the theory. Success would corroborate it, not prove it—you can’t prove—but failure of the experiment would refute the theory. So is arithmetic a scientific theory? Can one refute it? Can one do an experiment that would refute it? So someone told me yes, what’s the problem? Take a basket, put two tangerines in it, add three more tangerines, and count. If you get five, then you corroborated the statement two plus three equals five. If you get minus pi, then no. Okay, so there, you’ve refuted it. Never mind that you know it won’t happen because you’re convinced the theory is right, but still this is an experiment that could refute the theory, and seemingly the theory is scientific. Then ask yourself: wait, suppose I got minus pi. I put in two tangerines, then three more, counted, and got minus pi. Good thing it didn’t come out imaginary. So now the question is what do I do with that. Of course every physicist will tell you: there was an error in the experiment. What does that mean? It means you will never really change your assumption that when adding tangerines, two plus three equals five. If it didn’t come out that way, you’d say there’s some error in the experiment, something happened here, impossible. You would never give up the claim that two plus three equals five. Therefore, at least practically, at least practically, it is not really falsifiable, because even if the experiment fails you won’t discard the theory. Okay. But there’s something deeper here than that. Suppose I didn’t find any flaw in the experiment and became convinced: adding tangerines to a basket does not work by arithmetic. Arithmetic does not describe this process of adding tangerines to a basket. Okay? What does that mean? Does it mean I refuted the arithmetic claim that two plus three equals five? Of course not. Exactly. What I refuted is the claim that adding tangerines is a model for arithmetic theory. Meaning that adding tangerines is a domain that can be described by arithmetic. But that is a claim in physics. It is not a claim in mathematics. Mathematics cannot… what can be refuted is the claim in physics that says that a certain mathematical domain or mathematical principle describes some domain of reality. Why did I say this in mechanics? Because in mechanics I said: here, I will refute for you the statement five plus five equals ten. Not only is it falsifiable—I’ll actually falsify it. Take a body, apply a force of five newtons toward the north. Apply another five newtons toward the west, toward the east. Okay, what is the resultant force? What is the total force acting on the body? Ten? Five and five? No. Five root two. That’s the Pythagorean theorem. So does that mean five plus five is not ten? Here, we refuted arithmetic, that five plus five equals ten. No. What we refuted is the assumption in physics that adding forces is described by arithmetic addition. It is not true; it is vector addition. Okay, so notice—why am I bringing these examples? Because these examples show us that the process of conceptualization is dangerous. It is not trivial. The process of conceptualization basically takes our understandings of the world, our claims about the world, and builds some model—mathematical, logical, doesn’t matter—some model that is supposed to reflect them, supposed to fit them perfectly. And the assumption that this model really fits the reality it is trying to describe—that is not an assumption in logic. That is an assumption in physics in this case, or whatever, a factual assumption; it is not logic, and that is where there can always be problems.

So I return to our topic, I close the parentheses, because we too are going to try to produce some conceptualization of the concepts positive commandments and prohibitions. And usually people don’t bother to define these concepts for themselves. Everybody understands: these are positive commandments, these are prohibitions, we grew up on this, it’s all very clear. And in a moment I’ll show you that it is really not clear at all, and I’m going to try to conceptualize, to offer a conceptualization of these things. But a conceptualization, as I said earlier, is a claim. Meaning, either I’m right or I’m not right. It’s not a definition that you are forced to accept because I defined it; I’m allowed to define whatever I want. A conceptualization is a claim that needs to be examined to see whether it is right or not. Okay, so in this context we have, I think, a very good example of the failure of intuitive thinking: everyone understands what positive commandments and prohibitions are—but no, it turns out we probably don’t fully understand it, and it’s worth paying attention to this and trying to define the concepts more clearly. And Maimonides, at the beginning of the eighth root, I think his words really reflect this—he got it. Maimonides understood that it may be easy for us to understand these concepts because in our language we already have a conceptual system prepared for this. But in a language in which, in a culture whose language does not contain this conceptual system, at least not in this form—say they have a concept for positive commandments, they have a concept for prohibitions, but no shared concept for both things—it could be that they would not even manage to understand why these are two subcategories of one concept. What is the concept decree or commandment, what we today call by extension. “Commandment” means positive commandments, and by extension we also call prohibitions “commandments” in order to describe the common concept of these two types of commandments. Therefore this is something that requires definition, and we will see various difficulties that will force us to look for a definition, and then we’ll see how the definition solves the issue.

So I’ll begin perhaps with the words of Maimonides in the ninth root, and I also mentioned this root, this principle, in Maimonides. Here, do you see? Maimonides in the ninth root—I already explained about the roots, right? These are Maimonides’ rules for counting the commandments, appearing before Sefer HaMitzvot, printed before Sefer HaMitzvot, and this is an introduction to Sefer HaMitzvot, where Maimonides defines according to what rules he counted the commandments. The ninth root: that it is not proper to count prohibitions and positive commandments, but rather the things prohibited and the things commanded. That means, we count—as we already discussed—we count the contents and not the commands, and I said that in the second part of the root there is apparently a contradiction. Know that all the commands and warnings of the Torah concern one of four things: beliefs, actions, character traits, and speech. By the way, the concept “beliefs” in Maimonides has a double meaning. Because in Maimonides, what are the Laws of Character Traits about? What do the Laws of Character Traits deal with? With character traits, right? Not worldviews or outlooks—that’s the Laws of the Foundations of Torah. The Laws of Character Traits are about traits. Here there appear beliefs, actions, traits, and speech. So beliefs and traits are two distinct concepts—like “the righteous and the pious”; here is proof that the pious are not the righteous, because otherwise why count both? Okay, so here too when Maimonides says traits and beliefs, that means these are two different things, not the same thing. Now true, here this is a translation. I said Sefer HaMitzvot was written in Arabic. The one who translated it translated it as “beliefs.” I don’t know, but I think Maimonides also has the concept “beliefs” in the sense of outlooks in writings he wrote in Hebrew; he himself also uses it in this dual meaning. This is also true in the Sages, by the way. “Just as their thoughts differ”—what is said about “Blessed is the Wise One of secrets.” Right? Their “thoughts” there means character traits, not worldviews; people always quote this as though it means there are different worldviews and pluralism and everything is wonderful. “Thoughts” means different character traits, different personality traits. In any case, yes: four things—beliefs, actions, character traits, and speech. And this, that He commanded us to believe one belief among beliefs, such as what He commanded us to believe in unity and the love of God, blessed be He, and fear of Him; or He warned us against believing a certain belief among beliefs, such as warning us against believing lordship belongs to any being besides Him. So now he starts to count within these four categories—beliefs, actions, traits, and speech. Each of them has positive commandments and prohibitions, meaning eight categories. Positive commandments and prohibitions within those four categories. He gives examples for each of the eight categories. Maybe a remark in parentheses that is also important for us: are there also things—apparently this means that Jewish law basically includes everything, beliefs, actions, traits, speech, everything. There is nothing outside it, there are no lacunae in Jewish law, no things that remain neutral, as if from the standpoint of Jewish law you can do whatever you want. And that is not true. Maimonides in his Commentary on the Mishnah on Pirkei Avot, the commentary to chapter 1, writes there that there are five types of speech. There is speech that is a commandment, there is speech that is proper, meaning positive but not commanded, there is neutral speech, there is reprehensible speech but not a prohibition, and there is forbidden speech. Five types of speech. The middle one is neutral speech. You want to say it, say it; you don’t want to, don’t say it. There are also actions, and actions too can be divided into the same five categories. Chovot HaLevavot, for example, argues that no, there is no neutral action, either the action is positive or it is negative, there are no neutral actions. But that’s a strange claim. I think it is pretty clear that it is not true. There are neutral actions. I decide in the morning to eat this kind of roll or that kind of roll—that’s neutral, it makes no difference if I eat this or that. So also in the world of actions, one can divide them into those five categories, while Maimonides here, with his eight categories here, really includes how many out of those five categories in the Commentary on the Mishnah? Two. Only obligation and prohibition. Only the two extremes in either direction. We are not including the proper, the reprehensible, and the neutral here. Right? Only the forbidden and the obligatory can appear in four planes: beliefs, actions, character traits, and speech. But that includes all the forbidden and obligatory. Beyond that there is the reprehensible and the proper, and there is the neutral, and those too can be in actions, beliefs, traits, and speech. So in principle there ought to be twenty categories: beliefs, actions, traits, and speech, each with forbidden, reprehensible, neutral, proper, and obligatory or commanded. Okay? So that is really twenty categories, of which Jewish law deals with eight. We discussed that in previous sessions. Okay? The reprehensible and the proper are the realm of ethics. Again, another eight. Right? And the neutral is what remains: the remaining four, the neutral of those four things. Meaning there are eight that belong to Jewish law, eight that belong to ethics, and four neutral. Here we are dealing with the eight that belong to Jewish law. Okay?

So Maimonides says—I’m skipping all the examples he gives here for each of those categories—“And once these matters have been established, it is fitting that the matters commanded or prohibited be counted, whether action or speech or belief or trait, and we do not pay attention to the multiplicity of commands that came regarding that matter if it is one of the commanded matters, nor to the multiplicity of warnings that came regarding it if it is one of the prohibited matters, for all of them are only for reinforcement.” Meaning, if the Torah commands something several times, positive commandment or prohibition, that doesn’t interest me. I do not pay attention to the multiplicity of commands. If the Torah repeats it many times, that comes to reinforce the matter, to say it is severe or important, and all sorts of things like that. “For sometimes one warning after another returns to one and the same matter for reinforcement, and likewise one command after another comes for reinforcement as well.” What? Sometimes yes and sometimes no. Nachmanides attacks Maimonides here on this point. Nachmanides argues there is no such thing as repetition merely for reinforcement; every repetition comes to teach something. Maimonides says no. There are repetitions that came for reinforcement. In the Talmud you can’t say that in all places. There are places where the Talmud derives from them—for example, “You shall not boil a kid in its mother’s milk,” from which they derive three different prohibitions. But there are places where it doesn’t. The Torah commands keeping the Sabbath twelve times; not every one of those places gives rise to some halakhic detail. “Except when you find language among the Sages distinguishing the matters, and the commentators explain to you that each prohibition or each positive command includes a matter other than that included by the other prohibition or command, then it is certainly fitting to count it.” Meaning, if there is some novelty in the repetition of the command, then perhaps one should count it, or count it, or I don’t know, see it as another detail within another counted commandment. But very often it is repeated—this is what you said earlier. Sometimes the repetition contains some novelty, and then the Sages tell us so, they derive something from it. But he is speaking about the cases where there is no novelty in the repetition, and so it was repeated only to reinforce the matter. Such a case will not be counted, because we count contents and not commands. “Even though the plain sense of the verse indicates that it is one matter”—meaning, even where it seems on the surface to be the same matter, if the Sages derive something else from it, then perhaps we count it separately. By the way, maybe not even then. In meat and milk Maimonides does not count three prohibitions; he counts one with three details. Okay? But there may be an additional prohibition there even though it looks the same. For example, “in plowing and in harvesting you shall rest,” which on the surface is merely a repetition of “you shall do no work,” because plowing and harvesting are simply two of the thirty-nine categories of labor. So the Torah repeated it; there is nothing to count there. But the Sages at the beginning of Moed Katan understand that this refers to the Sabbatical year altogether and not to the Sabbath. So even though it appears on the surface to be repetition, the Sages learned something else from it, and then it is counted separately: plowing and harvesting in the Sabbatical year are counted separately. Okay? But there are times when they learn from it only another detail, and then it is not counted separately but only included as a detail of an existing commandment. We talked about the fact that some roots are classificatory roots, right, they tell us how we classify the commandments. “However, when there is a received tradition that this command or warning carries such-and-such a matter, and this repeated command or warning carries another matter, then the prior principle and the fitting assumption is that Scripture does not repeat itself except for a matter, and then it is fitting to count this separately and that separately. But when there is no additional matter there, then know truly that it was repeated only for reinforcement. And also so that it become known that this is a very great transgression, since one warning came after another warning, or that it was repeated to complete the law of the commandment so that from it a law among the laws of another commandment be learned, as the Talmud explains.” Fine, etc. In short, we do not count that sort of thing. “Thus it has been clarified to you”—I’m skipping a bit—“thus it has been clarified to you that every prohibition that does not come to add another matter is called redundant and superfluous, and is not included in the count of the commandments.” Meaning that it is repeated. “And even if they say that it is so as to transgress two prohibitions by it, still it is a redundant prohibition.” As has been explained from that statement. There is a Talmudic passage at the beginning of Eizehu Neshekh. The Talmud discusses the prohibition of neshekh and the prohibition of tarbit, and the Mishnah already talks about it, that in every case where I lend at interest to someone, there is here both the prohibition of neshekh and the prohibition of tarbit. What is the difference between them? So Rashi explains: neshekh means I bite him, I take more money from him. Tarbit means I increase my wealth improperly. These are two aspects, two sides of the same coin. Taking interest from him is both biting him and increasing my wealth improperly. So these are two prohibitions—how he loses and how I gain. Yes, the Talmud asks, then why were two prohibitions stated here? Do they have no practical difference? Even though there is a kind of sport among the later authorities to try to find practical differences between them, the Talmud says there is none. So it says: in order to transgress two prohibitions by it. The Torah said two prohibitions here so that you know that every act you do contains two prohibitions. Now you have to understand: it contains two prohibitions why? Because on the practical level it’s the same thing—taking interest from someone. But on the conceptual level these really are two things. One is the harm to him, interpersonal wrongdoing, the biting. The second is my own transgression: I increased my wealth improperly. I am not okay in terms of how I conduct myself, regardless of whether he was harmed or not. So there are two aspects here, and they are distinct aspects, even though on the practical level they always appear together. So this is called transgressing two prohibitions by it. Increasing your wealth is one side, and biting—these have two different meanings. What do you mean? In murder too, there is the aspect that you murdered, that you committed an act. Yes, but there the Torah did not state both, did not establish a prohibition on both, I don’t know. “To transgress two prohibitions by it,” because here it thought one should transgress two prohibitions by it, and in murder there are not two prohibitions for its own reasons. But from the fact that after it writes this, what I understand here is that the Torah wants to tell me that I transgress two prohibitions. Apparently it wants to say there are two aspects here, and these aspects are independent. It may be that in murder the whole problem really is just that you harmed another person, perhaps—I’m just suggesting. By contrast here there is really a separate issue in what this does to you beyond the question of what you did to someone else. A kind of greed, perhaps, or however you want to call it. Greed is not problematic only because you harm someone else because of it. Simply devoting too much effort and energy solely in order to increase wealth is something reprehensible, perhaps in itself, even without the question whether you harmed someone in order to accumulate that wealth.

Now Maimonides brings this in the Laws of Lender and Borrower, that one who lends at interest transgresses two prohibitions, neshekh and tarbit. But if you look in his list of commandments you’ll see one prohibition, the prohibition of interest. He doesn’t count two; he counts one. And even in a case where the Sages say that the matter was stated “to transgress two prohibitions by it,” even that for Maimonides is still not an indication that he will include it in the count of commandments as two separate prohibitions. If the content is the same content, then it is simply the same thing. And perhaps there is an interesting point in this context that I’m remembering. Rabbi Yitzchak Hutner in Pachad Yitzchak says that once a certain sage asked him why Maimonides counts the commandment of loving the convert, “and you shall love the convert.” Why does he count this commandment? After all, this is included in the commandment of loving one’s fellow. One must love every Jew; the convert is a Jew. If you love every Jew, then in particular you must also love converts. So maybe this is a duplication—why does Maimonides count it? The question is understandable. So he says there an interesting point. He says apparently one can learn from here that we don’t understand correctly the commandment of loving the convert. Suppose I have a neighbor who is a convert. I don’t know he is a convert, but factually he is a convert, and I love him because he is a Jew, or just because he is a nice person I love him. Have I fulfilled the commandment of loving the convert? He says no. Not that I fulfilled it just incidentally, as we would usually say. I fulfilled it incidentally; I didn’t notice, but I did it. Usually with transgressions we say incidentally, but here it would be fulfilling a commandment incidentally, okay? Or unintentionally, if you prefer. So perhaps commandments require intention, perhaps not—that’s a different discussion. He says no, here it has nothing to do with whether commandments require intention or not; you did not fulfill the commandment. The definition of the commandment is to love a person who is a convert because he is a convert. The “because” is not a reason among the reasons for the commandment, why one should love him. The reason is… because he is a convert. No—that is part of the definition of how one fulfills the commandment itself. One fulfills the commandment itself by knowing that he is a convert and because of that loving him. That is called the commandment of loving the convert. And therefore if I loved that convert—if there were no commandment to love the convert—I would still have to love him because he is a Jew. One must love every Jew, okay? But one cannot say that the commandment of loving the convert adds nothing, because the commandment of loving the convert tells me that one must love him because he is a Jew, and then I performed one commandment, and I have to love him because he is a convert, and then I performed another commandment, the commandment of loving the convert. If I performed the first commandment, I did not fulfill the second, and vice versa. They are two different things.

What is the difference between a case where it says “to transgress two prohibitions by it” and an ordinary place where we say it comes to reinforce? After all it’s the same thing. No. When it comes to reinforce, it is not “to transgress by it,” it is not “to transgress two prohibitions by it.” That’s the point. An interesting question; in a moment I’ll get to that, okay? Just a second. Maimonides’ claim is basically that loving the convert and loving one’s fellow is not a duplication. Is that similar to neshekh and tarbit? No, because with neshekh and tarbit it is “to transgress two prohibitions by it,” and in the count of the commandments it still does not enter. This one does enter the count of the commandments. Why? Because the difference between this and that is also a difference at the practical level, at the level of performance, what you have to do, what is imposed upon you. True, these are commandments of the heart, if you like, or of speech—this is probably traits, okay, among those four categories here. But they are different commandments even though ostensibly you love the same person—we’ll come to a case where with regard to the same person you love him once because he is a Jew, once because he is a convert, fine? But still, because the “because”—because he is a Jew or because he is a convert—is part of what is supposed to be present in your awareness when you fulfill that commandment, that means these are two different ways of fulfilling the commandment. You fulfill it in thought or in the heart, doesn’t matter, but it is still two different ways of fulfilling the commandment. Therefore it really enters the count of the commandments as two. But in neshekh and tarbit there is no difference at all—not in thought, not in meaning, not in anything. In practice: it is forbidden to take interest, that’s all. What is written here. There are two reasons: A, it harms the other person; B, it improperly increases my wealth. But those are reasons on the plane of rationales, if you like. That will not enter the count of the commandments. But it is still considered two prohibitions in the sense that, for example, if lashes applied there, you would be lashed twice. It is linked to restitution, so there are no lashes. Tosafot in fact asks what practical difference there is to “transgress two prohibitions by it,” since there are no lashes here. He understands “transgress two prohibitions by it” to mean receiving eighty lashes. Then he asks: but there are no lashes for neshekh and tarbit, so what is the meaning of “transgress two prohibitions by it”? But I’m saying, conceptually, when I say “transgress two prohibitions by it,” there really are two prohibitions here. This is not a game. In the count of the commandments it doesn’t enter. If you like, it is one doubled prohibition. That is not the same as when the Torah says twelve times to keep the Sabbath or not to desecrate the Sabbath. There it is not “to transgress two prohibitions by it.” No, I will not be stoned twelve times if I did labor on the Sabbath, or if it were lashes I would not receive lashes twelve times because the Torah repeats the same thing twelve times. I did not violate twelve prohibitions. In neshekh and tarbit I violated two prohibitions, the prohibition of neshekh and the prohibition of tarbit. But because on the practical plane it appears in the same way, it does not enter the count of the commandments, though it is still two prohibitions in every respect. In principle one would receive lashes for both. Or say even on the plane of “a positive commandment overrides a prohibition.” Right, the rule is that a positive commandment overrides a prohibition. What happens when there are two prohibitions? A positive commandment against two prohibitions. There is a dispute whether a positive commandment overrides two prohibitions or not. So if there is a positive commandment against neshekh and tarbit, it will presumably be a positive commandment against two prohibitions, not against one. For the count of the commandments it does not enter, but it is two prohibitions. That answers what you asked earlier. Okay? So this is not the same thing Maimonides is talking about here. Here Maimonides is not speaking only about the count of the commandments. Here Maimonides says this is not two prohibitions at all; they just repeated it twice to tell you it is important or severe or something like that. He adds as a note—that’s what he said—even if they say it is “to transgress two prohibitions by it,” what I marked here, that’s the second category. Even in a place where it really is two prohibitions, if on the practical plane you do it in the same way, it imposes the same obligation on you, then it will not enter the count of the commandments. But there it is still two prohibitions. This is only not entering the count of the commandments, and since Maimonides’ concern here is the count of the commandments, he also inserts a note about that. These are two different principles, two different things that do not enter the count of the commandments, but they differ. One of them is not two prohibitions at all; the other really is two prohibitions but does not enter the count. And in both cases Maimonides says it will not enter the count of the commandments. For him that is what matters here. That is the example he brings. Yes, “it is already known that the command concerning the Sabbath, to rest, is repeated in the Torah twelve times.” He is speaking of positive commandment, not prohibition. “Would anyone among those who count the commandments think to say that among the positive commandments is resting on the Sabbath and that it is twelve commandments?” There is a positive commandment of rest on the Sabbath. Rest meaning not to do labor. But would anyone even imagine that there are twelve positive commandments here, even though the Torah commands it twelve times? No. Because it comes only to reinforce. Nachmanides argues no, it comes to teach all kinds of things, details. Even so, we do not count it because those are details within the commandment of resting on the Sabbath. But yes, it is not repeated merely for reinforcement, rather to teach something. “And similarly the warning against eating blood comes seven times. Would any intelligent person think and say that the prohibition of blood is seven commandments? This is not something over which anyone would err.” There is no such thing. Therefore we do not count the commands, but the contents.

In previous lessons I discussed the fact that in the second part of this root Maimonides seems to say the opposite—Rabbi Yerucham Fishel Perla already asks this. Because in the second part Maimonides says that a general prohibition is counted as one prohibition, even though it commands five different things, like “you shall not eat over the blood,” for example. It commands five different things, and it is counted as one prohibition because there is only one verse. So here Maimonides writes that we follow the contents, regardless of the many commands. And in the second part he says that we follow the commands: there is one command, so we count one, even though there are many contents. And I said there is no contradiction here, because for Maimonides, in order to count something he requires both things: that there be independent content and that there be a command. And if one of those two things is missing—either there is no independent content or there is no separate command—then it will not enter the count of the commandments. That is the ninth root. I now move to the sixth root.

The sixth root: that a commandment that contains both a positive commandment and a prohibition should have its positive component counted among the positive commandments, and its prohibitive component counted among the prohibitions. The heading itself is already interesting. Why? After that he details it; we’ll see in a moment. What is he saying here? On the surface it seems he is coming to qualify the principle he gave in the ninth root. In the ninth root he says that if there is duplication in the Torah, we count only once. Right? Here in the sixth root Maimonides says: that is all if the duplication is among positive commandments or among prohibitions. But if the duplication is between a positive commandment and a prohibition, with the same content—say, resting on the Sabbath. So there is a positive commandment to rest on the Sabbath, not to do labor, and there is a prohibition against doing labor on the Sabbath. So here there is duplication. But the duplication is between a positive commandment and a prohibition. Here Maimonides says we do count both commandments. Here the rule of the ninth root will not apply. Even though there is duplication of content, we count both commandments. And he adds something else: we count the positive commandment with the positive commandments, and the prohibition with the prohibitions. Why even say that? Isn’t it obvious? Not at all. Not obvious at all. Because what does it mean to count the positive commandment with the positive commandments? Let’s say resting on the Sabbath. There is a commandment to rest on the Sabbath, and there is a prohibition against doing labor on the Sabbath. Fine, that is a positive commandment and a prohibition of the sort he speaks about here. Now I might have said: count both of them with the prohibitions. Even if you count two, that’s one innovation. Even though they are the same content—not doing labor. He says fine, but if one is written in the form of a positive commandment and the other in the form of a prohibition, we count two, not one. Fine, we count two, but maybe both are really prohibitions? Why? Because in the final analysis, what does the idea here, what does this content say? Not to do labor—that’s a prohibition, that’s its essential content. It is once phrased this way and once phrased that way, but practically it’s a prohibition. So even after you’ve taught me that we count two commandments here, Maimonides’ second point is no less novel: that those two commandments, the positive one is counted with the positive commandments and the prohibition with the prohibitions. Who says? Why? There are two novelties here, and we need to understand both. Of course if I understand that this is a positive commandment and that is a prohibition, then it is easier to understand why here we count two, because I understand that these are apparently two different things and not the same as duplications of positive commandments or duplications of prohibitions. But we need to understand in what way this is different. After all, it is still duplication. In both cases we are talking about not doing labor on the Sabbath. So why is this not ordinary duplication?

So Maimonides says as follows: “Know that one and the same matter may contain both a positive commandment and a prohibition in one of three ways.” Meaning, in Jewish law there are three contexts or three forms in which duplication between a positive commandment and a prohibition can appear. “Either a certain act among acts is a positive commandment, and one who transgresses it transgresses a prohibition, as with the Sabbath and festivals and the Sabbatical year, where doing labor on them is a prohibition and resting on them—that is, not doing labor—is a positive commandment, as will be explained. And similarly fasting on the Day of Atonement is a positive commandment and eating on it is a prohibition.” So that is the first category. This category is the one that will interest us further on. Yes, so think for example of the Sabbath. In the end, the same requirement—that we not do labor on the Sabbath—is stated once in the Torah in the form of a positive commandment, to rest on the Sabbath, and another time in the form of a prohibition, “you shall do no labor.” But basically it is the same requirement, not to do labor on the Sabbath. There are also other positive commandments concerning the Sabbath—don’t confuse them. There is a positive commandment to remember the Sabbath, say kiddush and havdalah—there is some dispute. There are rabbinic restraints which perhaps are of Torah origin according to Nachmanides, there is the resting of one’s animal, perhaps the resting of one’s child. But we are speaking only about this positive commandment that duplicates the prohibition—the positive commandment not to do labor, to cease from labor. Fine? That is the first example.

The second category: “Or there may be a prohibition preceded by a positive commandment, as they said regarding the rapist and the slanderer, ‘and she shall be his wife,’ and this is a positive commandment, and afterwards it is said ‘he may not send her away all his days,’ this is a prohibition.” Notice, here there is a positive commandment and a prohibition concerning the rapist and the slanderer. There is a positive commandment—if you raped her, you must marry her—and after you marry her there is a prohibition: he may not send her away all his days. You cannot divorce her—unless she wants, but not against her will. Okay? This too is some type of duplication: you must marry and you are forbidden to send her away. You understand, this is not the same sort of duplication as on the Sabbath. The content is entirely different. The obligation to marry is to perform an act of betrothal and actually marry her, and the prohibition against divorcing is a prohibition against dismantling that state. Not related. On the Sabbath it is really duplication of content. Here nobody would think this is duplication; it is not duplication of content, it says two different things. This is called a prohibition preceded by a positive commandment. Here there is a positive commandment to marry her, and afterward comes the prohibition, “he may not send her away all his days.” That is the second category.

The third category: “Or there may be a prohibition and afterward it is converted into a positive commandment,” which is what is called a prohibition linked to a positive commandment. “As in ‘you shall not take the mother with the young,’ and afterward ‘you shall surely send away the mother.’” This is the opposite case: first the prohibition appears, and if you transgress the prohibition—“to link” means to repair—if you transgress the prohibition, you repair it by fulfilling the positive commandment. Say, restitution of theft is linked to repayment: “and he shall return the stolen item that he stole.” If you stole, you transgressed the prohibition; the correction is “and he shall return the stolen item.” Okay? So basically there are three categories: duplication between prohibition and positive commandment, which is what occupies us in this lesson; there is a prohibition preceded by a positive commandment, like “he may not send her away all his days”; and there is a prohibition linked to a positive commandment. The question is whether the positive commandment comes first and then the prohibition, or the prohibition comes first and then the positive commandment. Those are the other two categories. But in the Sabbath it is neither before nor after; it is the same thing itself that has two faces, one face of prohibition and one face of positive commandment. And that is really the issue that interests us.

He says: “And each of these types should have the positive commandment within it counted among the positive commandments, and the prohibition within it among the prohibitions. For the Sages explicitly said regarding each one that they are positive commandments and prohibitions, and many times they say ‘its positive commandment’ and ‘its prohibition.’” And you see that with keeping the Sabbath there is its positive commandment and its prohibition, two different things. “And this is clear.” Up to this point, by the way, this is not yet proof. Up to here it is only proof that there are two prohibitions here—well, one positive and one negative commandment. But we already saw, as with neshekh and tarbit, that even if there are two prohibitions that still does not mean that in the count of the commandments we should count two. So the fact that the Sages said “its positive commandment” and “its prohibition” only means that there is a positive commandment here and a prohibition here, and therefore if you do labor on the Sabbath, you have both violated a positive commandment and transgressed a prohibition. That still does not mean that they should also be counted in the count of the commandments as two. Where does Maimonides get that from? Maimonides says: “And it is clear that the matter of the command in these cases is other than the matter of the warning, and they are two distinct matters. He commanded one of them and warned against the other.” You see? Commandment and warning. The shared expression is decree, as he says in the eighth root. Commandment means positive commandments; warning means prohibition. “And in this root no one erred.” Meaning, this is a root agreed upon by everyone, including the author of Halakhot Gedolot, including everyone. By the way, yes. No, in fact Rabbi Yerucham Fishel Perla claims that Saadia Gaon does not accept this. When Maimonides says “in this root no one erred,” that is a hint that Maimonides apparently did not know Saadia Gaon’s count of the commandments. I mentioned last time the discussion about that issue. In any event, this is what Maimonides says: there is some type of duplication here, and with that it seems to me the structure is this. First of all, we learn from the Sages that when the Torah says the same thing in the form of a positive commandment and a prohibition, there is here a positive commandment and a prohibition. Like “to transgress two prohibitions by it,” so here too there is a positive commandment and a prohibition. That still does not necessarily say anything about the count of the commandments. It only says that, as with transgressing two prohibitions, there are two prohibitive elements here. The next step that Maimonides takes—that one can also count this in the count of the commandments as two commandments—is a step he makes on the basis of reasoning. And this is what he adds: “for it is clear that the matter of the command in these cases is other than the matter of the warning.” Because command and warning are two different things. So this is not duplication at all—that is what Maimonides says. Once I already understand that when I have a commandment to keep the Sabbath, yes? that is a positive commandment, even though what it tells me is not to do labor, once I understand that, no proofs are needed. From there it is already clear that it should be counted separately in the count of the commandments: the positive commandment with the positive commandments and the prohibition with the prohibitions. That is Maimonides’ second novelty. It seems to me that this is exactly a positive and a negative commandment. Precisely. And this came to him by reasoning. “It is clear”—he does not prove this, and that is an important point: he does not prove it from the Sages. Very often Nachmanides attacks Maimonides for his proofs from the Sages. And Nachmanides’ claim many times—I don’t know if in this chapter, but several times—is that the Sages were not dealing with the count of the commandments at all. Why are you bringing me proofs from the Sages for the count of the commandments? The Sages did not discuss the question how many—for example, “to transgress two prohibitions by it.” They say you transgress two prohibitions, but that does not mean we count two commandments here. Nowhere in the Sages, apart from Rabbi Simlai—I spoke about this last time—who says 613 commandments were said to Moses at Sinai, apart from Rabbi Simlai you will not find in halakhic discussions how many commandments are counted here. I said because there is no practical consequence to it. The Sages do not deal with this. So you can’t bring proofs from the Sages to the count of the commandments. Nachmanides attacks Maimonides. And the answer is that Maimonides never brings proofs from the Sages to the count of the commandments. That is a mistaken reading of Maimonides. Maimonides brings proof from the Sages for a certain understanding that he, by reason, is convinced must be reflected in the count of the commandments. The proof from the Sages is that when we see this duplication on the Sabbath, keeping the Sabbath and not doing labor on the Sabbath, this is a positive commandment and a prohibition. We see that in the Sages. And from there onward Maimonides says by reasoning: fine, now the positive commandment and the prohibition are two different things. The matter of warning and the matter of command are clearly two different things. Therefore this will appear twice in the count of the commandments. That is already Maimonides’ conclusion; that is not proof from the Sages. It is reasoning. The proof from the Sages is only that this is a positive commandment and that is a prohibition. So that is the Sages’ novelty, that this is a positive commandment and this is a prohibition. Maimonides’ novelty is that if this is a positive commandment and that is a prohibition, then the ninth root, which says duplications are not counted, does not apply here. In the case of a positive commandment and a prohibition, duplications are counted. That is Maimonides’ novelty, the second novelty. The first novelty is the Sages’; the second novelty is Maimonides’. Okay?

Now let’s really try to understand the novelty of the Sages. What is the meaning of this? Look—Saadia Gaon, I said Rabbi Yerucham Fishel Perla claims, against what Maimonides says that no one disagreed with this, that Saadia Gaon apparently does disagree. So claims Rabbi Yerucham Fishel Perla. He says: “But the view of our master the Gaon, of blessed memory,” Saadia Gaon, “in all this is very far from the view of all the other medieval authorities (Rishonim), and the whole root before us, the sixth root, is neither known to him nor accepted by him at all. And in every commandment that contains a prohibition and a positive commandment, as long as there is no additional novel matter in each that is not included in the other, if there is no novelty in one over the other, they are both counted only as one commandment.” This needs to be understood well. When Maimonides says that we count those two commandments separately, he is not claiming that this is because there is some practical difference between them. Because if it were because there is a practical difference between them, that is already written in the ninth root, that when there is duplication with a practical difference, that is not duplication. It is pretty clear that Maimonides here, in the sixth root, wants to say: even if there is no practical difference, if the duplication is between a prohibition and a positive commandment, then even if there is no practical difference, the ninth root does not apply here. Here we do count two commandments. Therefore Saadia Gaon—or Rabbi Yerucham Fishel Perla on his behalf—is right to say: what Maimonides says here is that we count the positive commandment and the prohibition not because there is some practical difference between them. There is no practical difference; it is duplication. Fine, but if that is really what Maimonides says, Saadia Gaon does not accept it. If there is no difference, then it is duplication. Why count two things that say the same thing? What difference is there between saying “rest on the Sabbath” and “you shall do no labor” and saying twice “you shall do no labor”? You said the same thing. If the commandment is more explicit… now the question is, then let us count only one prohibition. Do you remember Maimonides’ second novelty? The first novelty of Maimonides is that we count two commandments. The second novelty is that the positive commandment is counted with the positive commandments and the prohibition with the prohibitions. There was room to say that they are both prohibitions. Now regarding Saadia Gaon too you can ask the same question. Saadia Gaon sees that there is a commandment to rest on the Sabbath and a prohibition against doing labor on the Sabbath. So he counts one commandment because this is duplication. Which one? A prohibition or a positive commandment? I don’t know, good question, we need to check. The act itself… ostensibly, right? So let’s see what he says. “If the commandment is made clearer by the prohibition than by the positive commandment, then the prohibition is what is counted in the list of prohibitions, and the positive commandment is not counted again at all. And if the commandment is made clearer by the positive commandment, then only the positive commandment is counted in the list of positive commandments, while the prohibition is not counted at all. But when one of them includes a novel matter not included in the other, one should count only the one that includes more.” What does he mean by “the commandment is made clearer by the prohibition than by the positive commandment”? It is not clear, not clear, but just a second. Detailed more? In a moment. But I suspected he means to say what better fits the content of the commandment. For example, with the Sabbath it is a prohibition, because both the positive commandment and the prohibition really come to prevent me from doing labor on the Sabbath. So in terms of content it is a prohibition. The commandment is understood better? The content of the commandment, yes—the content better suits being a prohibition and not being a positive commandment. Okay, he inserted it into his wording, yes. He says “made clearer,” as if to say it fits better in the language of the commandment, yes. But I’m not… not entirely sure that’s so. Because for example with the Sabbath it seems to me that Saadia Gaon counts it only as a positive commandment, not as a prohibition, if I remember correctly. I even wrote it here. Never mind—in any case it does not always line up with Saadia Gaon. It does not work in all of Saadia Gaon’s cases. And therefore never mind, you have to choose in some way, but the very dilemma of what to choose sharpens the point that is important to me here. Because there really is some kind of choice here that must be understood. Maimonides, who chooses to count the positive commandment with the positive commandments and the prohibition with the prohibitions—why? Why is the commandment to rest on the Sabbath counted with the positive commandments? What it requires of me is not to do labor, so why is it a positive commandment? In what sense? Or if I push the question even further: what is the definition of a positive commandment at all? If you tell me that even a prohibition on doing something can be a positive commandment, then what exactly is the difference between a positive commandment and a prohibition? Just the wording. Okay, you studied Talmud, I can tell. In a moment we’ll see. I say this critically, sorry for the… we’ll see in a moment. There’s an article by Aharon Shemesh that says exactly this. We’ll see shortly. I didn’t study the article in detail, but… no, never mind, I’m only saying that this form of thinking—it’s not because of the… so that is basically what… ah no, regarding rest on the Sabbath specifically, Saadia Gaon actually does count both a prohibition and a positive commandment. Here, it’s written for me—positive commandment 31 and prohibition 156. Yes. Yes. So Rabbi Yerucham Fishel Perla, there on positive commandment 31, squeezes that somehow, but fine. In any case he says: “At all events it is clear that according to our master the Gaon, of blessed memory, a positive commandment and a prohibition within one commandment are certainly one matter and one thing, since the essence of the commandment is one in both. And the Merciful One wrote it in a positive commandment and a prohibition only in order to magnify the severity of the punishment of one who transgresses it, and this has no relevance to the count of the commandments at all.” By the way, that is a bit of a hint. Because what does it mean “to magnify the punishment”? Punishment exists only for prohibitions; there is no punishment for positive commandments. So ostensibly it seems that the main commandment on the Sabbath is a positive one, and they added the prohibition so that there should also be punishment, to magnify the severity of punishment for the matter. But maybe he means punishment in heavenly law, and then he says in Heaven they will punish you also for violating a positive commandment, not only a prohibition; and then it could be that the prohibition is the main one and the positive commandment was added so that in Heaven you will be punished more because there is another aspect of severity in the transgression. “For in the count of the commandments we have only the acts that we were commanded to do or to refrain from doing.” What is he saying here? We do not go by the formulation but by the content. This is a hint to his own comment on the ninth root; here we are in the sixth root. Because in the ninth root, do you remember, Rabbi Yerucham Fishel Perla said: wait, after all we are speaking about the contents of the commandments; we are not counting the number of commands. Maimonides says that twelve times being told to keep the Sabbath is counted as one commandment. Why? Because there is one content here. Why do I care that there are twelve commands? Meaning, for me in the count of the commandments what matters is what this imposes on me practically. If all these commandments impose on me keeping the Sabbath, then that is one commandment. I don’t care that I am commanded twelve times. He says here, according to his approach, the same thing: what is imposed on me on the practical level? Not to do labor. So this positive commandment is really a prohibition. So this is just like a duplication in the ninth root between two prohibitions. What difference does it make that the Torah writes it in positive language? In practice what it demands of me on the practical plane is a prohibition, and what matters is not the formulation but the practical content. Therefore he says that according to his approach this is really only one commandment, “unlike all the other counters of the commandments apart from the Sefer Mitzvot Katan, which in its list of commandments also followed our master the Gaon’s approach,” like Saadia Gaon in this, “to count a positive commandment and a prohibition of one commandment only as one commandment.” Fine? Meaning his claim is basically that Saadia Gaon’s view is singular against the rest of the medieval authorities. Here Maimonides is following the majority view, and according to Saadia Gaon this is simply duplication like any other duplication.

And really, this question of Saadia Gaon, of Rabbi Yerucham Fishel Perla, is basically the question I’ve been aiming at throughout this whole lesson. There really is a problem here to which Maimonides has to give us an answer. Maimonides says that the positive commandment—and this is Maimonides’ second novelty, not the first one, to which one can almost fail to pay attention altogether—this is the interesting novelty here—that the positive commandment of keeping the Sabbath is a positive commandment, and the prohibition against doing labor is a prohibition. Why? What defines this commandment as a positive commandment if all it requires of me is not to do labor? Now we arrive at defining the concepts—the introduction I gave at the beginning as to why it is important to conceptualize and define concepts. So let’s try to understand what a positive commandment and a prohibition are, or really why these things bother Rabbi Yerucham Fishel Perla—how did he understand what a positive commandment and a prohibition are? Afterwards we’ll try to think about what Maimonides thinks, but first of all: what is the conventional view? Why is Rabbi Yerucham Fishel Perla twisting himself into knots here? How would you define the difference between a positive commandment and a prohibition? What is a positive commandment and what is a prohibition? Yes, right. Meaning, in legal language: is this a command concerning an act or concerning an omission? Omission means refraining from doing something. Okay? If what is required of me is non-performance, then that is a prohibition. And if what is required of me is action, then it is a positive commandment. Or in more halakhic, analytical language, however you want to call it: a positive commandment is a commandment whose fulfillment is by active performance and whose violation is by passive non-performance. If you don’t do it, then you violated it, you neglected a positive commandment. A prohibition is the opposite: its fulfillment is by passive non-performance, and its violation is by active performance. Right? That is the initial definition of the difference between positive commandment and prohibition, and therefore Rabbi Yerucham Fishel Perla says: what do you want? The positive commandment to rest on the Sabbath is a prohibition, it is not a positive commandment. He attacks Maimonides’ second novelty. Consequently the first novelty also collapses, because once both are prohibitions we are back to the ninth root, and then there is no sixth root. We are back to the ninth root that if there is duplication between two prohibitions, then you count only one. He attacks him on the second novelty and not on the first. And ostensibly he is right. I’ll formulate it in logical language. I say: what is the difference between telling me “put on tefillin” and telling me “I do not want you not to put on tefillin”? That’s a double negation. The first is a positive commandment and the second is a prohibition. Why? In terms of content it’s the same content. Can there be two verses that are logically equivalent but nevertheless are different commandments? How is this different from writing “rest” twice? That is basically what Rabbi Yerucham Fishel Perla asks, right? He says this is duplication like any other duplication. It’s only a difference in wording—what difference does it make? And that raises the question, according to Maimonides and as we saw according to the vast majority of the counters of the commandments and the medieval authorities, how do they define the difference between a positive commandment and a prohibition? Apparently they do not accept the definition—I’ll now call it, following Shemesh—the performative definition. That is the performative definition: how one carries out the commandment. If one performs it actively, it is a positive commandment. If one performs it by refraining, it is a prohibition. That is a performative definition. But it turns out that Maimonides and almost all the counters of the commandments and the medieval authorities do not accept that definition, except for Sefer Mitzvot Katan and Saadia Gaon. So what do they say instead? What is the difference between a positive commandment and a prohibition? Where did the double negation disappear, and why in fact did it not disappear?

Examples of this—you need to understand, every pair of commandments that belongs to this category of the sixth root raises the same problem. How can there be duplication between a positive commandment and a prohibition? How can there be a sixth root in Maimonides at all, when there is duplication between a positive commandment and a prohibition? But how can there be duplication? If a positive commandment is performative, meaning to do something, and a prohibition means not to do something, then a priori there cannot be duplication between a positive commandment and a prohibition. If there is duplication, then this isn’t a positive commandment and a prohibition. Okay? So Rabbi Yerucham Fishel Perla is basically denying the very existence of the sixth root. Not by saying there aren’t… what is he even talking about in the sixth root? About when there is duplication between a prohibition and a positive commandment? There is no such thing as duplication between a prohibition and a positive commandment; it’s an oxymoron. It’s like saying a square triangle. If there is duplication, then it’s not a prohibition and a positive commandment—they are duplicates, they are the same content. If it’s a prohibition and a positive commandment, then there is no duplication. How can there be duplication between a prohibition and a positive commandment? Rabbi Yerucham Fishel Perla does not accept that very sentence. Not as a halakhic dispute, not as a dispute about commandments; it’s a logical dispute. You are speaking to me in a language of oxymorons, square triangles. Duplication between a prohibition and a positive commandment is a square triangle. Okay, that is basically Rabbi Yerucham Fishel Perla’s claim.

But there are examples that have nothing to do with duplication. For example, there is the prohibition “do not stand idly by your neighbor’s blood.” If I see someone drowning in the river and I’m passing by and I can save him, then if I do not save him, I have transgressed the prohibition “do not stand idly by your neighbor’s blood.” Is this prohibition, according to the performative definition, a prohibition or a positive commandment? It is a positive commandment, right? I’m supposed to save him. If I did not save him, then I transgressed it. Meaning, if by passive non-performance one transgresses it, fine, and by active performance one fulfills it, then it is a positive commandment. What about “you shall not place blood in your house” and “you shall make a parapet for your roof”? If I didn’t put a parapet on my house, I transgressed the prohibition “you shall not place blood in your house.” If I put up a parapet, then I didn’t transgress the prohibition. So is it a prohibition? It’s a positive commandment. It requires me to put up a parapet; it requires me to act. It’s a positive commandment. Now perhaps Rabbi Yerucham Fishel Perla would say: fair enough, it really is a positive commandment. And “do not stand idly by your neighbor’s blood” is also a positive commandment. Who says it isn’t? We know from the Sages that they tell us: “take care,” “lest,” “do not”—these are prohibitions. So that definition doesn’t really hold up. It’s not just Maimonides; this is not Maimonides’ invention. It’s already like that in the Talmud. There is something here showing that the performative definition does not really put its finger on the difference between a positive commandment and a prohibition. The difference between them is not a performative difference. But if it is not a performative difference, as Rabbi Yerucham Fishel Perla asks, then what is it?

So Aharon Shemesh, of blessed memory—he passed away at a relatively young age; he was here in the Talmud department—in his article in Tarbiz argues that if you examine the Talmudic discussions, then in the earlier discussions the difference between a prohibition and a positive commandment is performative. And in the later discussions, he says, the difference is linguistic. It depends on how the Torah phrases the commandment. If the Torah says “on the seventh day you shall rest” in the form of a positive commandment, then that is a positive commandment, even though from a performative perspective it requires me to cease, it requires me not to do something. Meaning he argues that over the generations of the Amoraim there is a shift: in the earlier discussions the definition is performative, and slowly a linguistic definition takes hold and replaces the performative definition. By the way, this is a widespread phenomenon in the Talmud. Also from Mishnah to Talmud, and also from earlier to later generations in the Talmud, the level of abstraction rises as the generations advance. Thought becomes less concrete and more abstract. And if you continue on to the medieval and later authorities, of course the process continues further. All the abstractions of later authorities the medieval authorities never dreamed of, and the Amoraim certainly not. But abstract thought—the more generations pass, the more abstract thought becomes. That’s just how it is, a feature of the world. I’m not speaking now evaluatively, whether that’s good or bad. Factually, that’s what happens. What? Is the linguistic more abstract? Wait, ostensibly yes, and there is some type of abstraction here because it basically says: I don’t accept the concrete definition—if it demands something of you, that is not the definition in practical terms. Then what is? We still need to see. But it is not the simple practical definition; I need some type of abstraction.

Now my problem with this—and this was my criticism earlier of this form of thinking—is that Shemesh stops there. What do I mean? I ask myself, as a yeshiva student, fine—you showed, and it’s a nice distinction, that the performative criterion does not distinguish between positive commandment and prohibition, and then you said, fine, so the conclusion is apparently that the criterion is linguistic. But language cannot be the reason; at most it can be a sign. You can say that if the Torah formulates it as a positive commandment, then apparently it intends it to be a positive commandment. But you can’t say that the definition of this as a positive commandment is because the Torah phrased it that way. I ask myself: and why did the Torah phrase it that way? Why did the Torah choose that? Just because it felt like it? Did it draw lots? After all, if you are basically telling me, look, really the commandment to rest on the Sabbath is a prohibition, or “do not stand idly by your neighbor’s blood” is really a positive commandment, but the Torah for some reason chose to phrase it in the form of a prohibition and therefore it will be a prohibition, or a positive commandment—if the wording is what determines it, is it really just arbitrary? A whim? Why did the Torah phrase it that way? What did it intend? Clearly behind the linguistic criterion there has to be some substantive criterion that the linguistic criterion reflects. But you can’t be satisfied with saying that the criterion is linguistic. Let me give an example. There is Rabbi Yose the Galilean, whose opinion is that offerings of lesser sanctity are the owner’s property. The Talmud says in several places that there can’t be a more lenient eating-permission in offerings of lesser sanctity than in offerings of higher sanctity, where everything is burned on the altar; with offerings of lesser sanctity there is permission to eat, and therefore it is the owner’s property. Now you ask yourself—I once had an argument with my study partner—what does it mean that it is the owner’s property? We said, for example, that one can betroth a woman with it or eat it. That doesn’t mean it is the owner’s property. It only means that the laws of sanctity said regarding offerings of lesser sanctity are different laws, and still the Torah determines what you do with it. How is it different from offerings of higher sanctity? You eat it, but you eat it as a commandment. When you say it’s yours, you can’t bring me the practical implication that one can betroth a woman with it as the explanation of why it is yours. You have to explain to me that it is yours; then the practical implication is that one can betroth a woman with it. But you can’t bring me the practical implication as the definition. You have to explain to me why it is mine. After all it is sacred; it has sanctity. What do you mean, the owner’s property? It’s holy. Now once you show me that it is mine, the practical implication will be that I can betroth a woman with it. You can’t say to me, ah, why is it mine? Because I can betroth a woman with it. You’re mixing up cause and effect. We have a tendency to mix up the consequences of things with the things themselves. I don’t want to drift too far into philosophy, but I could give many fascinating examples of how people confuse the implications of things with the things themselves.

Let me give a halakhic example instead of a philosophical one—there are many examples. For example, what is ownership? What does it mean that I own something? Usually people will tell you: owning something means I have rights to use the thing and someone else does not have rights to use the thing. And I claim that the fact I have rights to use the thing is a consequence of the fact that I am the owner. If I am the owner, I have rights to use the thing. In that chapter—in that chapter, I remembered, in one of the series I talked about this, I don’t remember. But my being the owner is some condition that exists in its own right, some metaphysical or meta-legal relation between me and the thing. It has consequences—namely, I have rights to use the thing—but rights of use are the legal consequences of my being the owner. My being the owner is a factual claim. And it is wrong to confuse the two, and in Jewish law there are errors that stem from this, which can be addressed separately.

There is—because I can’t continue anymore, time is up, so I’ll just finish this point—there is Leibniz, the German philosopher from the eighteenth century, I think—the one who invented the infinitesimal together with Newton. Invented or discovered, whichever you prefer. So he upheld the principle of the identity of indiscernibles. Meaning, if there are two entities that have exactly the same set of properties, then it is the same entity. It is one entity, not two. He has a wonderful proof of this. What is the proof? Let us assume, for the sake of contradiction, that they are two entities. Fine? We have entity A and B, they have the same set of properties, and I claim they are still two entities, let’s call them A and B. Then entity B has the property that it is not entity A, and entity A does not have that property. That contradicts the fact that they have the same set of properties. Therefore the assumption that these are two entities leads us to a contradiction. So it is one entity. He is of course wrong, and his mistake comes from that same confusion. He identifies the entity with its set of properties; for him, an entity is a set of properties. But philosophically that’s nonsense. Jorge Luis Borges, the Argentine writer—he was a genius, by the way, I recommend reading him—has a wonderful story about this. It’s called “Tlön, Uqbar, Orbis Tertius.” It doesn’t matter, one of his short stories. In it he tells about some planet he made up out of his fevered imagination, where they combine various properties and from them create nouns. Say, “the bird’s cry in space with the color of clouds yesterday morning”—that is a noun, and its name is Moshe. Why? Because if a set of properties is the object, then what’s the problem? I can gather any set of properties, and that set is an object. By the way, this is the problem Frege has in his definition of number, for those who know the mathematics. He too, in my view, confuses properties with the thing—a philosophical mistake, in my opinion. So that is not right. The object is the bearer of the properties; it is not the set of properties. The properties are properties of the object, therefore you can’t just collect a set of properties and say every such set creates an object. Only if there is a particular object that bears those properties, then the set of those properties are its properties. But the properties are not it; the properties are its properties. So that is not the same thing. Okay?

Anyway, Leibniz’s proof—homework assignment—it begs the question; it is not a proof. For our purposes, what I want to say is this: offerings of lesser sanctity have properties like things that are monetary property. But those properties are the result of the fact that it is monetary property. I cannot use those properties to explain that it is monetary property, or to define why it is monetary property. Rather, they are consequences of the fact that it is monetary property. The same applies to a commandment. You tell me that the Torah’s formulation is an indication that this is a positive commandment or a prohibition. But formulation is only an expression of the difference, which is supposed to be a real difference. The formulation represents the difference; it is not the difference itself. You can’t tell me the difference exists because there is this wording. No—the difference in wording exists because there is a real difference. Fine—what is the definition of the thing? What is the definition? No, a definition is always a definition through properties. But a definition is not the thing itself; it is the definition of the thing. The thing—I ask ontologically, what is the thing? Not how do you define it in the dictionary, but what is it. I’m saying ownership is not a set of usage rights. When you ask me what the properties of ownership are—which is what is usually called a definition—I’ll tell you usage rights or something like that. But it is wrong to identify the definition with the thing. The definition is an intellectual act; the thing is, ontologically, something that exists in the world. A definition is a process of thought; it is not the same as what happens in the world. It is connected, but it is not what happens in the world itself.

Okay, in short, I’ll leave you here with a question mark. There will be suspense until next time. I’ll just say in passing that in a certain sense I have a criticism of Shemesh’s treatment, even though he did excellent work—strange that until him no one had done it—because this is such a fundamental question: what is the difference between a prohibition and a positive commandment? It is so obvious a question that it is very strange no one ever asked it, at least not in this form. You can find hints, as I said earlier. On the other hand, he somehow stopped midway. Meaning, he asked the question, put his finger on some problem that is a distinction, and turned the question mark into an exclamation mark. Meaning, he says okay, there is a difference in wording, therefore the wording difference is the difference. But there is a question mark here; you need to answer it, not stretch it out and turn it into an exclamation mark. Okay? That’s one side. On the other hand, actually, in a certain sense I’d say that this really is the role of an academic, or of an academic article. Because the explanations I will suggest are explanations of a lamdan, not of a scholar. Meaning, if they make sense to you, you’ll accept them; if not, then not. But that is not a fact. And a responsible scholar is one who sticks to facts. He wants to tell you what the objective facts are, regardless of my worldview or your worldview, at least theoretically. Okay? And in that sense I actually very much agree with the limitation he imposed on himself—to stop at pointing out that the difference is a difference in formulation. That is a fact: that the difference is linguistic and not performative. I, as a lamdan, will ask myself: okay, and why? What does the difference in formulation express? But that really is not the academic’s role; it is the role of someone learning the matter for himself. And therefore in a certain sense it is not even criticism; it is simply pointing out a disciplinary boundary. Okay? Fine, we’ll stop here. The solution to the riddle next time.