Processes and States in the Context of Response, Lesson 1

Table of Contents

• General Overview
• Repentance as a process versus repentance as a state
• “I will sin and repent” and the limited value of the penitent
• A contradiction in Maimonides: is there a commandment to repent or only to confess?
• Two tracks of repentance: halakhic and essential
• Nachmanides versus Maimonides: ושבת עד השם אלוקיך as a command or as a prophecy
• The roots of Sefer HaMitzvot: unique content and command as conditions for inclusion in the count
• Obligation without command, and the halakhic implications of counting the commandments
• Meshekh Chokhmah: there is no logic in commanding repentance apart from confession
• Giving a bill of divorce as a model for the difficulty of defining a process
• Zeno’s paradoxes of motion and the distinction between a state and a potential
• Velocity at a point and the difference between “being located” and “standing still”
• Consciousness as a kind of “camera” and the need for examples in order to understand a process

Summary

General Overview

The text presents repentance as a process with value of its own, and not only as movement from a state of sin to a state of righteousness. In that way, it explains how one can understand the saying of the Sages that a penitent is superior to a completely righteous person. It rejects the simple explanation that the superiority of the penitent comes from greater effort, and proposes instead that the superiority has to do with the fact that the completely righteous person does not undergo the very process of return itself. From there it moves to an analysis of Maimonides’ view and the apparent contradiction between Sefer HaMitzvot and the opening of the Laws of Repentance, proposing that Maimonides recognizes an obligation to repent, but that it is not counted among the commandments because there is no explicit command. Finally, it illustrates the difficulty of grasping and defining processes through the topic of giving a bill of divorce and through philosophical paradoxes about motion, arguing that human consciousness grasps static states and therefore has difficulty defining a process except through many examples.

Repentance as a process versus repentance as a state

The statement that a penitent is superior to a completely righteous person is hard to understand if repentance is defined only as arriving at a perfect state, because the perfect state is that of the completely righteous person, and in terms of states there is no “more than that.” The text argues that the rabbinic statement assumes that repentance is not exhausted by the result; rather, there is value in undergoing the process itself. Therefore, the penitent is superior in the sense that he has gone through a process that the completely righteous person has not. It rejects the interpretation that the penitent is superior because he invested greater effort, arguing that the completely righteous person also invests effort, and may even have invested more, which is why he did not fail. It clarifies that superiority in rabbinic comparisons is not an absolute “bottom line,” but depends on a particular dimension, and gives as examples: “The Land of Israel is equal to all the commandments,” “fringes are equal to all the commandments,” and “a sage is superior to a prophet.”

“I will sin and repent” and the limited value of the penitent

The text cites the Talmudic statement about אחטא ואשוב (“I will sin and repent”), that such a person is not given the opportunity to repent, and presents a Hasidic explanation according to which the initial thought is that the person wants to turn himself into a penitent in order to become “superior” to a completely righteous person. It concludes that one should not sin for the sake of attaining the status of a penitent, but if he has already sinned, there is value in doing repentance. It presents this as a side note within the broader distinction between the value of the process and absolute comparisons between spiritual types.

A contradiction in Maimonides: is there a commandment to repent or only to confess?

In Sefer HaMitzvot, positive commandment 73, Maimonides formulates it so that when the sinner returns from his sin, he should confess, and the text understands this to mean that there is no commandment to repent; rather, there is an obligation of confession if he has already repented. In the introduction to the Laws of Repentance, Maimonides writes that there is one positive commandment, namely that the sinner should return from his sin and confess, and the text understands this to mean that there is one commandment that includes two components, similar to the four species. It notes that confession appears there as part of the process, whereas the other standard components of repentance, known from Saadia Gaon, do not appear in that formulation. It raises the difficulty that understanding confession as a conditional positive commandment yields an unreasonable result: someone who repented but did not confess would come out worse than someone who did not repent at all. It therefore suggests that the classification as a conditional commandment cannot fully stand.

Two tracks of repentance: halakhic and essential

The text argues that there are “two, two tracks of repentance”: practical halakhic repentance, with its four stages including confession, and essential repentance, in which genuine inner change by itself constitutes repentance even without all its halakhic details. It says that in essential repentance “you don’t need confession, you don’t need anything,” and explains this as a way of resolving the difficulty that it cannot be that someone who repented but did not confess is in a worse state than someone who did not repent at all. It notes that there is a whole body of discussion on this that he does not enter into here, and places it within his remark that “I’m speaking here in Petah Tikva.”

Nachmanides versus Maimonides: ושבת עד השם אלוקיך as a command or as a prophecy

Nachmanides interprets ושבת עד השם אלוקיך as an explicit positive commandment, whereas Maimonides, in chapter 7 of the Laws of Repentance, writes that “the Torah has already promised that Israel will in the end repent,” and interprets the verse as a promise and prophecy, not as a command. The text sees this as proof that according to Maimonides there is no explicit command to repent, and that is why it does not appear for him as a counted commandment. It raises possibilities such as distinguishing between the sins of an individual and the sins of the collective, but concludes that he does not know of any other good answer and offers a principled explanation based on Maimonides’ rules for counting the commandments.

The roots of Sefer HaMitzvot: unique content and command as conditions for inclusion in the count

The text explains that Maimonides lays down “roots” that determine what enters the count of the 613 commandments, and some of them deal with what is not a commandment, while others deal with what is included within another commandment or what has no separate command. It cites the ninth root and quotes Yerucham Fishel Perla’s discussion of an apparent contradiction between its different parts, resolving it by saying that Maimonides requires two conditions together: unique content and a command. It concludes that the commandment of repentance can be an obligation, even a Torah-level obligation, and still not be counted if there is no explicit command for it according to Maimonides’ interpretation of ושבת עד השם אלוקיך. It adds that the Mishneh Torah includes everything one is obligated to do, including rabbinic laws such as Hanukkah and Purim, and therefore Maimonides writes in the Laws of Repentance that there is a “positive commandment” to repent and confess even though it does not appear as an enumerated commandment in Sefer HaMitzvot.

Obligation without command, and the halakhic implications of counting the commandments

The text argues that something not appearing in Sefer HaMitzvot does not prove that there is no obligation, and does not even prove that there is no Torah-level obligation. It gives the example of a partial forbidden measure, which is Torah-level and yet does not appear in the count of the commandments. It emphasizes that, in the formal sense, a commandment is from the language of command, and that there is a distinction between a command and a divine expectation, bringing examples such as the calls found in Deuteronomy, and also Rashi’s opening comment on the Torah, which raises the question “Why did the Torah not begin with החודש הזה לכם?” on the assumption that there are no commandments in Genesis. It presents the example of ועשית הישר והטוב as something that is expected but not counted as a commandment in the formal list, and stresses that this has implications, such as the rule that a positive commandment overrides a prohibition, which depends on there being an actual command. It also notes that the number 613 itself is not beyond question, citing Nachmanides’ hesitation and the broad agreement that there is a tradition of 613 even though the details are disputed.

Meshekh Chokhmah: there is no logic in commanding repentance apart from confession

The text cites Meshekh Chokhmah, who argues that there is no logic in commanding repentance, because leaving the sin and not returning to it are already included in the fact that the act is forbidden, similar to Maimonides’ discussion in the fourth root of broad commands such as ושמרתם את כל מצוותי, which are not counted. It presents the claim that the only thing it makes sense to command is confession, because verbal confession does not follow from reason, whereas refraining from the sin itself does. The text points to the underlying assumption here, namely that repentance is basically just “simply not to sin,” and argues that if the process of repentance has value of its own, then it makes sense to speak about an obligation of repentance and not only about confession. It concludes that the discussion can remain even within a process-oriented but result-focused conception, in which the value of the process lies in what it brings about beyond merely “being a completely righteous person,” and not necessarily in the process as something valuable in itself.

Giving a bill of divorce as a model for the difficulty of defining a process

The text cites many passages in the Talmud in tractate Gittin that spell out cases of valid and invalid giving, and argues that the unusual multiplicity of cases points to a difficulty in giving a general definition of ונתן בידה (“and he shall place it in her hand”). It describes an attempt by Ketzot to infer that giving is not acquisition and is not mere physical transfer, because a bill of divorce written on something from which benefit is forbidden can still be valid, even though according to some medieval authorities there is no ownership over it; and on the other hand, giving can be done through transferring ownership of a courtyard while the bill of divorce remains where it is. It describes the efforts of Kehillot Yaakov to propose a complex definition that becomes more and more qualified, until the complexity comes to resemble the multiplicity of cases itself, and concludes that this is why the Talmud chose examples rather than a rule. It connects this to a “casuistic” approach of cases as opposed to a “positivist” approach of rules, and argues that the difficulty comes from the fact that people try to define giving through the states of “before” and “after,” instead of grasping the giving as a process, as “the transition itself.”

Zeno’s paradoxes of motion and the distinction between a state and a potential

The text presents the paradox of Achilles and the tortoise and the paradox of the flying arrow, and criticizes philosophical and mathematical solutions that attribute the problem to infinity or to differential calculus as an “English-English dictionary” that does not explain but merely replaces one language with another. It compares solutions that prevent the paradox from being formulated to ad hoc solutions such as Russell and Whitehead’s theory of types, which forbids self-reference instead of solving the problem, and criticizes the tendency of analytic philosophy to treat the problem as a mere “artifact of language.” It also mentions the uncertainty principle as something that blocks the very formulation of the paradox, but argues that this still is not an explanation if the uncertainty principle itself is not understood, and prefers to explain uncertainty through the arrow paradox rather than the other way around.

Velocity at a point and the difference between “being located” and “standing still”

The text proposes that the paradox comes from an imprecise formulation: at every moment the arrow “is located” in a place, but it is not “standing still” there, because “standing still” means having zero velocity. It argues that the confusion comes from the assumption that the concept of velocity does not exist at a point, because velocity is measured through differences in place and time, and it distinguishes between an operational definition of velocity and an essential definition of it. It brings the Doppler effect as a way of measuring velocity without requiring a segment of time and distance in the ordinary sense, in order to support the claim that velocity at a point is a defined concept. It offers the example of a body striking a wall and argues that, in the essential sense, the velocity at the moment of impact is what it was a moment earlier, except that it is not translated into change of place because the wall prevents it from being actualized, whereas in the operational sense one would obtain a velocity of zero.

Consciousness as a kind of “camera” and the need for examples in order to understand a process

The text argues that human consciousness grasps the world statically, like a camera taking dense “snapshots,” and therefore it does not see processes but infers them from differences between states. It says that this is why one needs many examples when trying to teach a concept that is itself a process, like giving a bill of divorce, because there is no direct way to grasp or define the process itself except through end states and an accumulation of cases. It sketches the theoretical possibility of an “alien” that grasps processes directly and sees velocities rather than locations, and argues that for such a being the integral would be basic and the move from velocity to location would be natural, whereas a concept like “a completely righteous person” would be for it a computational output rather than a primary experience. It concludes that our difficulty in understanding “giving” or “repentance” comes from the static lenses of our perception, and that the fact that we struggle to define a process does not make it fictitious, but rather requires us to learn it through examples.

I want to talk about—unfortunately, as I announced, I only remembered last night that I hadn’t sent in a topic—so I do intend to start something new now. I want to talk a little about the process of repentance, but from a particular angle, not about repentance in general. The relation between process—two ways of looking at the world: a process-oriented way of looking and a state-oriented way of looking. The background to this is really an interesting statement of the Sages, who say that a penitent is preferable to a completely righteous person. When they say that a penitent is preferable to a completely righteous person, it’s actually a bit hard to understand. I mean, on the face of it, when we look at a penitent, the ideal state of a penitent is that he has returned to being completely clean. So at most, assuming his repentance is full and complete and all that, he has become a completely righteous person. In what sense—how can it be—that a penitent is better than a completely righteous person? Yes, preferable to a completely righteous person. You probably know the joke that they say that in the place where penitents stand, completely righteous people cannot stand—because it’s too crowded. But I’m not talking about that aspect. So this statement really says—the meaning of it, what lies behind it—is that apparently the process of repentance, or repentance itself, is not exhausted by reaching some perfect state. Usually when we think about repentance, we say to ourselves: what is repentance? Repentance means I was in state X and I need to get back to state Y, to a better state. And repentance is exhausted by the fact that now I’m already in state Y. Meaning, the result of the process of repentance is basically its goal. But if that were so, then you couldn’t say that a penitent is preferable to a completely righteous person. There’s nothing beyond a completely righteous person in a state-oriented outlook. The perfect state is a completely righteous person—what could be more than that? When I say that a penitent is preferable to a completely righteous person, I’m really saying that apparently the goal of repentance, or the concept of repentance, is not just arriving at a whole, complete state. I’m not even talking now about complete repentance; there are of course also partial repentances. It isn’t reaching the complete state, or not only reaching the complete state, but there is something in the process itself. In the very fact that I moved toward the complete state, there is significance beyond the fact that now I’m in it. And only if you understand it this way can you perhaps understand why a penitent is preferable to a completely righteous person. Very often you hear explanations like: well, because the penitent had to invest some effort, because he was in a worse state; it’s not like the completely righteous person who is in the ideal state. I don’t agree with the simple version of that interpretation. A completely righteous person also needs effort. The fact that someone failed doesn’t mean he invests more effort afterward when he fixes things. The completely righteous person may invest more effort, and precisely because of that he never failed in the first place. He remains completely righteous. True, the author of the Tanya writes that a righteous person is someone who has no evil inclination at all, while an intermediate person is someone who never sins at all but still has an evil inclination, and overcomes it. Fine, that’s an initial statement of his there, but even in that framework—what does it mean that he has no evil inclination? Was he born that way? No. Maybe he reached that state. But in order to reach that state he invested exactly the same work that a penitent invests, if not more. He didn’t even fail along the way. So I don’t think this can be attributed to work or effort. Maybe you could call it a kind of carrot, some bonus to encourage the penitent—fine, those are all technical explanations. It seems to me that behind this rabbinic statement there really stands a conception that the process of repentance is not measured only through its results. That’s basically what is written there. Rather, the very doing of the process has some value. And in that sense the completely righteous person really did not undergo this process. Meaning, true, he is in a complete state, but he did not undergo this process. And therefore in that sense the penitent is preferable to the righteous person. By the way, just parenthetically, when they say that something is preferable to something else, or someone is preferable to someone else, there are often objections: wait a second, but somewhere else we see that the second is preferable to the first. From one aspect this is preferable, from another aspect that is preferable. Meaning, superiority is not always a bottom-line ranking. Superiority is often a concept. What? Where does the term “preferable” appear? No, they say that something— not exactly the term “preferable,” the point is that one thing is better than another. Elsewhere you say that the other one is better than this one. In which sayings of the Sages? For example, penitent versus completely righteous person—there’s a dispute there on this matter, for example, who is preferable: is the penitent preferable or is the completely righteous person preferable. The Talmud itself brings a dispute about this. But there are places where they bring all kinds of contradictions—it doesn’t matter right now, I don’t even remember more examples at the moment, but there are many. And the point is that when they say that something is preferable, yes? The Land of Israel is equal to all the commandments, and fringes are equal to all the commandments—there’s a midrash like that. What? A sage is preferable to a prophet? Yes, a sage is preferable to a prophet, fine, but there the question is the reverse. But the Land of Israel is equal to all the commandments, and fringes too are equal to all the commandments, so of course that can’t literally be true, right? I mean, all the other commandments include fringes, and the Land of Israel is equal to them. When you say that fringes are equal to all the commandments, that includes the Land of Israel. There’s no—this isn’t… Clearly, when you make comparative statements of this type, comparisons are always comparisons with respect to a certain aspect, a certain dimension. There may be another aspect with respect to which it’s not so. Okay, this isn’t… Therefore, obviously this is not—say, those who say, “I will sin and then repent, I will sin and then repent,” the Talmud says, “They do not give him the opportunity to repent.” So the Hasidim explain: why really, what was the initial thought? The initial thought was that he wants to become a penitent, who is preferable to a completely righteous person. So he says, “I will sin and then repent,” in order to become even more righteous than the completely righteous person. So they do not give him the opportunity—they do not give him the opportunity to repent. So basically, don’t be a penitent; it’s better to be a completely righteous person. But if you already sinned, then there is some value in doing repentance. Fine, that’s just a parenthetical remark. In any case, the claim is that within the process of repentance, its value is not only in the product, in the result that you arrive at, but in the process itself. And actually, in this context I’ll present a perhaps very slanted view before I continue. There’s a contradiction in Maimonides that the Minchat Chinukh already points out. Maimonides, in the Book of Commandments, positive commandment 73, writes that the positive commandment is that when the sinner repents from his sin, he should confess. Meaning, there is no commandment to repent; rather, if you repent, you have to do it also by confession, confession verbally. So the actual repentance itself is not a commandment. But in the introduction to the Laws of Repentance, Maimonides writes: one positive commandment—one positive commandment in the singular phrasing—and it is that the sinner should repent from his sin and confess. Not, “when he repents he should confess,” but “that he should repent and confess.” And that is one commandment, but one commandment that includes two details. Very often we have a collection of obligations that add up to one commandment. The four species are one commandment, even though they contain four details, but that doesn’t mean… each of the details is of course binding; it just isn’t defined as a full separate commandment among the 613 in a distinct way, but it is an obligation incumbent on us. So in this formulation, as the Minchat Chinukh asks, you see in Maimonides that there is a commandment to repent. There is a commandment to repent and confess. And in the Book of Commandments it appears that there is no commandment to repent, only that if you repent, the way to do it is by confession. Yes, maybe one more comment about the Book of Commandments formulation: what does it mean, “if you repent, do it by confession”? Suppose I repented and didn’t confess—then I have neglected a positive commandment, right? Because it’s like a conditional positive commandment, yes? If you repent… The location of the commandment in the Book of Commandments is among matters of sacrifices. Right. Sin-offering and guilt-offering and… and… It looks like part of the process; meaning, if you get to the point of bringing your sacrifice, that’s… He explains there the aspect of the commandment of repentance within the framework of… Okay, but he says there is no commandment to repent. The formulation says there isn’t—even with the sacrifice there is no commandment to repent. What you need is that if you repent, you should confess; that’s his formulation. Okay, but that’s the framework in which he places it there… Within that framework he doesn’t bring an obligation. Even within that framework he could have said that when you bring a sacrifice you must repent and must confess. He doesn’t write that. You committed some sin, you have to bring a sin-offering or a guilt-offering, and there he explains the process that goes along with it. Yes, fine, but there is no obligation… He explains what the process is, right. There is an obligation to bring a sacrifice, but not to repent. And confession isn’t called… confession yes, but not… No, confession itself is one detail of repentance. Meaning, one of the details is to confess the sin. But there is abandoning the sin; there are four things—beginning with Saadia Gaon it is accepted that repentance contains four things. There is abandoning the sin, regret, acceptance for the future, and confession. Confession is brought there; the other parts are not brought. Again, the simple logic says you do need to do them, but in Maimonides’ legal formulation it does not appear that there is an obligation to do so. I’m saying, within this matter, in the context of the Book of Commandments, let’s think about someone who repented and did not confess. Okay? So there is neglect of a positive commandment. Is his state worse than someone who didn’t repent at all? How can there be a commandment to repent? Huh? How can there be a commandment to repent? Why? You have to perform commandments and so on. It’s something very hard to say to a wicked person: there’s another commandment, to repent; you have to perform commandments. Why? No. “And he shall restore the stolen item that he stole”—what is that? It simply says: there is a prohibition against stealing, and if a person comes and repents, then there is a commandment to restore the stolen item that he stole. Why is it attached to a positive commandment in a certain sense? He says, if you weren’t doing commandments and now you begin doing them, did you repent or not? So that’s the other side of the same question. What extra thing is there in repenting? That’s what Meshekh Chokhmah asks. I’ll get to that in a moment. Fine, Meshekh Chokhmah asks this. So I’m saying, let me stay for the moment with Maimonides in the Book of Commandments: when Maimonides says that when the sinner repents from his sin he should confess, then this is really a conditional positive commandment. A conditional positive commandment like fringes. If there is a four-cornered garment, you have to put fringes on it. If you didn’t wear a four-cornered garment, nothing happened. But if you wore a four-cornered garment and didn’t put fringes on it, then you neglected a positive commandment. I think we discussed this once—that the commandment of fringes is not an existential positive commandment, as some later authorities write; that is a mistake. It is a conditional obligatory positive commandment. An existential positive commandment cannot be neglected. The commandment of fringes can be neglected; there is neglect of a positive commandment. If you walked around with a four-cornered garment and didn’t put fringes on it, you neglected a positive commandment. An existential positive commandment cannot be neglected: if you didn’t do it, nothing happened; if you did it, you have a commandment. Okay, that is called a conditional obligatory positive commandment. It is conditional on something you do. If you wear a four-cornered garment, then the obligation to put fringes on it is imposed on you. Seemingly, the wording of the commandment of confession in Maimonides is also that of a conditional positive commandment: if you repent from your sin, you must confess. But if not, then not. Meaning, you can choose not to repent. But it can’t really be entirely like that. Let’s say confession—if you confess but do not repent, then it isn’t confession. Huh? What are you—if you confess and didn’t repent, then what are you…? Fine, but still there is no obligation. But if I neither confess nor repent, then nothing happened. I didn’t do anything; there is no commandment to repent. It could be that if you repented and didn’t confess, it’s not like if you confessed and didn’t repent—then you say that isn’t confession. Very good, but I’m saying: I didn’t confess and I also didn’t repent. No problem, so everything is fine. Right. So basically the point is that it really cannot be a conditional obligatory positive commandment. That’s what I want to say. Because then it comes out that someone who repented and did not confess—like someone who wore a four-cornered garment and did not put fringes on it—has neglected a positive commandment. So his state is worse than someone who didn’t repent at all. In terms of simple reasoning, that’s not plausible. Okay, therefore in this story there are many stories in the Talmud—Elazar ben Dordaya and so on—where he repented and so on, and there was no confession there. Okay, for that I need another whole analysis, but there isn’t time to get into it here. I argue—this is what I discussed in Petach Tikva—that there are two tracks of repentance. There is practical halakhic repentance with the four stages, with confession and everything, but there is essential repentance that needs nothing. Meaning, no confession, nothing. If you truly changed inwardly, that is repentance that does not need all the legal details of repentance. If you do repentance in the deeper, essential sense. But that is another whole topic; perhaps another time we’ll talk about it. Therefore I’m saying that this is not a conditional obligatory positive commandment; maybe it is more similar to something existential, even though it is phrased like a conditional obligatory positive commandment. It cannot be that someone who repented and did not confess is in a worse state than someone who did not repent at all. But overall, the process—you said there are four stages, and the last is confession. Meaning, you didn’t repent if you didn’t finish by also saying the confession. Right, but if you repented—then the condition is not… but clearly there is some process of repentance here. If you abandoned the sin, regretted it, accepted the future, but didn’t verbalize it, you can’t say that I did nothing. It certainly isn’t worse than someone who didn’t even do that. So therefore this probably still needs to be something like an existential positive commandment and not a conditional obligatory one. Fine, so that’s a comment on Maimonides’ wording in the Book of Commandments, but let’s return to the contradiction. So the Minchat Chinukh essentially asks: is there a positive commandment of repentance or isn’t there? Nachmanides writes explicitly that “ושבת עד ה’ אלוקיך”—“and you shall return to the Lord your God”—is a positive commandment. But Maimonides—one sees clearly that Maimonides holds there is no such commandment. Where do we see that? In chapter 7 of the Laws of Repentance, Maimonides writes: “The Torah has already promised that Israel will ultimately repent, as it says, ‘והיה כי יבואו עליך כל הדברים האלה והשיגוך ושבת עד ה’ אלוקיך’”—“And it shall be, when all these things come upon you and overtake you, and you return to the Lord your God.” So Maimonides understands “ושבת עד ה’ אלוקיך” as a prophecy, not a command. A promise that in the future we will return. Nachmanides reads it as a command: “ושבת עד ה’ אלוקיך”—there is a positive commandment. So you see that according to Maimonides there is no positive commandment. But then the question arises: what happens at the beginning of the Laws of Repentance, where Maimonides does say that there is a commandment to repent and confess? Fine, I don’t know a good answer to that issue. Maybe there is a distinction here between sins of the individual and sins of the collective? Maybe if you have sins of the individual, then you need to repent, but sins of the collective—there are repentances where the High Priest confesses on behalf of… That’s already a question of Yom Kippur versus repentance, but why doesn’t Maimonides bring… why doesn’t Maimonides bring the positive commandment upon the individual to repent? Maimonides doesn’t bring any positive commandment to repent. It seems to me there’s no avoiding explaining it in the following way; it’s the only way I know. In the Book of Commandments, Maimonides prefaces the work with a collection of roots or principles, as I’ve mentioned several times, rules that define, or characterize, what counts as a commandment according to Maimonides. Some of these rules concern the legal status of the commandment. For example, the first principle: rabbinic positive commandments are not included in the count of the commandments; they are not included in the count of the 613. Why not? Because it is not a commandment in the full sense; it is a rabbinic commandment and not a Torah commandment. The second principle deals with commandments derived from exegesis, where Maimonides’ view is also that these are rabbinic positive commandments; we already spoke about that too. Reasons for commandments are not included in the count of the commandments. It says regarding the king: he shall not have many wives, “so that his heart not turn away.” So “that his heart not turn away” is an explanation of why he should not have many wives. “That his heart not turn away” is not counted in the tally of commandments, and so on. So there are roots that explain why certain commandments were not counted because they are not commandments. But there are roots that explain that certain commandments were not counted either because they are included in other commandments. They are commandments, yes, but not separate commandments; they are included—like the four species. So you don’t count four commandments, you count one, because that one includes all four species. And there are roots that say that Maimonides includes in his count only commandments for which there is an actual command in the Torah. For example, in the ninth principle Maimonides writes—at the beginning of the ninth principle, and I think I mentioned this once—that if the Torah repeats the same content several times, you count it only once. For example, the commandment to keep the Sabbath is mentioned twelve times, and Maimonides says: fine, but it is only one positive commandment, because it is the same content. The Torah repeats it perhaps to emphasize its importance, but in the end you count only one positive commandment. In the second part of the ninth principle—it’s a long principle—in the second part Maimonides says that you do not count general prohibitions. For example, “לא תאכלו על הדם”—“you shall not eat over the blood.” From this they derive all sorts of laws: that a court may not eat on the day it decrees a death sentence, not to eat before prayer—Maimonides apparently holds this is a Torah prohibition—and several others, the stubborn and rebellious son, “לא תאכלו על הדם”, and so on. So Maimonides says there too: you count only one commandment and no more. So Yerucham Fishel Perla, in his edition of Saadia Gaon’s Book of Commandments, at the beginning devotes an essay to each of Maimonides’ roots. He checks who agrees with it, who does not agree with it, whether Saadia Gaon agrees with it. In the essay on the ninth root he says there is a contradiction in Maimonides’ words. Because at the start of the ninth root Maimonides says you do not count a commandment that repeats itself several times except once. So that means what determines things is not the command, but the content, right? If there are many commands and one content, we count one commandment. In the second part of the root Maimonides says seemingly the opposite: what determines things is the command, not the content. Because if I have one command that breaks down into several contents—a general prohibition—you count it once, so you see that the command is what determines things, not the content. So how does that fit with what Maimonides says in the first part of the root, where it seems the content determines things—if the same command is repeated several times, if it’s the same content it is counted once. Meaning, the content determines it, not the commands. So there’s a contradiction between the first part and the second part. Fine, I don’t understand that question. It’s obvious that what Maimonides is saying is that you need both things. Meaning, you need unique content and you need a command. In order for a commandment to count, to be included in the tally of the commandments, it needs unique content and it needs a command. What do we see from this? Again: the first part deals with a case where there is a command but the content is lacking. The second part deals with a case where there is content but no separate command for it. Either one of these cannot be counted because you need both requirements. It is separate content; it is not simply repeating the content of another commandment. It has its own content. Okay? So what do we see from this? That according to Maimonides, a commandment that is included in the tally of the commandments is only a commandment that has its own content—meaning that it commands us something—and that has a command, that is, a verse that commands. Meaning, if there is something that we are obligated to do, yes, but there is no command attached to it, then according to Maimonides it cannot enter the tally of commandments, because there is no command. That doesn’t mean we are not obligated, but it won’t enter the tally of commandments. Fine? Now, is there a command for repentance? According to Maimonides, no. Because “ושבת עד ה’ אלוקיך”, Maimonides interprets as prophecy, as a promise, not as a command. So according to Maimonides, even if there is an obligation to repent, since there is no command for it in the Torah, it cannot appear in his tally of commandments. Therefore Maimonides cannot bring a commandment to repent. But in the Mishneh Torah there are laws of Hanukkah and Purim in the Mishneh Torah. In the Mishneh Torah all the laws are included. Everything that must be done appears in the Mishneh Torah. That is his whole purpose: to put all Jewish law into one book. We discussed once how it is the only halakhic codex in history, the Mishneh Torah. So Maimonides basically includes in the Mishneh Torah also rabbinic commandments, rabbinic laws, right? Everything. Meaning, everything one is obligated to do has its place in the Mishneh Torah. So in the Mishneh Torah, Maimonides writes that there is a commandment to repent. Why? Because of course there is an obligation to repent. In the tally of commandments it will not appear because there is no command for it. But if there is an obligation—there is content to that obligation—but no command for it, then it cannot be defined as one of the 613. What? Is it rabbinic? No, absolutely not. It is simply not a commandment enumerated in the tally of commandments. There are Torah obligations that are not counted. A partial measure. In Yoma there is a dispute between Rabbi Yohanan and Resh Lakish about a partial measure; in practice we rule that it is Torah-level like Rabbi Yohanan. There is no commandment for a partial measure, no prohibition for a partial measure; it does not appear in the tally of commandments. But that explains the placement of the Laws of Repentance at the end of the Book of Knowledge. Because Maimonides’ method is to place Torah commandments first at the head of each book, and only at the end to bring rabbinic commandments like Hanukkah at the end of the Book of Times. Maybe… Yes, I’m just not entirely sure that it is really correct to define this as a rabbinic commandment. It is a Torah obligation without a command. I don’t know; I’ll get to that. But it may still be that it is less than a commandment with an explicit command, and therefore it’s at the end. And the fact that he puts it there in the Book of Knowledge is because the Book of Knowledge is about the foundations and outlook of Torah. Yes, but I think there are several good explanations for that. Meaning, when you look at the Book of Knowledge in general, I think the Laws of Repentance definitely belong there and nowhere else. Yes, but in every section Maimonides begins with what commandments are included there. And in every section there is a commandment. Right. Since regarding the tally of commandments, my claim is no. I’m claiming no. It isn’t the tally of commandments but a summary of the chapters. Obviously, because at the beginning of the sections there is identity. But here there isn’t identity. So if you ask me what the commandment is in a formal sense, look in the Book of Commandments; there you will not find the commandment of repentance. There he doesn’t say there is a commandment? Why, of course he does. A commandment—of Hanukkah and Purim—of course he says so. Rabbinic positive commandments of Hanukkah and Purim, fine? Okay. Now he brings everything—that’s exactly the point. And here too, a positive commandment to repent and confess; he won’t say rabbinic because it isn’t rabbinic. So there is—one has to do it—but there is no command for it, so in the Book of Commandments it cannot appear. Understand: when something does not appear in the Book of Commandments, that does not mean there is no obligation to do it, and not even that there is no Torah obligation to do it. But if there is no command for it, it will not appear there. How can there be a Torah obligation without a command? We already talked about this, but I’ll remark on it again. So therefore it seems to me that really the necessary solution, according to Maimonides, to this contradiction is that there is an obligation to repent, probably even a Torah obligation. A Torah obligation—but since there is no command for it, it cannot appear in the tally of commandments as a separate commandment. And therefore in the Mishneh Torah, where Maimonides brings everything that must be done, he also brings the obligation to repent. In the Book of Commandments, where he brings only the commandments according to his definition, he does not bring the commandment of repentance there. So in the end Maimonides too agrees that there is an obligation to repent, even if he does not present it as a commandment in the formal sense. There is an obligation—even apparently a Torah obligation—to repent. That seems to me the likely reasoning. Meshekh Chokhmah—this is what I noted earlier—says, aside from the simple side of repentance, after all we are in the middle of the book of Deuteronomy, and basically the whole book of Deuteronomy is “Return, O children,” and “What does the Lord your God ask of you,” and so on—the whole book is more or less a call to repent. Calls are not commandments. Calls are not commandments. It can be a command, but it is still an obligation… No, that’s why I’m saying the obligation is written there explicitly. No, it is not written as a command; it is written as… I once mentioned Rashi’s first comment on the Torah, where Rabbi Yitzhak said: why did the Torah begin with Genesis? Why did it begin with Genesis and not with “החודש הזה לכם ראש חודשים”—“This month shall be for you the beginning of months”? So they give various answers there. I ask a question: notice what is in the question. The question says that the entire book of Genesis and the first two-and-a-half portions of Exodus are basically unnecessary. Why? Because they contain no commandments. What, we don’t learn anything from them? Even before Rashi’s answers about “He declared to His people the power of His deeds,” isn’t the question that we learn nothing from them? Of course we do learn from them, right? From what the Patriarchs did, we learn many things. So what is the problem? Why are they unnecessary? Because they are not commandments. Meaning, the fact that we learn something from some passage still does not mean it is a commandment. A command is not the same thing as an expectation. The Holy One, blessed be He, expects many things of us. And when the Holy One, blessed be He, commands us, that is what is called Jewish law. Jewish law is the command. Beyond that there are many things that the Holy One expects from us, some of them written, some perhaps not even written. But commandments, they are not. “And you shall do what is right and good”—that is even written in the language of a command, and almost no one counts it in the tally of commandments. Not a commandment—not that it is not a commandment at all; it is not a commandment. Not a commandment because we are not commanded. Because we are not commanded. No, it is not a substantive commandment. We are not commanded. There is an obligation because there is an expectation from the Holy One that we do it, but there is no command. Meaning there is no commandment among the 613, in the tally of the commandments, but that does not mean it isn’t a commandment. No, it means there is no commandment, because commandment comes from command. If there is no command, then it is not a commandment. There is an obligation, there is an expectation of the Holy One, but not a command. But if you have, say, a traffic law example—you’re allowed to drive 50 kilometers per hour in the city, but there is an expectation that if there is a kindergarten or people in the street… No, that is even law. What? That’s the general duty of care. It’s even law. No, but before the law established a general duty of care, it was still obvious that everyone is expected to drive with the required caution, even if the signs do not prohibit some specific thing. But if there is a commandment to confess, isn’t that a result of there also being an obligation? It’s a kind of… part of the commandment… It’s only confession, not repentance. But you can’t confess without repenting; otherwise you’re just mouthing empty words… But that’s what I’m saying: it’s an existential commandment. Don’t confess and don’t repent—nothing happened. But if there is a commandment to confess… There is no commandment; it is a conditional commandment. If you repent, do it in the form of confession, and if not, then not. If you drive a car… Do you incur positive punishment? There is reward and punishment in the heavenly court, I assume, but not in an earthly court. In an earthly court it’s commandments and transgressions. Criminal violations. Yes, but matters between one person and another… there is providence from heaven. I don’t know—the Holy One expects us to be human beings, not only to perform commandments. So I assume there is reward and punishment for that. So is there a difference in reward and punishment between commandments and these things? I don’t know. What happens when there is a clash? “Turn from evil and do good”—if you treat that as a command, then a positive commandment overrides a prohibition, so that won’t be so. In a place where this isn’t a commandment, it won’t override a prohibition. Because in order to override a prohibition you need a command. There are halakhic implications if something is defined as a commandment or not defined as a commandment. And also the whole matter of the 613 itself—that the tally of the 613 is something original; it isn’t necessary. Fine, Nachmanides hesitates about this at the beginning of the Book of Commandments, and in the end Nachmanides says: but we have a tradition, and apparently it is indeed 613. He hesitates whether to take this aggadic statement and build the whole structure on it. The Tashbetz hesitates about it, the Radbaz, all of them—Nachmanides and Maimonides and all those who counted the commandments—all agreed… Right, they all agree there is a tally, there are 613, and they don’t know what they are. And that’s the whole issue. When there is a dispute in Jewish law, then what? There is a dispute over what counts as selecting, say. So now the question is—what this thing essentially says is that even according to Maimonides there is an obligation to repent, or an expectation from the Holy One that we repent, even if it does not emerge from a command, even if it is not formally defined as a commandment. Then the question arises: what is this thing? Meshekh Chokhmah comments there on the verses in Deuteronomy that in fact there is no logic in commanding repentance. Why? What does it mean to command repentance? To abandon the sin and not continue sinning—that is already written in the commandments themselves. Maimonides, in the fourth principle, when he speaks about commands that encompass the entire Torah, like “You shall keep all My commandments,” says that these commands are not counted. Why are they not counted? Because when the commandments were stated, they already tell us to do them. So what else is written there? Why do I need a command telling me to keep the commandments? The commandments must be kept by virtue of the fact that they are commandments. Now Meshekh Chokhmah says the same thing about the commandment of repentance. What is there to command about repentance? Abandoning the sin—precisely because it is defined as a sin, you need to abandon it or not do it in the future. So there is nothing to command regarding repentance. Therefore he says all there is to command is confession. Because they tell you that when you repent, do it in the form of speech. That I could not derive from reasoning alone. By reasoning alone I could have said that it is enough to abandon the sin and not sin further, and that’s all. So the commandment—the only part of the repentance process that makes sense to command—is the process of confession. One could perhaps discuss regret a bit. Right, because regarding regret too, what does it mean to regret? One needs not to sin, to abandon that sin and not sin further, and that’s all. Why regret? Why do I need to regret what happened? So maybe that is already part of confession; confession expresses regret. But that is what Meshekh Chokhmah wants to argue. But again, what is Meshekh Chokhmah assuming? That’s why I said we needed to get here. What is Meshekh Chokhmah essentially assuming? He assumes that the essence of repentance is to abandon the sin. In other words, the completely righteous person is certainly preferable to the penitent. Right? Because Meshekh Chokhmah is basically claiming that there is nothing in repentance beyond simply not sinning. If there were significance to the process of repentance, as I said before—that the process itself has value, not only the product, not only the fact that I don’t sin, but the process of return itself has value—then obviously there would be a point in commanding repentance. Obviously there is significance to the obligation of repentance, because otherwise I would say: I just need not to sin, that’s all. What does it mean to repent? To repent means that there is also a point in returning—for example, regretting, okay? And maybe confession too is part of this. Later it may be that what we said, that the penitent is greater than the righteous person, is because of the understanding he has there. Maybe because he corrected the sin and now returned, on the level of his understanding he is on a higher level than the righteous person. But not that the process itself is something that is itself a commandment or something like that. But I think that’s not—not—not to say something else. It means—so what is the process? That understanding is the result of the fact that I underwent a process of repentance. It is a result, but… but there is no commandment to do that. Ah, so here you’re saying that within conceptions of process as the essence of repentance, you can still discuss whether the process is a value in itself or whether the process leads to some result—and not the result that I am a completely righteous person, but some result of undergoing the process. Fine. So only within that can you define the question whether this is consequentialist or whether the process itself matters. I’m willing to accept this definition or that one. Isn’t it simple that repentance is some essential change within the person—not that I am still wicked but decided not to commit these sins, but without any essential change? Yes, but even if you make an essential change, is what matters the state I arrive at—that now I am already a different person—or what matters is that I underwent the process of change? Okay, Maimonides even in the second part says, “I am no longer the same person,” and so on and so on. Yes, but “I am no longer the same person” could just mean: forgive me for what was, because I’m no longer like that one, I’m already someone else. Still, I come before the Holy One as a completely righteous person, not as a penitent, and tell Him: leave aside what I once was, that no longer exists, and now I present before Him what I am now. There, in Maimonides, it does not necessarily say that there is value in the process, I think. Say there is a process. What? And isn’t the righteous person also always in an ongoing process all the time? No. The righteous person does not undergo a process of repentance. He undergoes other processes, but not a process of repentance. Okay, a process of something else, a process of… Yes. I already said that in terms of effort—when people say the penitent makes more effort—I don’t think that is correct. The completely righteous person can certainly involve a great deal of effort. What Maimonides says in his commentary—there is an enormous difference between a “penitent,” in quotation marks, as we call him—really someone who was very far away—and someone who wasn’t involved, and someone who needs… he is usually an ordinary person, but he committed a sin; he sinned. So between the two cases we are talking about, and the expression in this and in that, these are two cases of someone who… Okay, so someone sinned in a particular matter, in a certain area, but was not completely far away. Why does that matter to us? I didn’t understand you. Why does that matter to us? Before anything else, because all the discussion here is about process and what the difference is between… within one commandment there is a process; with one transgression too there is a process; I change the state. There are totally different states. Fine, but in that same case where they said the penitent is preferable to the completely righteous person, whatever you decide—whichever case you decide—what did they say there? They said there is value to the process of repentance and not only to its product. I don’t care what it’s about, which of the cases it was said about, whether it’s about coping or some abstract direction one ought to take. I’ll bring perhaps another example of this issue, because that’s where the penny dropped for me. In a completely different tractate, though somewhat related to one of the earlier series we discussed—the series on conceptual Talmudic analysis; I don’t remember if I mentioned it there. There is a question among later authorities how to define the concept of giving a bill of divorce. When the Torah says, “וכתב לה ספר כריתות ונתן בידה”—“and he shall write for her a bill of severance and place it in her hand.” They try to characterize what it means to give a bill of divorce. The Ketzot begins some attempt to make clarifications of this sort, but doesn’t really reach conclusions. In Kehillot Yaakov there are almost three very long sections trying to define it. And the basis of the matter is that there are dozens upon dozens of cases in the Talmud trying to illustrate valid giving and invalid giving. He wrote her a bill of divorce and placed it in her courtyard and transferred ownership of the courtyard to her. He wrote her a bill of divorce and put it in her courtyard; “placed it in her hand” is enough there. A bill of divorce in her hand while a cord is in his hand—some kind of thread by which he is still holding the bill. Strange cases. It is so striking—and this is very rare in the Talmud, by the way. The number of cases the Talmud brings in order to illustrate what counts as a valid giving and what counts as an invalid giving, or of giving—some of them about severance, if this is severance… severance too is also a feature of giving the bill of divorce: whether there is severance in it or not. I’m not talking about a condition… not severance in the sense of an eternal condition. One defines what severance is and one defines what giving is; these are two concepts. No, even in the concept of severance there are two things. There is severance like, “on condition that you never go to your father’s house again”—that is an eternal condition; I’m not talking about that; that is a question of severance. But there is severance because the giving itself must be a severing giving. For example, a bill of divorce in her hand while a cord remains in his hand—that is a problem of severance according to a certain dispute between Maimonides and Rashba, if I remember correctly. But it is a problem of severance not in the sense of “on condition that you never go to your father’s house again,” where she is still bound to him in the substantive sense, but in the sense that there is a deficiency in the act—you did not transfer it to her. That is a different concept of severance. So there are dozens upon dozens of cases there trying to define what a valid giving of a bill of divorce is. And already from the Talmud itself you can see the difficulty arise: why doesn’t it just give us the definition? Why illustrate in a hundred thousand cases something instead of simply saying… just say what the definition is. And indeed the later authorities try to do the Talmud’s work in its place: to take the cases and try to infer from them what the definition is. The Ketzot begins with two extreme cases. He says, for example: if he wrote it on something from which no benefit may be derived, it is valid. He gives her a bill of divorce written on something from which no benefit may be derived. Now the problem—the Ketzot says this is a dispute among the early authorities—but according to some of the early authorities there is no ownership over things from which no benefit may be derived. If there is no ownership over such things, then how can it be that when I give her the bill of divorce this is called a valid giving? This bill was not mine before, and after the giving it does not become hers either, because there is no ownership over things from which no benefit may be derived. So from here, says the Ketzot, we see that giving a bill of divorce is not an act of transfer of ownership, right? It cannot be that it is a transfer of ownership, at least according to the early authorities who say there is no ownership in things from which no benefit may be derived. On the other hand, it is not necessarily physical delivery either. Why? I put the bill of divorce in my courtyard and transferred the courtyard to her. The bill stayed there; it was there and remained there. When I put the bill in my courtyard, that was not a giving—I put it in my courtyard. Right? Now I go to the woman, and I give her a deed transferring ownership of my courtyard. This is a valid giving of a bill of divorce. This is pure transfer of ownership. There is no physical delivery here at all. And that’s okay. So the Ketzot says: I don’t understand—is transfer of ownership the giving of a bill of divorce, or is physical transfer of the bill the giving of a bill of divorce? It’s neither this nor that. So what is it then? Fine, he gets a bit stuck there, the Ketzot. Kehillot Yaakov continues and tries to suggest a more complex definition, and then for every definition he offers he brings a counterexample, because there are dozens upon dozens of examples in the Talmud and several chapters in Gittin. And each one rules out another definition. In the end it is very interesting—in the end he is left with a definition where, it seems to me, the number of qualifications to it is more or less the number of cases. Usually when you want to give a good definition, you want to give one simple definition that covers all the cases. But Kehillot Yaakov, in the end, when he succeeds in reaching some definition that answers all the cases or fits all the cases, comes out with a definition so complicated that we gain nothing from the process of defining. In the end it is no less complicated than simply giving me all the cases. And that is exactly why the Talmud didn’t give a definition. The reason the Talmud didn’t give a definition is that it felt it was impossible to give a simple definition; it is more correct to illustrate it. We once spoke about working by rules and casuistry in legal conceptions. And here this is a very nice example of the Talmud preferring cases—a casuistic approach, as jurists call it—and not a positivist approach, meaning from the rules to the particulars. What is the meaning of this difficulty? Why is it really so hard to define giving a bill of divorce? That is what bothered me—one of the first articles I wrote. I think what is hard to define there is that every attempt to define the act of giving a bill of divorce is really made through states. What was the state before the giving and what is the state after it. Suppose giving a bill of divorce is a transfer of ownership. Transfer of ownership means it was mine before and I transferred it to be hers. Physical delivery—the bill was in my hand and afterward it is in her hand. But if the giving of the bill of divorce that the Torah requires is a process, then it is not defined through a state, through moving from state A to state B, but through the transition itself. Then it is very hard to define such a thing. Meaning, how do I define a process? We always define processes through end states. What was before and what will be after. But when I want to define the process itself, we have no way to do that. I’ll explain it more later, but we have no way to do that. And since that is so, what the Talmud does is give lots of examples, because through the examples we can build within ourselves some idea of what the process is supposed to look like. Giving is an action, it is a process. And once giving a bill of divorce is essentially defined as a process and not as a state of before and after, then we have no good way to define it. Therefore we have no choice but to use examples. And this brings me to the next part of the lecture. It’s a somewhat philosophical, or scientific, mathematical section. I want to define this difficulty a bit more clearly. I’ll start maybe with—I mean, just to put this in context again: for me, giving a bill of divorce is a kind of process that the Torah requires, just as repentance, as we saw earlier, is some kind of process that the Torah expects of me—perhaps not commands, but expects me to undergo. And I’ll try to understand the significance of a process, as distinct from a state—getting from state A to state B—what is there in the process beyond that. Okay? There is a well-known paradox, one of Zeno’s paradoxes. Zeno was a Greek philosopher from Elea who reflected on the concept of motion. He presented various paradoxes arising from the assumption that there is motion in the world. Let’s see how this connects to us. One of the paradoxes is Achilles and the tortoise: Achilles never catches the tortoise. You probably know it. If Achilles runs ten times faster than the tortoise, then he gives the tortoise a head start of ten meters in the race. Okay? By the time Achilles closes those ten meters, the tortoise has already moved another meter. Right? By the time Achilles closes that meter, the tortoise moves another ten centimeters. By the time Achilles reaches those ten centimeters, the tortoise moves another centimeter, and so on. In short, Achilles never catches the tortoise. Okay? So that is one reflection on the concept of motion. In the end it is just a geometric series, convergence of a geometric series. There is only a little mathematics needed for this. But there are more complicated paradoxes, and they too were linked to mathematics, and I think wrongly. One of them is the paradox of the flying arrow. Zeno presented the following paradox. Suppose we shoot an arrow. At every moment when we look at the arrow, the arrow is either standing in a different place. Look for one second, or one moment: it is standing here. A moment later, look—it is standing here. Another moment later, it is standing here. So when does it move? At every moment it is standing somewhere else, so when does it pass between the places? That was Zeno’s question. There are various formulations that are not necessarily equivalent to one another, by the way, but I won’t get into philosophical niceties here. Broadly speaking, that is the paradox. Now this too—the standard solutions, there is an article by Russell on this and several other classic articles on this paradox—in my view, none of them solve it. They tie it to infinitesimal calculus. The idea is that the continuum—when you look at space, say, or at time—this is some kind of continuum. You cannot describe a continuum as a collection of points alone. A collection of points has to satisfy all sorts of conditions. And this perspective is actually treating discrete points on the continuum. It ignores the relation between those points needed for them to constitute a continuum. Not every set of points constitutes a continuum. And therefore you have to move to infinitesimals, which means that we look at the basic unit of the line as an infinitesimal, a differential—it is not a point. Mathematicians cringe when I say things like this, but there are even descriptions by mathematicians who build it this way, like Leibniz and not like Newton. Leibniz built calculus on the basis of infinitesimals, unlike Newton. Leibniz worked like a physicist and Newton worked like a mathematician. In any case, I think this is not right. It is not right because—it is true, but it doesn’t solve the problem. It doesn’t solve the problem because it’s an English-English dictionary. An English-English dictionary takes one word I don’t understand and explains it with ten others I understand even less. So here too: when you take a phenomenon I don’t understand and explain it with something else I also don’t understand, what have you done? You haven’t given me an explanation; you only showed me that it is analogous to infinitesimals. Okay, so now I ask that question about infinitesimals. What happens in infinitesimals? How do you move from one point to another? What is this differential? The differential too is defined from points. I can ask the same questions there. The fact that one can define this mathematical theory called differential calculus in a contradiction-free way does not mean there is no problem. It only means that in that language they managed to avoid it. Like in the introduction to—there is a book by Bertrand Russell and Whitehead, Principia Mathematica. Three thick volumes, and I don’t know whether anyone ever read them. Aside from Russell and Whitehead maybe nobody ever read them, it seems to me. But I at least managed to get through the introduction, and beyond that I leafed through it—it was awful. And in the introduction there they bring what is called the theory of types. There are paradoxes of self-reference—like the liar paradox, for example. That paradox, which I think we discussed once, arises from self-reference, from something referring to itself. Okay? Or all sorts of other paradoxes. The barber who shaves all the people who do not shave themselves. A set that contains itself as an element. All sorts of paradoxes of self-reference. There he offers a solution. What is the solution? He says there is a hierarchy of statements, a hierarchy of statements built from different types, and each type can refer only to statements that belong to a lower type in the hierarchy. And then, of course, no statement can refer to itself. Wonderful. This is of course somewhat ad hoc, but let’s say for present purposes that’s the gist. Excellent—did that solve the problem? Obviously not. It simply forbade us to express it. Those are Stalin’s solutions to problems. Meaning, if you have a problem they cut off your head and then there’s no problem. Meaning, you haven’t solved the problem. You’ve simply forbidden, in your language, the saying of the sentences that create the problem. That is not a solution. Right? So in mathematics too, suppose they managed to formulate infinitesimals coherently. That only means they built a language in which the problem does not appear. It will be impossible to formulate the problem, and that doesn’t solve it. Now, what is the solution to the problem? Not how to build a language in which it cannot even be said. And here things get a bit stuck. Analytic philosophers? Russell didn’t do this for nothing; he was an analytic philosopher. Analytic philosophers claim that any problem a language manages to avoid is not a real problem; it is an artifact of language. That is the assumption of analytic philosophy, and in my opinion it too is a mistaken assumption, but that is another topic. So I’ll tell you why this is—perhaps before that, one solution suggested for this issue was infinitesimals. A second solution—I don’t even remember whether I saw it somewhere or thought of it myself, but it seems to me a natural solution—comes from the uncertainty principle. According to the uncertainty principle in quantum physics, you cannot know—or according to other formulations, a body does not have—velocity and position at the same time. Right? If a body is located in a fully defined place, then it has no velocity. If the velocity is fully defined, then it has no position. It cannot be that you know a body’s velocity and position at the same moment. Right? Now you understand that within that context, it is impossible to formulate the paradox of the arrow in flight. Because we are essentially saying that at every moment the arrow is in a different place and has a defined velocity. We are speaking of an arrow moving at a given velocity, okay? So it has—it cannot be that it has no position. Meaning, if it has a defined velocity, it has no position. So you can’t look at the arrow in this place and the arrow in that place—it simply can’t be done. Yes, but the point is that if you know the velocity or the position—Heisenberg, right?—you have to know the minimum that you can say. No, you’re speaking about exact position. There is no h-bar, nothing. Meaning, if you have exact position, there is no velocity. The uncertainty is infinite. Okay, but you’re talking here about something the size of an arrow. We aren’t talking about a point particle. Let’s talk about a point-arrow. You know how physicists, when they begin dealing with a donkey, they begin with a point-donkey. Let’s first understand how a point-donkey works, and then we’ll speak about a real donkey. Okay, so the solution to the flying arrow according to the uncertainty principle is of course also an English-English dictionary solution, right? You take a phenomenon I don’t understand and use it to explain something else I don’t understand. Okay, now I don’t understand the uncertainty principle either, so in what sense can this be considered an explanation of the arrow problem? Therefore I say: these things are not really solutions. Maybe one should think about it the other way around. Actually, that connection was interesting, and in the article I wrote I went the other way. I tried to explain the paradox of the arrow in flight, and then I returned to the uncertainty principle and explained the uncertainty principle through the arrow, not the arrow through the uncertainty principle. The claim was basically this. When I look at—I’ll maybe give the bottom line right away and then explain. The bottom line is that there is something imprecise in the wording of the paradox. No—again, this is not an analytic solution; it is a real one. What I am essentially saying is: when I look at an arrow flying, at every moment it is in a different place. Now the question is when it moves from place to place. It is not correct to say that at every moment it is standing in a different place. At every moment it is located in a different place. Standing and being located are not the same thing. Standing means being there at zero velocity. Okay? And it does not have zero velocity; it has velocity. So at every moment it is located in a different place. Okay, what confuses people? What confuses people is that they think the concept of velocity cannot exist at a point. What is velocity? How do we define velocity? The definition of velocity is: it was in this place at this time and in that place at that time. Difference in places divided by difference in times—that is velocity. And if you want infinitesimals, then say the velocity is not constant, so you take points very, very close together—as close as you want—in the limit. But it is still difference in place divided by difference in time, difference in place divided by difference in—velocity divided by difference in time. That is what is called velocity, right? That is the derivative. And therefore people think velocity at a point is a fiction. Because one needs to understand: after I differentiate the position function—suppose there is a moving body, and the place of the body looks like something times t-squared, a times t-squared, say; that’s constant acceleration. So basically the velocity is something times t. Okay? That means that for every t we take, we substitute it and find the velocity. There is velocity at a point, at a point in time. Every point in time has a velocity, and a different velocity. It isn’t an interval of time; it’s a point. How do people usually treat this? Usually they say it is only a fiction. Really, velocity exists only over an interval of time. But I say: it is the interval around that point, an arbitrarily small interval around that point. The efficient way to speak about it is to speak of velocity at a point. But that is supposedly only a fiction. There is no velocity at a point. Velocity is always over an interval. Why? Because that is the conception of velocity as a quantity arising from differences. Difference in place divided by difference in time. And I claim that is not correct. I claim there is velocity at a point in time, and the fiction is actually the infinitesimal method. Meaning, the way to calculate velocity is to go to some interval around the point, see what distance the body traveled in that time interval divided by how long it took, divide them, and thus calculate the velocity. If there is a limit as I make the interval smaller and smaller and smaller, that means I reached the velocity at the point through that calculation. But the fact that to calculate the velocity I need to look at an interval does not mean there is no velocity at a point. There is velocity at a point, but in order to calculate it I need an interval. Why? Because calculating velocity from place is a differential calculation; it is difference in place divided by difference in time. What do I actually want to claim? That one must distinguish between the operational definition of velocity—how you calculate it—and the essential definition of velocity. Here, let’s take as an example a little physics and math, but you don’t need to understand the details, only the principle. There is what is called the Doppler effect. The Doppler effect—that’s what the police radar guns work on. They send a beam at the car, the beam returns at a slightly different frequency. The frequency of the wave is slightly different; the difference in frequencies is proportional to the speed of the car. That’s how the wicked police are helped by the Doppler effect. Now think about this: this is, conceptually, completely different from ordinary speed measurement, apparently. In fact it isn’t, but apparently it is. It is a completely different concept from ordinary speed measurement, because the wave strikes the velocity at a point in time, and that changes the frequency of the wave, and through the differences in frequency I know the velocity of the body. So this is a way to measure velocity without needing an interval, but at a point. I measure the speed of the car at a point in time— theoretically. In the practical world it always takes some time, but in principle this is a measurement at a point in time. That is an indication that the concept of velocity at a point in time or at a point in space is well-defined. The fact that in order to calculate it we need to go to an interval around that point is due to our limitation. We don’t know how to calculate it directly; we have to calculate it through differences. So basically—I’ll formulate it a bit differently—velocity is basically something different from change of place. Velocity and change of place are not the same thing. Change of place is an expression of the fact that a body has velocity. They are not identical. It is not that change of place is the velocity; rather it is a consequence. If a body has velocity, then if we wait a bit, we will see that it changes place. But velocity is not change of place; change of place is an indication that the body has velocity. Velocity is its potential to change place. It is not the actual change of place itself. Therefore in principle a body can have velocity and not change place. A body—again, physicists, I apologize—I throw a body at a wall, okay? It hits the wall and stops there. What is its velocity at the point where it hits the wall? Every physicist will tell you: zero. Meaning, a moment before it had velocity, at this point in time it had velocity from one side, but from the other side it has no velocity because it stops in the middle. There is some point here, yes, it is a closed interval. So it has no neighbor from this side, but it has a sort of neighbor from that side, if one may speak of a neighbor. How should one deal with this? We don’t know how to deal with this in infinitesimals; it doesn’t work. The velocity of the body when it hits the wall is zero—so every physicist will tell you. And I tell you that is not correct. The velocity of the body at the moment it hits the wall is the velocity it had the moment before, but that velocity is not translated into change of place, because the wall does not allow that potential to pass from potentiality to actuality. So it will become heat, it will bend the wall, it will send the ball back, depending on whether the collision is elastic or plastic or whatever. But what this really means is that the body has velocity and there is something that does not let that potential emerge into actuality in the form of a change of place. So here we have a case where a body has velocity and no change of place results from it. Okay? Now, again, physicists do not know how to handle such a thing, because we work with infinitesimals. Velocity means difference in place divided by difference in time. So you have to say the velocity is zero at the wall point because it doesn’t move. In the operational definition, the velocity is zero; in the essential definition, the velocity is eight. I’m giving this as an example—again, what I’m doing here is not mathematically careful—but I’m trying to illustrate the idea. And the idea is really that one must distinguish between the question whether a body has velocity and the question whether it changes place. Now I return to the arrow paradox. From here I don’t know whether I should stop or continue, but anyway: with the arrow too, this is exactly the point. At every single moment the arrow has velocity. At every moment as such, yes? At a point in time. It does not change place, because you can’t change place at a point in time or at a point in space. What does it mean to change place at a point in space? If you are here, then you are here. You are not elsewhere. Right? So Zeno is right when he says that at every moment the body is in a different place. But he is not right when he says that at every moment the body is standing in a different place. You ask me when it moves from place to place? When it is located, it is also moving. It has velocity. It is in a certain place and at the same time also has velocity. True, you will not be able to see change of place at a point in time, because change of place is already the actuality. Velocity is the potential, the potential for a change of place to be produced. So if you do not wait, you will not see that a change of place has been produced. But really there is here a certain point of potential for change of place that is present—it exists—even at a point in time. And therefore I think this is the solution, and there is no need to get to infinitesimals. On the contrary, this also explains infinitesimals, or infinitesimals explain this. Now, I’ll get to the uncertainty principle later, but the point I really want to make is this: why are we so confused around problematic dynamic points of this kind? Because when we look at the world, we look at it through the lenses of a camera. A camera—when we make, say, a film—how is a movie camera built? You make a film by taking pictures very densely packed in time and projecting them in sequence, right? And it appears to us that something is moving there. Nothing is moving there. That is only our illusion. They show us one picture and then another picture a moment later and another picture another moment later, and if the density is high enough, then it looks to us as though there is a dynamic process here. But we build it out of states. You see the relation between processes and states? We build the process out of the states. Why? Why does it really work like that? Why don’t they make a camera that directly captures the motion? Because our cognition is built in a static way. When we look, we see the state. We do not see the process. We can see that there is a process in the background if we see a different state. If we see a different state, we will understand—not see, understand—that there is a process in the background. We have no way of seeing processes. We cannot grasp processes. Process, for us, is an abstraction. But that is only for us. It does not mean there are no processes in the world. It means we are built in such a way that we perceive the world like a camera. Therefore even when we create a film, we create it by means of a camera—snapshots at high speed, lots of snapshots at high speed. But imagine theoretically that some alien came along built differently from us, orthogonal to us altogether. Meaning, it is built like a movie camera. It sees processes. Meaning, when it looks at a body, it sees only velocity; it does not see the body’s place at all. It sees only that it has velocity. That’s what it sees. It sees, it grasps in some way that the body has velocity. This alien has no eyes; it has something else. I don’t know what. It has a Doppler camera. Meaning, it sees only velocity. It does not see the change of place. Okay? Then what will it do? In its calculus, of course, the integral will be the basic operation. Then it will go from velocity to place, not from place to velocity. Meaning, integral as opposed to derivative. It doesn’t matter; that’s just a side comment. The point is that its cognition is built opposite to ours. And such a creature could in principle exist. At least theoretically. And such a creature would see velocities, not positions. Position for it would be the result of a calculation. A fiction. What are positions? It doesn’t know what positions are. There are velocities. Now, you understand, if there is such a creature, the fact that we are built in a certain way does not mean that that is really the true picture. Now, when someone comes to explain a process to me, I, being a static creature, a creature with static perception, camera-like perception—it is impossible to explain to me what a process is. Impossible to explain. What can be explained to me are states. The state was here and afterward here and afterward here. I understand that behind this there is a process. A process of intellectual abstraction. I understand that behind this there is a process. But in principle, if my cognition were built differently, then one could directly tell me what giving a bill of divorce is or what repentance is. I wouldn’t even understand what a completely righteous person is. The alien does not understand what a completely righteous person is. It understands what a penitent is. A penitent is someone moving forward; he has the potential for progress. A completely righteous person is the integral of a penitent. It doesn’t understand what that is. Therefore there is a problem in explanation, and therefore giving a bill of divorce requires many examples. Because we look at it through static lenses. It is impossible to explain what giving is. You can give us all kinds of definitions, and from that we will build some construction in our minds that understands what giving is. But there is such a thing as giving. The fact that we do not manage to understand it does not mean it is a fiction. It only means that our way of understanding it is through very many examples. Fine, I still…