A Look at Torah and Torah Study – Lesson 12 – Rabbi Michael Abraham

Table of Contents

• From Deism to Theism, Probability, and Tradition
• A Philosophical Starting Point and the Obama Analogy
• David Hume, the Witness Argument, and a Critique of the Kuzari
• Persuasion, Assumptions, Rhetoric, and Demagoguery
• Tolerance, Pluralism, and the Question of “Brainwashing”
• Analytical Learning, Giving a Get, and Explanatory Power
• Neural Networks, a “Torah Mind,” and Carving by Removal
• Intuition in Halakhic Rulings and the Arrow-and-Target
• Negative Attributes, Maimonides, and Euthyphro
• Negative Attributes as Carving by Removal and Projection onto Our Concepts
• Dynamic Actions, Zeno, and Velocity at a Point
• A Critique of Ad Hoc “Solutions” and a Comparison to Russell
• Dynamics versus Statics, Film, and Human Senses
• Back to Giving a Get: The Difficulty of Defining an Action

Summary

General Overview

The lecturer presents abduction as a tool of everyday explanation and defends the legitimacy of using it in relation to faith as well, while distinguishing between philosophical proofs that lead to deism and the possibility of moving from there to theism through a change in one’s starting point regarding probability. He argues that one’s attitude toward testimony about revelation, miracles, and tradition depends on whether the existence of a transcendent being has already been accepted as something reasonable, and he criticizes rationalism/scientism that narrows the discussion in advance to only what science allows. From there he moves to a broader methodological question about persuasion, rhetoric, and demagoguery, and then returns to analytical study in Jewish law through the topic of giving a get, proposing a model of “carving by removal” and neural-network-like training to explain how halakhic intuition is formed in a way that cannot be put into an economical formulation. Finally, he uses Zeno’s arrow paradox, velocity, and the way we perceive dynamics to explain why dynamic actions like “giving” are hard to define, and connects this also to understanding Maimonides’ doctrine of negative attributes as a kind of carving by removal that produces understanding without positive formulation.

From Deism to Theism, Probability, and Tradition

The lecturer says that the physico-theological proof in the Kantian sense leads only to deism, but maintains that the deistic and theistic questions are not independent of one another. He uses Bertrand Russell’s celestial teapot example to argue that in the absence of a reason, it is not even “fifty-fifty” but rather zero justification for the assumption, and adds that “to arouse doubt you need a reason,” as also appears in Jewish law. He cites the Talmud in tractate Shabbat 30 about someone who claims before Rabbi, “Your mother is my wife and you are my son,” and quotes Rabbi Kook in Ein Ayah, who explains that casting doubt requires some basis, some concrete grounds, a monetary uncertainty with substance, and similar halakhic expressions.

A Philosophical Starting Point and the Obama Analogy

The lecturer argues that if one first arrives at the philosophical conclusion that there is a transcendent being who created the world, then a claim about revelation at Mount Sinai is no longer a “celestial teapot,” and cannot simply be dismissed out of hand, even though one may still accept it or reject it and discuss tradition and credibility. He illustrates this with an analogy about a Black president in the United States: before such knowledge, the claim sounds absurd, but once you’ve “crossed the Rubicon” of the very possibility, additional details like “Barack Obama” and “Obamacare” become reasonable subjects for discussion. He says that in historical questions that are not settled in a logical-mathematical way, the conclusion depends on what seems plausible in advance, and therefore arguments about Mount Sinai, tradition, and miracles rest to a large extent on one’s starting point.

David Hume, the Witness Argument, and a Critique of the Kuzari

The lecturer connects the discussion to David Hume’s witness argument and its popularity among atheists in the twentieth century, describing it as cries of triumph on Wikipedia and the claim that “Hume destroyed faith.” He says that Hume’s argument is built on the assumption that a miracle is a priori improbable, and therefore testimony about it is rejected, producing a self-reinforcing process: every testimony is rejected because it is improbable, and therefore it remains improbable. He describes the tradition argument as relatively weak and says that the good name of the Kuzari argument is overrated, but argues that tradition does have some weight—not decisive, but also not neutral—and that one’s attitude toward it changes dramatically between an atheistic starting point and a deistic one.

Persuasion, Assumptions, Rhetoric, and Demagoguery

The lecturer says that bringing an atheist to repentance through a logical argument is not possible, because in the assumptions of a logical argument the conclusion is already “sitting there,” and someone who holds atheistic assumptions will not accept deistic or theistic assumptions. He argues that persuasion usually works by showing a person that he “doesn’t think what he thinks he thinks,” and sometimes by showing him that he is a deist without having defined himself that way—especially in the case of a “secular” person who does not observe the commandments but has not clarified his philosophical position. He explains that decisions in many arguments rely on intuitions and assumptions that are not logically proven, and therefore persuasion is carried out through rhetorical tools that try to move intuition, not only through formal logic.

Tolerance, Pluralism, and the Question of “Brainwashing”

The lecturer says that he wants to persuade “everyone of what is true,” and that there is no moral flaw in trying to persuade so long as one uses proper tools and not demagoguery and manipulation. He distinguishes between tolerance and pluralism, arguing that tolerance means recognizing another person’s right to hold a different position, not declaring that he is correct. He rejects the automatic identification of persuasion with brainwashing, and defines brainwashing as the use of demagoguery to mislead a person into thinking he is genuinely adopting a position when in fact he is being led astray.

Analytical Learning, Giving a Get, and Explanatory Power

The lecturer returns to the topic of giving a get and presents the claim that analytical study is not mainly the collection of rules, but a process in which the attempt to define an action fails to yield an economical definition. He argues that a good definition should be more economical than the number of cases it explains, and that a theory whose number of components is similar to the number of cases is not useful. He uses the language of “reducing the unfamiliar to the familiar and reducing the familiar to the unfamiliar,” and argues that transferring complexity to a concept that is itself more unfamiliar and more complex is not an explanation.

Neural Networks, a “Torah Mind,” and Carving by Removal

The lecturer suggests that learning resembles training a neural network in supervised learning: exposure to many examples of “valid/invalid” shapes internal “weights” so that one can judge a new case even without explicit rules. He says that in such a process a person internalizes “Torah in its abstract sense” and what is called a “Torah mind,” and that the cases are only a means of creating the perspective. He explains “carving by removal” as writing through subtraction, using the image of creating the letter het by digging out its surroundings, and the image of a sculptor removing excess stone, presenting this as a mechanism in which one rules out incorrect descriptions until an understanding remains that is hard to formulate positively.

Intuition in Halakhic Rulings and the Arrow-and-Target

The lecturer quotes something attributed to Rabbi Soloveitchik, that the halakhic decisor “shoots the arrow and afterward draws the target,” and argues that there is truth in this, in the sense that a great decisor sees the answer through intuition built from prolonged friction with halakhic topics. He says that afterward one looks for justifications, sources, and analyses, and sometimes one has to give up if the grounding does not work, but usually the initial intuition drives the ruling. He connects this also to the question of the weight of grounding versus intuition, and to the fact that different people will evaluate weak justifications differently depending on their starting point.

Negative Attributes, Maimonides, and Euthyphro

The lecturer says that the issue of negative attributes bothered him because it seemed like an empty double negation, and he refers to the discussion of contrary negation versus privative negation with models like 1 versus -1 and 1 versus 0, and examples like light and darkness as opposed to heat and cold. He argues that privative negation by itself empties the statements of content and leads to the conclusion that “you can’t say anything about Him,” but points out that Maimonides in the Guide for the Perplexed argues that after negative attributes, some understanding still remains. He connects this to the Euthyphro dilemma and argues that saying “the Holy One, blessed be He, is good” becomes tautological if the good is defined only by Him, whereas a meaningful description requires an independent scale, and he presents the tension this creates with regard to praise and blame.

Negative Attributes as Carving by Removal and Projection onto Our Concepts

The lecturer proposes a solution in which negative attributes function as carving by removal, similar to analytical study: one negates formulations and human descriptions until an intuitive understanding is built of what it is right to think and what it is not, even without the ability to give an economical positive description. He says that the human scale of mercy and cruelty is not directly relevant, but that there is a “projection” of what is relevant onto the axis of our concepts in the direction of “merciful” and not “cruel,” without turning this into a human psychological description of feelings. He compares this to training a neural network also on examples of “not,” where the negations organize the weights so that a capacity for recognition remains even though the information was negative.

Dynamic Actions, Zeno, and Velocity at a Point

The lecturer moves to Zeno’s arrow paradox and argues that the problem stems from confusion between “standing still” and “being located”: at every moment the arrow is in a certain place, but it is not standing still, because it has velocity. He argues that the solution is not “infinity” as some device that explains things, but rather the understanding that velocity is a quantity that exists at a point in time, whereas the derivative is a computational definition that requires an interval only in order to calculate the velocity. He distinguishes between a point with no length and an interval whose length approaches zero but still has dimension, and gives the example of free fall, where one calculates velocity at a discrete point in time.

A Critique of Ad Hoc “Solutions” and a Comparison to Russell

The lecturer criticizes solutions that create a language in which the paradox cannot be formulated instead of actually solving it, and brings Bertrand Russell’s theory of types in Principia Mathematica as an example that prevents self-reference at the cost of narrowing the language and losing legitimate claims. He describes this as a solution that does not explain but simply “cuts off” the problem, and calls these “Stalin-style solutions” in the sense of removing the possibility of even raising the paradox.

Dynamics versus Statics, Film, and Human Senses

The lecturer argues that we have difficulty perceiving dynamic processes, and therefore we operate through dense static slices like frames of a film, with the dynamics created by the integration the brain performs. He presents the theoretical possibility of a creature that perceives only dynamics and not statics, and argues that statics is something we impose on reality more than reality itself. He uses the example of a police radar based on the Doppler effect as an intuition for the idea that velocity is a point-like characteristic even if measuring it requires a procedure.

Back to Giving a Get: The Difficulty of Defining an Action

The lecturer explains that giving a get is a dynamic action, and therefore hard to characterize through static definitions of “before” and “after,” such as transfer of ownership or movement from the husband’s hand to the wife’s hand. He argues that such definitions are at most “computational definitions” that try to capture dynamics through endpoint states, but do not grasp the action itself. He concludes that the need for many cases and the casuistic structure of the Talmud reflect a way of building unformulated understanding through carving by removal, especially in dynamic concepts that language and systematic thought have trouble framing as rigid rules.

Yes, okay, sorry. We were talking about abduction, and we explained that just as science does this, you also can’t come with complaints against believers who do this with regard to an everyday explanation of the Torah. So my point is, okay, maybe you can defend God in the transcendent sense, maybe in deism, but the God of Israel, who also intervenes in creation and performed miracles—how can you justify that, and also that He gives… No, you’re pulling me into a topic from a different course. Over there I wasn’t talking about proofs for the existence of God; I was trying to use a certain kind of proof to illustrate the idea of abduction. If you want to get into that issue itself, I’ve written books about it. Meaning, we can get into it, but that’s not the topic of this lesson. Let me tell you in one sentence, since you asked: I think the route—say, what is called the physico-theological proof, in Kant’s language—that proof really leads only to deism. But those who think that the question of deism and the question of theism are completely independent are mistaken. That is, the difference between the philosophical God and the religious God—not necessarily Jewish right now, but more generally. Because in principle, Bertrand Russell once wrote—yes, the famous and proud atheist from the twentieth century, late nineteenth into twentieth—he once said that if someone came to him and told him that God had been revealed and asked him to do who knows what, A, B, C, then as far as he was concerned that was like a teapot… the example of the celestial teapot. Right? Someone comes and tells him that around the planet Jupiter there is some little teapot orbiting. So I say, wait a second, how do you know? I’ve never seen it. Right, because it’s small, you can’t see it. So now the question is: how am I supposed to relate to such a claim about a teapot? This is Bertrand Russell’s argument. People think, well, if I know nothing, then it’s fifty-fifty. He says no—if I know nothing, then it’s zero. Meaning, I have no reason in the world to assume that there is a teapot. Meaning, even to raise a doubt, you need a reason. Right? We know this in Jewish law too. To raise a doubt, you need a reason. Yes, that’s the Talmud in tractate Shabbat, page 30. The Talmud says there that someone came to Rabbi and said to him, “Your mother is my wife and you are my son.” Right? In short, you’re a mamzer—I slept with your mother and you’re illegitimate. So Rabbi… and there were two stories like this. So Rabbi says to him, “Would you like to drink a cup of wine?” He drank and burst. Killed him, brushed him off, however you want to interpret it. What does that mean? Rabbi Kook explains there in Ein Ayah—and I think this is a very important and correct idea—that in order to arouse doubt, you need a reason. Meaning, I have no reason at all to assume that you’re right. Meaning, it doesn’t even awaken doubt in me. Could it be? Sure, such cases have happened in the world. It’s not that he’s talking about miracles or something. No, it’s not miracles; things like that happen in the world. But still, in order to raise doubt that my case is one of those cases, there has to be some basis to the claim, some concrete grounds, all kinds of halakhic expressions that are used precisely for this point. So Bertrand Russell says the same thing here. Someone comes to me and says, “God was revealed to me at Mount Sinai.” I say, cock-a-doodle-doo—yes, the celestial teapot. But if you tell him, look, on the philosophical level we’ve reached the conclusion that there is a God. I have a good proof. Now, there already is such a transcendent entity that created the world and maybe even wants something from us. Maybe yes, maybe no, but it’s no longer absurd. Okay? And now someone comes and says, look, He was also revealed at Mount Sinai and told me who knows what, to redeem a firstborn donkey. Fine? Then I say to him: that’s no longer a celestial teapot. You can accept it, you can reject it, we can discuss it. But you can no longer dismiss it out of hand as some story with no basis at all, like Tinker Bell, right? That’s not true. So in that sense I think the deistic discussion is indeed a step toward the theistic conclusion. Obviously there’s still a way to go, but it’s not true that the two are independent. Meaning, it does make a contribution. And the example I always like to give in this context is Obama. Yes, if someone in the 1990s had said that the U.S. had a Black president, they would obviously have hospitalized him. Right? Now, just a few years later, a Black president was elected in the United States. I still remember the day I heard this—it was just unbelievable. I mean, some of you do remember it, if you’re old enough, but it was incredible. It was like a fairy tale. Okay? I remember I was really excited by it. Later I was less excited by what Obama did, but the act itself was a historic event, really. Now then, okay, so in the 1990s if someone had told you something like that, it would have been a celestial teapot. Right? Now after a few years you already know there is a Black president in the United States; he’s been elected, you crossed that Rubicon, okay? Now someone comes and says, you know, his name is Barack Obama and he passed the healthcare law, Obamacare—that was one of the central laws he passed, something more socialist, concern for healthcare and things like that as part of the agenda he had also promised before the election. It was one of the major things Obama did. Okay? Now I don’t know whether it’s true that he passed the healthcare law or not; say someone reported that to me, I don’t know. It could be true, it could be false. I already know there is a Black president in the United States. So whether his name is Barack Obama or Moshe Zuchmir, fine, I don’t know what his name is, but if someone tells me that’s his name, okay, then fine, why not? What? No problem. If someone had come and told me that before I even knew there was a Black president in the United States—told me that his name was such-and-such and he did such-and-such—I’d have hospitalized him. Do you understand? It’s the same thing. If I know that there exists a transcendent entity that created the world, that who knows what, maybe even demands morality from us—there are various things I can reach on the philosophical level. And now someone comes and says yes, and He was revealed at Mount Sinai, gave the Torah, and said to do this or not do that. Maybe yes, maybe no, but I no longer reject it out of hand. Meaning, it can already awaken doubt in me. Now we have to start discussing how reliable it is—the tradition, whatever, how plausible it is that He was revealed. It doesn’t matter; all kinds of aspects that can be discussed. In that sense, I think the physico-theological proof is important also for the atheistic discussion, not only for the deistic one. Meaning, it makes the first step on the way, and that’s a very important step. Because very often the relation to deistic arguments is one that, in the end, is not decisive. There are no unequivocal arguments whether yes, there was a Sinai, no, there wasn’t a Sinai. It depends very much on your starting point. And it depends very much on the question of what already seems plausible to you in advance. And then in the absence of proof—as they say, the burden of proof is on the claimant—so in the absence of proof I’ll stay with what seems plausible to me. Bring me proof, and I’ll have to give in, change my views, and if not, then I’ll stay with what seems plausible to me. And therefore in the final analysis, the conclusion rests on the question of what already seems plausible to you in advance, before all the deistic and theistic arguments. No, there is a way, but what seems plausible to you. No, so I’m saying, but often even that doesn’t seem plausible. The only thing is—he says—but it’s so implausible that there is a God that even if this seems plausible to me, I’m not willing to accept it. I’ve heard that from many, many people. Okay? Now, if I clear that hurdle—meaning I show him no, there is a God in the philosophical sense—then now let’s look at these arguments in themselves, like any historical argument. So once you’re speaking about something transcendent, metaphysical, outside nature, he won’t accept it even if there is evidence that something was created, unless it is necessary proof. And rightly so; I’m the same way. Meaning, if someone comes and tells me that a wonder happened to him on the way to the university this morning, I’ll tend not to accept it unless there’s very, very clear evidence. Why? Yes, so I’m saying: only if I have very, very clear evidence. Why? Because a priori it doesn’t seem plausible to me that such a thing happens. So if a priori it does become plausible, it doesn’t mean I’ll accept the conclusion automatically. But it does mean that if evidence is brought, I will definitely consider it. If it’s good evidence, even if it isn’t airtight, I’ll accept it—because why not? If I ask someone what time it is and he says ten fifteen—if I had asked earlier I might have arrived on time—he tells me ten fifteen. Now maybe he’s lying, maybe not, right? But my inclination is to think there’s no reason a person would just lie like that. I don’t know of any interests he has, and without interests why would he lie? So therefore I’ll accept what he says. Now this isn’t strong proof—he has no interest, okay. So if I had a great suspicion about him, that wouldn’t be enough to convince me. But if I assume from the outset that when a person tells me the time he’s probably telling the truth, then even if I have relatively weak indications, I’ll accept it. Why not? Right? Like the claim that he has no interest. What? I didn’t understand the argument. That a person without an interest doesn’t lie. Meaning the atheist has no interest in lying about the deist? No, no, I’m talking now about “what time is it.” In the context of tradition, that already gets into David Hume’s testimony argument, of a tradition being passed down, and the question how reliable such a thing is. And Hume argued—rightly—that the reliability is pretty doubtful, contrary to the good reputation that this Kuzari argument has gotten among us; it seems to me overrated. Meaning, not such a strong argument. But on the other hand, precisely for that reason, it depends very much on the foundation from which you enter the discussion. Because if you say, it sounds entirely… after all, if there is a God, then what’s the problem with Him being revealed? It’s no longer something outside my conceptual world. True, I haven’t seen Him being revealed, but fine, He decided to reveal Himself once. Not terrible. Meaning, it doesn’t mean I’ll accept it, but it does mean—fine, we can discuss it. Now a tradition comes and says, look, He was revealed. Now okay, tradition is not such a strong argument. Traditions can get distorted, there are myths, we know all the arguments. Okay. But you understand that there is a very big difference in how I’ll relate to such an argument from tradition if I come from the starting point that there is a God. He wants something from us, so why assume He wasn’t revealed? And here comes a tradition that He was also revealed. Excellent. Not a strong argument, the reliability of tradition, but there also isn’t a strong argument that a person doesn’t lie when he tells me the time. I wouldn’t accept that as a scientific claim. I wouldn’t publish a paper on it. Okay. Fine, but in day-to-day life, if I have no reason to cast doubt, then I don’t cast doubt. By contrast, the atheist who says, look, there is no God—it just isn’t plausible that such a thing could happen at all, there is nothing but matter and physics, say, for the sake of discussion—okay. Why would he accept such testimony? Obviously he won’t accept such testimony. Now true, there is a certain weight to a tradition that reaches me. You can’t deny that it has some weight. It isn’t coercive proof, but it also isn’t just neutral. Some tradition reached me, whereas on many things not even a tradition reached me—nothing. So why assume it happened? I have no reason at all to assume it happened. And therefore you say: where the arguments are not logical, mathematical, decisive, then of course my conclusion will depend on the starting point with which I arrive. Meaning, how plausible the story seems to me or not. And in that sense, this is true also regarding belief in God. Meaning, it’s like, yes, asking what time it is. If God is part of… it’s like David Hume. David Hume’s testimony argument, which became so popular in the twentieth century among all kinds of jubilant atheists, who explain that Hume destroyed faith, and anyone after Hume who even dares to entertain it is a complete idiot—which is simply absurd. I had some debate with Jeremy Fogel. You can see it, maybe on Philo-Two. And afterward I also wrote on my site—it’s just a nonsense argument. You can read about it on Wikipedia; see what cheers of joy there are there—decisive argument, simply no answer. Of course there is an answer, and the answer is exactly what I said here. Whoever does not have God in his world—why should he assume that God was revealed and told us things? That is exactly this discussion. And rightly so. True, someone who really does not believe in God—I completely identify with the argument that just because a tradition reaches me, so what? Pagans also have traditions, everyone has traditions. So what does that prove? Stories about the Baal Shem Tov also come down by tradition. So what, because of that does it mean that he jumped with his carriage over mountains? What does that prove? But if you say there is a God, and the Baal Shem Tov has the ability to jump over mountains, say, okay, now someone comes and says yes, and I also saw him when it happened, okay. If I reach the conclusion that he has those abilities, then I have no problem accepting a story that this happened. Right? Now Hume assumes that this is implausible because miracles don’t happen, and then says yes, if an implausible story reaches me, why should I accept it? And then of course, if you don’t accept it, then certainly it will remain implausible, because every time someone tells you such a story, after all you won’t accept it because it is implausible. Right? And then naturally it remains implausible, and therefore there’s no reason to accept it. Meaning, it’s a self-reinforcing process. Yes, it’s like… well, with this I’ll already finish, but you pulled me in because this is a subject close to my heart. There was once in our yeshiva in Gush, someone a year or two older than me, who was sick with… a well-known figure today, had jaundice for a long time. And we dealt with this last week. Ah, yes? Okay. Yes, exactly. So I already don’t remember. Fine. That’s exactly the point. Meaning, this kind of rationalism that says, I cling to the paradigm I currently hold—that’s rationalism, that’s not rationality. Okay? Very often rationalism, what is called scientism in English, that religious attachment to scientific thinking, is blatantly irrational. There are certain phenomena for which science is not the right tool to deal with them, and I’m certainly not one of those who disparage science or are anti-rationalist—I think I’m very much in favor of it—but I also understand the limits of rationalism. Meaning, to understand where I am not dealing with the question of whether God was revealed using scientific tools. That’s ridiculous. Meaning, maybe He wasn’t revealed, maybe He was; we need to discuss it. But the fact that science doesn’t allow it doesn’t mean much to me. Okay? It’s not… Fine, just to summarize, then: I understood that in the general discourse about God, the atheist’s opinion is rejected, and it becomes plausible—not neutral. In my opinion, yes. And you can make this jump from deist to theist because what stands before us is only the argument from tradition and the plausibility of how much a person wants to accept it, from what point he comes. Okay. So does that mean you can’t convince a deist to become a theist? No, you can. If you show him that if he’s a deist, then the transition to theism is not as far as it seems to him. Right. But still, in principle you can ask how people are persuaded at all. After all, you understand that the number of arguments in which one side persuades the other by knockout—meaning he shows him an internal contradiction in his words—is zero, right? And still, sometimes people are persuaded. Sometimes. Very often we also don’t… How does it happen? It happens because you show him that something he thought was right isn’t right; it’s worth his reconsidering it, and he reconsiders it if he is an honest person, and sometimes he reaches the conclusion that he really retracts, he no longer thinks that way. Here too it’s the same. You will never succeed in bringing an atheist to repentance by means of a logical argument, because in the assumptions of a logical argument the conclusion is already sitting there in some way. And if he is an atheist in his assumptions, then he won’t accept your assumptions. But you can show him that maybe he isn’t really an atheist, even though he thinks of himself as an atheist. I’m asking how one can bring an atheist to repentance, so I’m saying, for example, with this argument—say, to tell him, look, there is a tradition that the Torah came from Mount Sinai, say. Only as a sketch, of course—there are many details and many objections. A tradition without interests? No, no, a tradition without interests—there are people passing down a tradition to you, what is self-interested about that? They have no interest. They have an interest after they believe it’s true. After they believe it’s true, of course they have an interest in passing it on, but why do they believe it’s true? There is such a method that the kingdom of Israel is forever—fine, then you’re already getting into specific arguments, leave it, we can argue, but right now I’m talking only about the basic logic; we can argue over many arguments, that’s not the point. The basic logic: how does persuasion of this kind work? Persuasion usually reveals to you that you don’t think what you think you think. Okay? It almost never converts you from thinking X to thinking Y—that hardly ever happens. But very often a person thinks he thinks X, and in truth, when you dig a little deeper, you discover that that’s not correct—you don’t think X, you think Y. And sometimes I can help you do that digging. I can help—people, for example, don’t notice what I explained here just now: that if you’ve crossed the atheist barrier, then true, you can challenge the reliability of the tradition, but understand that that challenge is, say, forty percent against sixty percent—I’m just throwing out numbers. And remember that from a deistic starting point, sixty is also good against forty. From an atheistic starting point, sixty against forty is very bad. Okay? And sometimes the person doesn’t notice that very point. He’s a deist, but he doesn’t notice that a deistic starting point is different from an atheistic starting point, and your attitude toward a consideration that is sixty-forty should be different from the atheist’s attitude. And very often people don’t notice that. More than that: very often they don’t even define themselves as deists at all. I’m secular. Now ask the secular person what “secular” means. You can be a secular deist, you can be a secular atheist. “Secular” is only in the Jewish sense—someone who does not observe commandments, not committed to the Torah. Very often he hasn’t even accounted to himself where he stands on these philosophical questions. He’s secular because he doesn’t observe commandments. He hasn’t accounted to himself whether he’s a deist or not. So I can try to persuade him that there is a God in the deistic sense, or reveal to him that he is already a deist without having been aware of it, and then say to him: listen, the next step is called for if you really are at that point. Very often when we adopt basic assumptions—after all, every argument is based on basic assumptions—so how do we adopt those assumptions? We adopt them because we find in our intuition that we identify with those assumptions, right? Assumptions cannot be proven, because they wouldn’t be assumptions if they could be proven. Rather, my intuition tells me that this sounds plausible, I identify with it. Now when I persuade someone else, what am I really supposed to do? Exactly the same thing I do for myself—meaning, try to get his intuition to look differently at this claim, and maybe he will in fact reach the conclusion that he accepts it. And this is not done by logical considerations, just as my own assumptions are not accepted as a result of logical consideration—otherwise they wouldn’t be assumptions. There is always some primary basis that is a basic assumption, right? From there on you can work with logic. How do you get to them? Through intuition. So too persuading someone else, when we have a dispute over basic assumptions, is done with what one might call rhetorical tools and not logical tools, which basically means trying to get him to see things from my intuition and not from his intuition. Through pathos and not through logos? Through pathos, yes, but not through demagoguery. Where’s the line? I don’t know how to define the line, but on the other hand the fact that you can’t define the line doesn’t mean there is no line—that’s the sorites paradox. If it’s a lifestyle of observance of commandments in superlatives, emotionally, he’ll be convinced. No, if you use a lifestyle of observance of commandments in superlatives—come eat with us on Sabbath, see what a wonderful family we have—he won’t be convinced; he’ll be swept away, taken captive by that argument because it feels good to be in that place for some reason. To me that’s demagoguery. But if you tell him, look, something that works so well probably comes from above—not that you’re appealing to his emotion, but you’re using this pathos-laden description in order to raise a logical argument. Now whether he’ll be convinced or not, that’s not important, but that’s… A person can be persuaded by such a thing, and that’s legitimate persuasion. A person says, look, the ideal structure of a family is probably something given from above, because in fact those who don’t work that way—the structure of the family there works less well. It doesn’t matter, I’m not endorsing any of this at all, but just as an example of an argument, okay? Then that already is a logical argument; it isn’t just pathos. The pathos here is an indication of a logical claim, that is, an argument, okay? And that is persuasion. Now, many times we mix up rhetoric and demagoguery, and that’s a mistake. Rhetoric has a bad name. In the United States at least, in the past—don’t know if it still is—rhetoric was once a required subject in high school. In the previous century? No, no. Actually, for me the previous century doesn’t sound so terrible, but not that long ago. Meaning, I was already a very adult person when it was, don’t know when, maybe it still is, I have no idea, I’m not familiar, but that’s what I was told. And I’m very much in favor, because I think it teaches people to think, and logic covers a very, very small part, really, of proper and improper ways of thinking. In simple logic people usually don’t fail. Okay, people know logic—draw a conclusion—even ordinary people don’t fail in logic at the formal level, right? Usually it’s built on softer biases, not a logical contradiction, not a logical mistake, and there too there’s something to learn. There are biases and there are things more plausible and less plausible. It’s thinking about the plausible, not the valid, right? Not the true and false, but the more plausible and less plausible. But that is thinking in every respect; it has to be acquired, it has to be learned, one has to be skilled in it—and in fact, mainly in it. Because logic is a relatively simple thing, and in very few cases is logic really what decides the dispute; usually it’s there. And one of the things one needs to learn is the difference between demagoguery and rhetoric. Many times in rhetoric courses they teach you how to persuade, and when they teach you how to persuade, it’s very easy to slip into teaching you to be a demagogue. But you can also teach someone to present things in a way that gets the other person to see them from the angle from which you see them, and then the persuasion is entirely legitimate, because that is also how I myself adopted my basic assumptions. I’m simply trying to get him to see it from that angle—or he me, meaning I can also be persuaded; it goes both ways, okay? And most arguments are there. And it’s a terrible mistake that rhetoric isn’t taught, that people aren’t skilled in the use of rhetorical tools, and therefore it gets a bad name as if it’s all demagoguery. And where does that come from? It comes from this assumption that says everything is logic, and everything that isn’t logic is demagoguery. And that’s not true. There are things that are not logic—they are rhetoric—but that isn’t demagoguery. They are softer arguments. Analogy, induction—that’s not logic; the conclusion does not necessarily follow from the premises, but all of science rests on arguments of analogy and induction. Nobody says that’s demagoguery, except for a few critics, yes, from the new criticism, who also criticize science as masculine, chauvinist, European, Western, Protestant, whatever, all kinds of Marxist claims of one kind or another. Fine, we use it all the time and rightly so, meaning it is justified to use it even though it isn’t rigorous in the formal logical sense, okay? And one needs to know how to use these tools and how to guard against improper uses of these tools, okay, which is what demagoguery is. Fine, that’s enough preaching for today. But I did somewhat want us to see within this some additional things about legal ruling from last week, the world and its meaning. Is this about faith—you’re arguing in faith or arguing in methodology, rhetoric versus logic? Let’s talk afterward. Did you want to persuade someone? Why not? I very much want to persuade everyone of what is true. Why not? Today it seems like something bad to come and persuade someone of something I think—to bring him to repentance. What’s the problem? I want to bring everyone to repentance, because it seems right to me and I think they’re mistaken, and I want to bring them to repentance—what’s the problem? As long as I do it with proper tools, not with demagoguery and biases and so on, what’s the problem? Part of that same aversion to attempts at persuasion and so on comes precisely from the fact that you’re unwilling to make the distinction between rhetoric and demagoguery, and everything is called demagoguery. When people hear about an Arachim seminar—doesn’t matter, another seminar—that leaves casualties there by the thousands, meaning lots of people become religious, immediately everyone declares: that’s brainwashing. Why? Because it can’t be that a person was genuinely persuaded. If he was persuaded, it’s brainwashing. Why? A person can also be persuaded; it can turn out he was mistaken. Again, without expressing an opinion on what goes on in those seminars, but it’s not automatically brainwashing. Today there’s this sense that trying to persuade is morally wrong altogether. Fine, I’m already drifting further. Because I want that to be the truth, I want everyone to live according to the truth—why? I want everyone to live according to the truth and merit the Garden of Eden. And make the world better. What’s the problem? That’s what I want. Yes, of course. I want to persuade people. If I think I’m right, I want to persuade people and keep them from mistakes—spiritual, economic, whatever field, security-related, anything. The feeling that if you come to persuade someone then you’re not okay, you’re imposing on him, you’re not tolerant—what’s intolerant about my trying to persuade him? Tolerance is when I’m willing—meaning I recognize his right to hold another position. Fine, but that doesn’t mean he’s right from my point of view. To be tolerant does not mean to say that he is also right like me. That’s pluralism. There’s some confusion between tolerance and pluralism. If a person already has an inclination in your direction? Excellent. Then take that inclination. Then there’s no persuasion here. Fine, maybe I won’t succeed. Do you have a problem with my doing something I won’t succeed at? Fine, then I won’t succeed. But if there is someone with whom I will succeed, if he has that point, excellent. I also said this earlier, by the way: if I manage to persuade someone, it’s only because, inwardly, it was already there. Maybe he wasn’t aware of it, but it was already there. Right, very good. And I’m addressing those people. Not that I need to, because there are many people in whom, even though it is somehow inside them, yes, exactly. So what’s the problem? The difference between persuasion and brainwashing? Obviously. What do you mean? It’s a world of difference. What’s the connection at all? True, because of brainwashing a person also ends up persuaded, but that doesn’t mean that everyone who is persuaded has been brainwashed. There are people who are Jews—does that mean every person is a Jew? If you’re a Jew, you’re a person; that doesn’t mean that if you’re a person, you’re a Jew, right? Meaning, the dependence is not always symmetrical. So true, brainwashing is one way to persuade someone. Does that mean every persuasion is brainwashing? Of course not. There are persuasions where you really persuade a person by such-and-such arguments and he reaches the conclusion that he was mistaken and changes his position. What’s the problem? What distinguishes brainwashing from a legitimate tool for conveying the lesson? Why is brainwashing an illegitimate tool? Because brainwashing—no, brainwashing is not legitimate. Brainwashing is precisely the use of demagoguery to mislead him into thinking he thinks a certain thing, when in truth he doesn’t really think it; you’re only misleading him and he comes to a double mistake. Fine, okay, no, these are things more important than our lesson, I think. So it’s okay, I don’t have a problem with this waste of time. Fine, but I really do want slowly to get back. We talked last time about the issue of giving a get, a bill of divorce. And I tried to show through that issue that in-depth learning is not what we think it is. And it’s not just in-depth learning in Talmud; it’s something much broader than that. Very often, since our intellect, our thinking, is built in the form of definitions and rules—yes, in the form of systematic thinking, that’s the form systematic thinking takes for us—so when we try to analyze a topic, we do it likewise by establishing rules. Yes, analyzing cases, establishing rules, classification—all the tools of systematic thinking. And we saw that in the attempts to characterize giving a get, the result is unsatisfactory. If that’s what I wanted to achieve, the result is unsatisfactory. It’s unsatisfactory because the definition we arrived at, if any, is a definition whose number of components is more or less the same as the number of cases I am trying to describe with that definition. Right? Think of a scientific theory whose number of elements is more or less equal to the number of cases it explains. That’s a theory that’s no use to us. Right? I gave number series as an example of this point—you need a theory that has explanatory power, explanatory value. Such a theory requires far fewer principles and concepts than the cases it seeks to explain. Then you say: this is economical, it puts everything into one framework, so I’m willing to see this as an explanation. Okay? But if you keep adding more and more ad hoc elements and in effect the theory is no less complicated than the cases it explains, then it has no value. When we talk about grounding the unfamiliar—you remember I spoke about grounding in the familiar and grounding in the unfamiliar?—when the unfamiliar that you created is no less complex than the familiar that you came to explain, then what did you gain? You transferred the complicated familiar to an even more complicated unfamiliar. What did you gain? If you transfer it to a simple unfamiliar, then you gained simplicity. If you transfer it to the familiar, even if complicated, you gained familiarity. But if you transfer it to something unfamiliar that is also more complicated, then you gained nothing. Meaning, that’s not an explanation. And that is what happens in giving a get. And therefore I argued that the study of topics of this kind is actually very similar to training a neural network. In a neural network we give it examples—in supervised learning, controlled learning. So you give it an example; say facial recognition. You give it certain faces—say it needs to recognize my face. So you show it one photograph of me and tell it to identify it. If it says it’s me, excellent, check mark; if it says it’s not me, you adjust the internal weights so that it will say it is me. Then you show it another photograph of me from another angle, in different light or something, and again you keep going like that until you train the neural network. Then all the weights inside it are organized in such a way that all pictures of me it will say yes, and pictures of someone else it will say no. That’s my goal, fine? Now if I managed to train that network, then in the end it knows how to recognize even pictures it hasn’t seen. Okay, that’s really the goal. Pictures it has seen don’t help me. Pictures it hasn’t seen—it already knows how to identify on its own. But that identification is not based on a set of rules. That identification is based on some mechanism, and it isn’t entirely clear what the connection is between it and the ways in which we operate when we think, which are usually systematic ways in conscious thought. Systematic ways. But the fact is that it reaches the same results. Meaning that somehow we managed to shape the neural network—or by analogy, our brain, our thought, our intellect—to reach the correct results, while the path, the examples, were only a means of shaping the neural network. And now I throw away the examples I used; what remains for me is the neural network with the weights I arrived at, and it does the job—it knows how to identify the image it is required to identify, with high probability. Now here too, basically the same thing is happening. After I’ve seen all the examples—and with the examples I receive, this is really supervised learning, yes—I look at an example, and they tell me: this is a valid giving of a get. Another example: this too is a valid giving of a get. That example is an invalid giving of a get. I see dozens and maybe even hundreds of examples in the Talmud, in the medieval authorities (Rishonim), and so on. So in the end, when I come to judge a new example, I judge it not by comparison to the previous examples—or at least not only that—but through the neural network that has taken shape in me, with the assumption that it now judges correctly, meaning that it has been built correctly in some way. And I argued that in this process I am actually internalizing within myself, in my thinking, the Torah in its abstract sense that we discussed at the beginning of the semester. Yes, before it passed through illustrations and developed into the form it takes for us today, I am in fact taking into myself what in some places is called the Torah-mindset. Or this perspective that tells me the correct answer, even though very often I don’t know how to ground it or present an explicit argument based on Torah rules from which this result follows. But the correct result emerges; that means that somewhere inside me there is Torah in some kind of representation. And the goal of learning—this was basically the claim—is not at all to know which get is valid and which is not valid. The cases are only a means. They are a means for instilling in me this perspective that tells me which case is right and which case is not right. And that perspective is Torah, not the cases. The cases are applications. But that perspective is what is called Torah. I spoke about a scientific perspective as opposed to a technological one, right? That the goal is the laws of nature and not the cases or situations. Here I’m claiming that it’s not even the laws, but rather the understanding that stands at the basis of the laws—we talked about the different levels of development from the abstract to the concrete. That’s what we saw last time. And I said that in the end explanations of the kind involved in giving a get—I called them “inscribing by hollowing out” explanations. Yes? In the laws of writing on the Sabbath and in writing sacred scrolls this comes up, but with writing on the Sabbath it appears in the Talmud. There they discuss what happens when I create a letter by removing its surroundings. I think I talked about it—say you want to create the letter chet. So instead of writing the letter chet, you dig in the middle and dig from the side and leave the letter chet protruding. You didn’t touch it—you just removed the side. Just as a sculptor makes a sculpture from a block of stone, he only removes. What remains, he didn’t touch—that is, he only removed everything that got in the way. The sculpture was already in the stone beforehand; he only removed everything beyond the sculpture. Right? Now we all understand this isn’t true, but physically that is what he did. Okay. So what does that actually mean? That very often I have a way to write the letter chet without really writing it, by removing all the other things and what remains is the letter chet. For me that’s a good metaphor for what I described earlier regarding giving a get and in-depth learning in general. This is basically a kind of “inscribing by hollowing out” learning. What does that mean? I am basically removing various rules and understandings that don’t really work; through cases I show that they don’t work, remove this, remove that. Remove that. What I’m left with at the end, I don’t even know how to speak about. It’s that letter chet, right? I don’t know how to speak about it positively; I only removed all the possibilities of defining it positively. But it’s not true that I was left with nothing. I was left with some kind of understanding, which is actually the distilled understanding of what counts as a valid giving of a get. And I don’t know how to formulate it, at least not economically. I can formulate it in some way that piles up lots and lots of principles whose number is roughly equal to the number of cases, but I can’t formulate it directly. And therefore there’s no question why the Sages didn’t say the rule of what a valid giving of a get is but instead gave so many examples. They didn’t say it because there’s no way to say it—we don’t know how to say it. All we know is to learn from the examples which descriptions are not correct, and through inscribing by hollowing out we hope that the correct description will remain inside us. Then we will already know how to work with it and look at things. And therefore in the end, a halakhic decisor who looks at things—a great decisor, it seems to me, who looks at things—very often he sees the answer, he shoots the arrow and afterward draws the target. Meaning, he understands the answer from everything he has carved out within himself until now. Rabbi Soloveitchik—someone once told me, I didn’t read it inside—that he says the decisor always shoots the arrow and afterward draws the target. Now I don’t think that’s always true, but I do think there’s a lot of truth in it. Meaning, there is something in the initial intuition that tells us this is what is right. Afterward I do need to look for justifications, and sometimes I need to be honest—sometimes when it doesn’t work, then one has to give up that initial intuition. But it’s true. That initial intuition is actually what says the first word, and that is the result of inscribing by hollowing out. Meaning, I have some intuition that was built inside me through friction with all the cases and topics and everything; it already tells me what is right and what is not right. And now I need to formulate it, ground it, bring sources, analyze. Sometimes I need to give it up; usually not, usually not. And apropos of what we discussed in the introduction, sometimes when I have a foundation that isn’t so strong and someone else, whose intuition is different, won’t accept it because it isn’t such a strong foundation—but since my intuition tells me that this is what is correct, then that foundation that I found I will regard as a sufficient foundation. Because his input was more developed in order to assess his output, like AI? Yes, yes. Input in the cumulative sense over a whole lifetime, not the input on this particular question. Yes, yes. The more examples you trained on, the more likely it is that your network is built more correctly. Could there be a person who didn’t study and yet has that same intuition? Obviously that also depends on innate abilities, not only on acquired things. Right, yes. Some people are more talented and some less. He can be a genius and know everything and arrive at the correct Jewish law but not know how to explain it to you. He doesn’t know how to explain. No, explaining—you don’t have to explain. The only question is the ruling, without explanations. He gets to the right answer but in order to write a document that explains it and convinces everyone maybe he doesn’t… It can happen, fine. Obviously. So the claim is that in the end, after we peel away all the possibilities of formulating general laws and giving analytical, systematic explanations, and we negate them, in the end we are left with something raw and abstract—but that is actually the truly correct thing. And therefore this returns us to the casuism of the Talmud that we discussed with the ukimtot, right? Why do they use cases and not rules? Because cases are exactly the way to build an unformulated understanding, whereas rules force it into a very rigid formulation and that doesn’t really work. And the way to produce an unformulated understanding is precisely through cases and not through rules. And therefore the casuistic structure of the Talmud, I think, reflects this conception. We talked about common law in Britain and more. I just want to make one more philosophical comment. Philosophical—“Jewish thought” as such doesn’t really exist, in my opinion. So I want to say a few words about negative attributes. The issue of negative attributes troubled me for a very long time. Because on the face of it, it sounded to me like nonsense. Meaning, Maimonides says that when we say about the Holy One, blessed be He, that He is merciful, we do not mean that He is merciful, because we don’t know how to describe Him really; we mean to say that He is not cruel. Okay, now what difference does it make whether you say He is merciful or not cruel? That’s a double negation. Meaning, not cruel is merciful—what did you gain by that? It’s a description to the same degree. When I say of someone that it is not true that he is not tall, that means he is tall, right? So what difference does it make whether I use two negatives or describe him without the negative? Two negatives are the same as a positive. So what is this all about? So you can say, well, maybe we’re dealing here not with an opposite negation but with an annulment negation. Already in Aristotle, I think—Greek philosophy already sees this—there are two kinds of negation. There is a negation that says the opposite of the thing, and there is a negation that says not-the-thing, meaning nullifying it, canceling it. Give an example. Maybe first the model, then the example. The model is, say, the difference between one versus minus one, and one versus zero. Zero is an annulment negation of one; minus one is an opposite negation of one. Say, cruel is the opposite of merciful—but the opposite, the true opposite, the contrary negation. But the annihilating opposite is neither merciful nor cruel; it’s something not on that axis at all. Fine? Not relevant to it. As when I say that a moral virtue is red. Moral virtues of the soul. A moral virtue is red. That is neither a true statement nor a false one; it’s simply irrelevant. Therefore I need to negate the color red from moral virtue. That negation is an annulment negation, not an opposite one. It’s not that I say the moral virtue is not red; “not red” means it has some other color, not red. No—the concept of color is irrelevant to it. That is an annulment negation, not an opposite one. Think about the relation between cold and heat and the relation between light and darkness. Cold and heat are opposite negation; light and darkness are annulment negation. How do I know? Add light and darkness—what do you get? Light, right? Darkness won’t cancel the light. That means darkness is zero light, not minus light. Right? But add cold and heat—combine cold water and hot water and you get lukewarm water, because cold isn’t non-heat, it doesn’t annul heat, it opposes heat, and therefore when you combine them they offset. Fine? That’s one indication. There are all sorts of other investigations involving light—whether darkness is merely the absence of light or something independent. In the simple view it’s the absence of light; darkness is the absence of light. What? To be without too many clever complications. Yes, sometimes wisdom is to be without too many clever complications. What? Cruel. No, now let’s come back here. So there are those who wanted to argue to me—I’ve carried this problem around for years—that when I say that the Holy One, blessed be He, is merciful, the intention is not that He is not cruel in the contrary sense, because in the contrary sense you’ve gone back to merciful. Not cruel and merciful are the same thing. Rather, in the annulment sense. Annulment means that mercy, cruelty—none of that is relevant to Him; those are human traits. The Holy One, blessed be He, is divested of all those attributes. But that too isn’t satisfying, because then you could also say He is cruel to the same extent, because it isn’t true that He is merciful. It’s no more true that He is cruel than that He is not merciful, that it isn’t true that He is cruel. What’s the difference? Cruelty and mercy have no relevance to Him—that’s what you want to say. That is the annulment negation. So there is no preference for saying that He is merciful over saying that He is cruel; you can say either equally. Right? Therefore we gained nothing by moving to annulment negation, because that merely emptied the statements of content. So now you’ve emptied the statements of content; you’re basically saying nothing can be said of Him. That is the only thing you can say. So say that once and be quiet from there on, and don’t tell me that He is merciful and jealous and avenging and gracious and slow to anger and all kinds of things like that, all of which are negative descriptions. All you’re telling me is that nothing can be said about Him. That’s all—so say that. Yet we do feel that this is meant to say something, right? When we say that the Holy One, blessed be He… It’s like in the Euthyphro dilemma. In the Euthyphro dilemma the question is whether the Holy One, blessed be He, wants the moral because it is good, or whether it is good because the Holy One, blessed be He, wants it. In Euthyphro it’s about the Greek gods, but translated into monotheism: does the Holy One, blessed be He, constitute the concept of the good, or is He subject to it? Now on the face of it, how can it be that He is subject to something? After all, He constituted everything; everything is from Him, right? But look at the price. If you really think that everything is from Him and nothing has meaning without Him, then saying that He is good is an empty tautology. Obviously, because whatever He is is what is called good. What’s the big idea? You didn’t say anything, right? But our feeling when we say that He is good is that we are saying something. It’s not like saying that He is evil, right? Meaning, we are praising Him, not condemning Him. But how do you praise Him? What standard are you relying on? What is your scale for determining good and evil? The scale has to be independent of Him; otherwise you said nothing. And that leads you to the other side of the Euthyphro dilemma. Clearly good and evil precede the Holy One, blessed be He, obligate the Holy One, blessed be He; He cannot decree that evil is good, there is no such thing. “Just as He is merciful, so you be merciful,” and so on—that’s fine, but what does merciful and gracious mean? Is whatever He does merciful and gracious? When He destroyed Amalek, was that merciful? Down to the last baby? Is that merciful? Yes, because that is what He did, and after all the definition is that He is merciful. Fine, then you said nothing. So do what He says, do what He does. Fine. You are not describing Him; you are only giving a command to a person—do what He does. No, when we come to describe Him, we are describing Him. The question is what this description means. It is empty of content if you understand that the description is basically constituted by the Holy One, blessed be He. Fine? There must be some scale—if you say these claims mean something, these descriptions mean something—that means there is some scale independent of Him. Good and evil do not depend on Him; they are imposed on Him. What Maimonides says—ask him. I’m telling you what I’m telling you. That’s what I’m asking. If it doesn’t mean anything, then Maimonides didn’t say anything either. So say: nothing can be said of Him, period. Don’t tell me stories about negative attributes and this and that. And Maimonides says that after the negative attributes, some understanding still remains in us. He most certainly does not say what you are putting in his mouth. What, according to your position, he should have said, is: nothing can be said about the Holy One, blessed be He, thank you very much, goodbye; an ox that gored a cow, we move on to an ox that gored a cow. That’s it. But as he talks about it, he devotes whole chapters to it in Guide for the Perplexed, and explains to you that those chapters also teach you something. He senses the question I was about to ask. He says, no, no—don’t think that negative attributes teach nothing; they do teach. Some kind of understanding remains with you. And I think here I come to the answer. I’ll end this here—I think this is the answer I want to propose to the matter. These are “inscribing by hollowing out” explanations of the Holy One, blessed be He. “Inscribing by hollowing out,” as I said in in-depth learning. What am I actually trying to do? Formulate through various principles the description of the Holy One, blessed be He, and I negate them through various such cases and others. But in the end some understanding of what the Holy One, blessed be He, is does remain. It is not exhausted by the words I described, because those words are only a means that I use and throw away, right? I formulate and throw away, formulate and throw away. But little by little this builds in me some kind of understanding by hollowing out. It builds in me some kind of intuitive understanding of what it is right to say of Him and what not, what it is right to think of Him and what not. To say is more problematic here. Okay? And therefore I think this may be a way to make sense of this strange theory of negative attributes, yes, in Maimonides and others. He didn’t invent it, of course. What? Like the sculpture, sort of? Like the sculpture, yes, exactly. Like in-depth learning, like the sculpture, like what I was talking about. This is the inscribing by hollowing out I was talking about. And it’s like when you train a neural network: you give it examples, and all the examples are what it is not. Did it learn something from the example they told it was not my picture? Yes, it learned. It arranged the weights in such a way that afterward, when my picture appears before it, it is more likely to identify it correctly—even though I gave it the example of what is not Michael Abraham. I trained it on that. So here too, this is really learning through negative attributes. But when you say He is not cruel, aren’t you saying He is not merciful? What remains? So I’m saying—that’s what I’m saying. When I say He is merciful, I mean to say that He is not cruel without saying that He is merciful. There is something there such that, true, the scale of mercy and cruelty in human terms is not relevant to Him, but the projection of what is relevant to Him onto that axis leans in the direction of mercy and not in the direction of cruelty. Don’t turn Him in the end into a human being with feelings of mercy and cruelty and what we know in ourselves. But it does give you some sort of projection onto the plane of our concepts. And these are not negative attributes of merciful versus cruel; rather they are negative attributes of abstracting mercy and cruelty away from their garments and toward some more abstract thing. And in that sense it is more similar to annulment negation than to contrary negation. It’s not on the axis where the opposite of merciful is cruel, but rather “not merciful” in the annihilating sense—meaning, still something remains there after I have annihilated, annihilated with an aleph, right, mercy and cruelty. Something remains there. There is indeed a difference between telling me that He is merciful and telling me that He is cruel. Now if you ask me what the difference is, you will force me to give you a positive description of it—but I can’t. If I could, then they would do it with a positive description. We can’t. But the feeling—and this is what Maimonides writes there—is that in the end, we really do learn something from it. Something remains with us from it even though all we did was negate the whole time. And I think this example of in-depth learning sheds truly wonderful light on that claim. For me, it made a light bulb go on about something that had bothered me for years, because it had just seemed to me like nonsense, all these negative attributes—word games. Fine. Now I want to enter this on a more philosophical level and continue to demonstrate this mode of relating, this “inscribing by hollowing out.” “Inscribing by hollowing out” kind of arranges your form, like improving the form? Okay, that’s very parallel to what I said. It shapes your neural network, in the metaphor. Yes. Right? Yes. But the more you deepen into it and more and more and more and more—exactly. And not because you learned more and more information; you didn’t, because you negated everything. But somehow it carved more and more into you, and a structure was created in you that is more correct. Fine? Yes, right, I enjoyed that too very much; really, this thing bothered me for years. These neural networks open your head up in many planes; really, it is an amazing phenomenon, really. It explains a great many things, and that’s why it’s so surprising. It surprises even those who created the neural networks, because they themselves don’t really understand how it succeeds in doing everything it does. What? Yes. People’s work over years. One second. Yes. No, but it’s also not clear how it does it, even after it does it—you don’t understand how that happens. How, how… I still remember when this came in; I was doing my doctorate. When it came in, they started—because it came from physics. And they started—someone showed me, yes, today he’s a professor here, a friend of mine—he showed me a network of ten sites with bonds between them, linear, yes, one-dimensional, ten bonds. He said to me: hit the key and it will guess your next keystroke. So I tried to evade it, and after five or six keystrokes it had learned me. And I was sure I was the most random, most creative, most able to fool it—no chance. It knows in advance what I’m going to do in 70 percent of cases, 80 percent of cases; you don’t get below 70–80 percent, you have to be a virtuoso to get below 70–80 percent prediction. And that’s nothing—that’s the most elementary and simple network there is, just ten sites, he wrote it on the spot in three lines of code. And it left me stunned. Now that was the first encounter. Now with large language models in general, you can really go crazy. Yes, so it truly is an amazing phenomenon. Fine, in any case, back to us. I want to speak a bit about giving a get from a more philosophical and abstract angle. My claim, basically, is that giving a get is very hard to characterize; not for nothing does this very topic require dozens upon dozens of examples, and specifically there we get so entangled with the definition, because this act of giving a get is a dynamic act. It’s an action. Yes, it’s an action. You give; you perform some action. And actions are hard to characterize. That’s the claim—I’m already giving the bottom line. Now I’ll try to explain what I mean. Fine? Actions are hard to characterize. You have to take cases in order to characterize actions. So let’s start for a moment with one of Zeno of Elea’s paradoxes, yes—Zeno was a Greek Eleatic philosopher who presented a list of paradoxes whose main purpose was to undermine the concept of motion. Yes, Achilles and the tortoise is perhaps his best-known paradox, but even there the solution is not as simple as people think. The paradox I want to talk about here is the arrow in flight. Zeno’s arrow paradox. There is an article on my website—whoever wants can search for “Zeno’s Arrow.” There it’s spelled out in greater detail. Zeno says this: suppose we observe an arrow in flight. At every moment we look at it, it is standing in a different place, right? Now a moment later it’s standing here. Then another moment later, it’s standing here. Right? Meaning, at every moment the arrow stands in a different place. Now the question is: so when does it move? If at every moment it stands still, how does the transition happen—meaning, when does it move from place to place? Okay? There are various formulations, but that’s the simple one, let’s say. That was basically the question. And so Zeno concludes from this—he says, well, motion is apparently some sort of illusion. It’s an illusion; there is no real motion in the world. There is no motion in the world at all, as Rabbenu said. Yes? So Zeno too said this by force of various paradoxes that the concept of motion creates, like Achilles and the tortoise or like the arrow. He says: if you assume the arrow is moving, it can’t be; after all, at every moment it is standing, and at the next moment it is standing here, and at the next moment it is standing here. So when does it make the movement from place to place? After all, at whatever moment you say it moves, it is also standing—just in another place. So when does it make the movement from place to place? Fine? Now people are used to explaining this through infinitesimals, that basically we are not speaking about points but about the infinitesimal. Fine? In the layman’s formulation of infinitesimals, the Leibnizian formulation, not the Newtonian one, we basically say that the unit that composes a line is not a point but an infinitesimal or differential. Okay? And my feeling toward this explanation is that it’s an English-English dictionary. Why, why really? Meaning, you explain this thing to me by means of a mathematical theory that I also don’t understand—so what did I gain? Why really is the line not made of points but of infinitesimals? Assume it—explain it to me. If you explain it to me, I understand. Then you’ve explained something unclear by grounding it in the familiar? Yes, through what is familiar. But when you take one unclear thing and explain it with another unclear thing, then what did I gain? More than that: the mathematical formulation is simply a formulation that manages to formulate the thing without falling into paradoxes. But that still doesn’t mean there is an explanation here of the problem. Very often I can use a formulation that avoids the paradox, but that is not yet solving the paradox. For example, in the introduction to Principia Mathematica of Bertrand Russell, he offers a solution to all the paradoxes of self-reference. Yes, like the liar paradox, like the barber who shaves all the people who do not shave themselves, and the question whether he shaves himself. If he shaves himself, then he belongs to that group of people he does not shave, so he does not shave himself. But if he does not shave himself, then he belongs to the group of people he does shave, so he does shave himself. Yes, all kinds of things—there are many examples like that. These are the self-reference paradoxes. Okay? So Bertrand Russell and Whitehead, yes, in the introduction to Principia Mathematica—Russell writes there—they propose a solution called the theory of types. The theory of types means we divide the statements in language into different types, into ranks, into different levels, and create a hierarchy among them. And every statement can refer only to statements lower than itself in the hierarchy. That’s the rule. You understand that in such a language there will be no self-reference paradoxes, right? Because a statement cannot refer to itself; it refers only to statements that belong to a lower level in the hierarchy. So by definition it cannot refer to itself. Is that a solution to self-reference paradoxes? Obviously not. He simply built a language in which the paradoxes won’t appear. Thank you very much. Maybe you can formulate it in English too, so because of that it’s not a paradox? What’s that got to do with it? I’m formulating a paradox now—give me a solution, don’t offer me a language in which it won’t appear. It won’t help me that you formulate for me a language in which it won’t appear. That only means that this language is constrained—there are things that cannot be expressed in it. That’s all. And in general it’s an ad hoc solution, suffering from every problem we can think of for a paradox-solution. Meaning, it also throws out a lot of babies with the bathwater, not just the desired baby. There are lots of things you can’t now express in the language, not just the paradoxical problems. For example, you can’t say that all the sentences in the language are composed of words. Is there any problem with that statement? It’s true. Okay? Not legal in Russell’s language, because that is a sentence referring to itself; it too is a sentence. It can’t refer to all the sentences in the language because it itself is also a sentence. Right? So that means that in Bertrand Russell’s language it will be impossible to express this, even though it is a true statement and there is nothing wrong with it. I’m just trying to show that Bertrand Russell’s solution is not a solution to the paradox; he merely created a language in which the paradox cannot be expressed. But that’s not solving the paradox. I too can create a language in which we simply don’t translate—we don’t translate the word “barber.” There will be a language in which the word “barber” doesn’t appear. There too you won’t be able to formulate the paradox, so have we solved it? No. We simply created a language that does not permit its expression. Those are Stalin-style solutions. Yes, Stalin usually, when he needs to solve paradoxes, simply cuts off the head of whoever raises the paradox and that’s it—you solved the problem. Okay? This is a Stalinist solution, only a bit more refined. Fine. In any case, so then what? In that article I argued that the solution has nothing to do with infinitesimals. There is a problem here in language. Yes, this is really an analytic solution; Bertrand Russell of all people should have understood it himself, because he more or less founded analytic philosophy. So the claim was that there is a difference between saying that at every moment the arrow stands in a different place, and saying that at every moment the arrow is in a different place. “Standing” and “being” are not the same thing. And when I look at an arrow in flight, it is not correct to say that at every moment it stands in a different place. It is in a different place. At every moment it is in a different place. What’s the difference? Standing means someone who is in some place and whose velocity is zero. Right? Being in that place means someone who is in that place and whose velocity is something—it doesn’t matter what. Do you understand there’s a difference between saying “stands” and “is”? Now when you ask when the arrow passes from place to place—at every moment that it is in a place, it is also in motion, and therefore it passes to the next place. There is no problem in that. Once you understand that we are not talking about standing in a place but about being in a place, the question doesn’t arise. It’s simply a conceptual error. Okay? It’s a bit hard for us to understand how an arrow can be moving at an instant of time. Because I say that “it is” means it has velocity—yes, that it is moving. But for movement you need some segment of time. At a point in time you can’t move. So that’s the next step in my argument. What leads us to think that? I’ll tell you what: infinitesimals. Differential calculus, yes? Exactly the thing they wanted to solve the problem with. When we define, for example, a body’s velocity—how do we define a body’s velocity? What times what? Velocity times time is distance—but what is velocity? Velocity, move the term: velocity is distance divided by time. Okay? Meaning, when I look at a body’s velocity, I say: when was it here, when was it here—divide the difference in positions, which is the distance it traveled, by the difference in times that it took, and the result is velocity. Now if the velocity is not constant, you have to do this over a very, very small interval because it changes, and that’s called a derivative. Never mind. Over a very, very small interval I do it. And then I get the velocity around a certain point, right? And by the way, when the velocity is not constant, the velocity can be different at every moment of time, but it is well defined by the derivative process: I simply take a very small interval around the point. Always an interval whose length approaches zero. Okay? That’s the point. Now do you know what the difference is between an interval whose length approaches zero and a point? This I once wrote—Rabbi Sheilat wrote some critique of one of my books, I think, and I think he was mistaken there. What is the difference between an interval whose length approaches zero, yes, infinitesimal, and a point? The difference is in dimension. A point has dimension zero. An interval whose length is zero has dimension one. Only its length is zero. A point has no length. It’s not that its length is zero; a point has no length. The concept of length is not defined for it, because the concept of length requires at least one dimension. In a point the dimension is zero. Think about the difference between—today we’re in a philosophical mood—think about the difference between someone who doesn’t see, someone who sees black, and a blind person. Does a blind person see black? No, no. A blind person doesn’t see—not that he sees black; he doesn’t see. There is a difference between seeing black and not seeing. Think about how—someone brought me this example some time ago actually, a nice example. When you think about what is behind you—the board here, yes? This board I don’t see. It’s not that I see black in its place; I simply don’t see it. It’s not… Do you understand? That’s a better example for a blind person. We always imagine a blind person as someone for whom everything is black before the eyes, like us with our eyes closed. But no—a blind person is someone for whom what is in front of him is basically as though it were behind him and not in front of him. Fine? Meaning, sight simply does not apply to him. Black is a kind of seeing, a neutral kind of seeing. But not seeing is not neutral seeing; it is simply not seeing. Okay? Now an interval, however small you want, has length. No matter how small it is, it has length; and in the limit the length is zero. Okay? But a point has no length at all—not that its length is zero; it has no length. Okay? Therefore in physics, when we define velocity, not for nothing did the infinitesimal come from Newton, because Newton was a physicist. Physicists need infinitesimal calculus because they deal with processes, like velocity for example. So how do we define velocity? You traveled a distance, so I subtract this location from this location to get the distance, and subtract the time you got here from the time you left, and get the time. The ratio between them is the velocity. If the velocity is not constant, I do it over a very small interval. Then I get the velocity around a certain point, right? And then the feeling that emerges from this is that there is no such thing as velocity at a point. Velocity at a point is a contradiction in terms; velocity is always over an interval—the question is at what velocity you traverse this interval, how long it took you to traverse the interval. There is no such thing as velocity at a point. But that’s not true. This definition is exactly the definition that creates Zeno’s paradox. Infinitesimals create the paradox; they don’t solve it. I claim that velocity exists at a point, and my proof is simple. At a point of zero dimensions? Yes. For every point in time you give me, I can tell you the body’s velocity. Even at zero time? Of course. Look, for example, at a body moving in—say—a body in free fall. Fine? Then its x is one-half g t-squared. g is gravitational acceleration; five t-squared, doesn’t matter—that’s what physics says, five t-squared. Yes, for every t. At t equals one it is at five; at t equals two it is at twenty. t-squared times five. Okay? Now what is its velocity? Differentiate it. The velocity is ten t. Fine? So at every t, every point of t—plug in t equals one, the velocity is ten. t equals one and a half, the velocity is fifteen. t equals a discrete point—you get a velocity. And it’s different at every point from the velocity at every other discrete point. Meaning, there is velocity at a point. The problem is just that we have no way of calculating it. And therefore there is an operational definition. The operational definition tells you: take a small interval around the point and see how long it took to traverse that distance, divide this by that, and in the limit as it goes to zero, that’s the velocity you get. Okay? But in the end you got a velocity at a point in time, not over an interval. You needed the interval only in order to calculate the velocity. Therefore the definition of delta x over delta t—the infinitesimal definition—is an operational definition. It’s a definition of how to calculate. But velocity itself is defined at a point. We calculate day in, day out—every physicist knows this—we calculate all the time what the velocity of a body is at a discrete moment of time, and at every moment of time. It’s just that in order to calculate it we need to resort to some interval around the point. Okay? Therefore it is a mistake to think that a body has no velocity at a point; that is Zeno’s mistake. A body certainly can have velocity even at a point in time. It is there, and it has velocity—ten meters per second. True, if you want to see that it traverses ten meters and that takes one second, you’ll need to wait a second. At a point in time you won’t see that, because velocity is the potential for a change in position. But velocity does not require an actual change in position. Velocity means I have a potential to change position. But the change in position itself does not necessarily happen, or will happen only after you wait some time—not at a point in time. At a point in time the body cannot move, but it can have velocity. That is the important point. And therefore Zeno’s arrow paradox is a mistake, because Zeno thought that a body cannot have velocity at a point in time. Okay? And of course it can. It is in that place and not standing in that place. It is in that place and its velocity is such-and-such. How will you see that? Wait another moment and you’ll see that it is in another place, at another velocity. That will be the actualization of the potential it had at the earlier point to change place. That potential is called velocity. Velocity is a potential for change of place. Fine? And the potential exists at a point in time. The actual change of place you will see only if you wait over an interval of time. Okay. And where do you stand on the point here? The point stands. Where are you measuring it? No, what are you talking about? If I stand at a point, it still has velocity. It passes by me. What does that have to do with it? No, if you’re on the road. Ah, if I’m moving at the same speed as it. Fine, then our relative velocity is zero. I’m speaking now when I stand still, not when I move with the point. Fine. So how does it actually move between t and t plus one? Like, in the tiniest possible interval of time. Okay, there is no smallest interval, of course; there is the density theorem. But fine, so how does it move from moment to moment? What do you mean, from moment to moment? It moves at that very moment, not between moments. At every moment it is both moving and being there, not also standing. Both moving and standing is a contradiction, but both moving and being there is not a contradiction. It is in motion. It is in motion every moment. Velocity—that’s the point—velocity is not change of place. Velocity is the potential for change of place. As a result of your having velocity, the potential is actualized in the form of change of place. But velocity is not change of place. For example, think of a body moving at speed and meeting a wall. A physicist—you ask a physicist what the body’s velocity is at the instant it strikes the wall—zero, right? But according to what I’m saying now that isn’t true. It has some velocity v—say an ideal wall that stops it in an instant of time, yes? That doesn’t happen, but suppose. Fine? It basically has velocity v, the velocity with which it arrived; it just doesn’t succeed in actualizing it. It has the potential for change of place, but it doesn’t succeed in actualizing it because the wall doesn’t let it. But that doesn’t mean it has no velocity; it has velocity. It’s only that the change of place won’t be the actualization of that potential. How will it be actualized? Either it will move backward if it is elastic, or it will emerge as heat if it is plastic, or it will come out in some other way. So here is another indication that velocity is not change of place. Velocity is the potential for change of place. Usually it comes out as change of place—that’s how the potential is actualized—but not always. How does it come out into actuality? What do you mean how? When you have a potential to change place, then there is the change of place. What happens between… The actualization of the potential. I don’t understand the question. What do you mean, how does it come out? It comes out into actuality. To have velocity means in the end to change place, and that’s the result. What answer do you want to that “how”? No, the “how” is that there was energy in it at the beginning, someone… No, how it happened that it has velocity—that’s fine, it got some energy. But now he says it already has the energy; how does it move to another place? That is the meaning of having velocity—that it moves to another place. What was Rabbi Sheilat’s criticism about the point? No, it doesn’t matter, I don’t remember exactly—it appears on my website. It was about one of my books in the trilogy, I think, and I argued that he was mistaken there. Where were we? Okay. So what I want to say, basically—yes, think, for example—there is another proposal for solving the arrow paradox. Earlier I formulated it via infinitesimals. Now I’m saying the infinitesimal is not a solution. I’m saying the opposite: what I explained here explains the infinitesimal, not that the infinitesimal explains this. Meaning, this is why the infinitesimal can tell you about properties of a body at a point even though you need an interval to calculate the property—because of what I just said. Because the property is not what you calculate; what you calculate is only the operational definition of the property. Fine? There were proposals to solve Zeno’s arrow paradox on the basis of the uncertainty principle in physics, not in mathematics. The uncertainty principle basically says that a body cannot have a definite position and velocity simultaneously—a definite position and velocity at the same time. That’s quantum theory. Fine? Now if that’s the case, then everything is fine. You cannot talk about the body standing at a point, because you’re basically saying its velocity is zero—you know both the velocity and the position. It’s impossible to know both the exact velocity and the exact position of a particle simultaneously. Why is zero not data? Zero is data, therefore impossible. No, the opposite: impossible. If you determine that it is zero and it is standing here and its velocity is zero, you have done something contradictory in quantum theory. Because velocity zero is also a velocity. It cannot be that you know both the velocity and the position simultaneously. Therefore you cannot talk about a body that stands. I freeze it in time. No, no, not freezing it at a point in time. When I say it stands—no, you can’t say that a body stands at a point in place at a point in time. Why? Because then you know both its velocity and its position, and quantum theory forbids that. It can’t be—if you know the velocity, you don’t know the position, and vice versa. It doesn’t matter; it’s a principle in quantum theory. I think about it—everything is moving all the time, not just the arrow. Doesn’t matter. At every point it stands, exists—good, I said not stands, fine. But now I’m before the solution, because now I’m back to the question. What was Zeno’s question? That at every point it stands in a different place. It moves, but at every point it stands in a different place. Quantum theory says: there is no such thing. A body that at a point stands at a point is an illegal sentence in physics. There is no such thing. Because you cannot know both the velocity and the position simultaneously… not all velocities… not any velocity, whether zero or ten, no matter what velocity. You cannot know exactly its velocity and its position simultaneously. That is the uncertainty principle of quantum theory. Small particles that can be measured… the arrow talks about something small; it talks about a point. Doesn’t matter that there are lots of points making the arrow; let’s talk about one point in the arrow. Right? A wonderful explanation. The only problem is that it suffers from the same issue. It’s an English-English dictionary explanation. Meaning, you explain one principle I don’t understand by another principle I also don’t understand. How does that help me? It puts my mind in order. It puts it in order, but it’s not an explanation on the philosophical level. You’re explaining to me that it’s true. I know it’s true; I don’t need quantum theory for that. I know arrows fly. For that I don’t need quantum theory. I’m only asking what Zeno’s mistake is. You say Zeno’s mistake is quantum theory? Quantum theory I also don’t understand—and it’s also mistaken—so how does that help me? I want to argue that my explanation also explains the uncertainty principle of quantum theory. I’m going the other way around. I’m not using the uncertainty principle to explain the arrow paradox. After I understood the arrow paradox, I understand the uncertainty principle of quantum theory. Because what I actually want to say is that in order to measure velocity I need some interval. I cannot measure velocity at a point. That does not mean there is no velocity at a point; it means I cannot measure velocity at a point. Okay? And that is, for example, a possible explanation of the uncertainty principle. Fine, one can still discuss it further; it’s not so simple because it assumes assumptions that are not obviously true, but never mind, that’s not our subject. Why am I saying all this? Because it basically means that we have some kind of problem describing dynamic processes. Dynamic processes, meaning like velocity, like motion of a body, like lots of things like that. We don’t know how to describe them. How should I describe this problem, and what do we do? Basically, think of two things—say, how do you create a movie? In a movie I see things happening, people walking, cars driving. You photograph static images, right? Frames like that, and you project them at a very high frequency one after another, and that basically creates some sort of illusion of dynamism in my head. But in fact it’s all static frames, right? Meaning, we really have no way to see dynamics. The dynamics are in our head. In the world there is only statics. Meaning, I see static images one after another and my head performs some kind of integration on them and turns them into a dynamic process, right? Meaning, we don’t know how to deal with dynamic things. We deal with them through slices, yes, through static slices, the denser the better. Like in cartoons. Yes, exactly like cartoons. In cartoons it’s more obvious, but it’s true in non-cartoon films too. From the sensors you get these snapshots, and the brain then connects them. Exactly. The brain connects the snapshots and creates from them a dynamic process. Now let’s go to the opposite side. What happens in reality itself? In reality itself what I want to argue is that there actually are dynamic processes. The statics are something we impose on reality. Meaning, in reality itself the body moves. It has velocity at a point in time, but we don’t know how to work with velocity at a point in time. So what do we do? We perform a calculation: we take an interval of time and calculate difference in position over difference in time and produce the velocity. Do you understand that what we are basically doing is taking the static slices and trying to reconstruct from them the dynamic process exactly as our brain does, right? We receive a collection of photographs and the brain produces a dynamic process from them. That is exactly what we do in infinitesimal calculus. And why? Because our perception is limited; it is static. Our eyes see a state. They do not see motion. Motion is created in the head when we see many states changing before our eyes, but each individual perception is perception of a state. It is not perception of… We have no way to grasp dynamics, and therefore we created infinitesimals. Another creature could have existed—not a human creature—that sees only dynamics. It would have had to produce statics by means of integrals, just as we produce dynamics by means of derivatives. It would start from dynamics and produce statics with integrals. It would not understand what it means to see states; it sees only dynamics. Okay? Think, for example, of—yes, today we’re philosophizing, but I think these are interesting things and they’re important for our purposes too. Think, for example, of police radar guns. There is police radar that works through the Doppler effect. The Doppler effect is that you send an electromagnetic wave to a car—or a moving body—it comes back to you and there is a slight difference in frequency. The difference in frequency between the wave you sent and the one that returned is proportional to the speed of the car, and that’s how they measure the speed of cars. Now on the face of it, this isn’t really precise, but only for illustration. On the face of it, that is a measurement of velocity at one instant. The wave hits the car at an instant and returns, which means I manage to measure the speed of the car at a single instant, unlike what we usually do, where we need to watch it moving, see how much distance it traversed and divide by how much time—we need to use some interval, maybe small but still an interval. Here one encounter at one point gives you the velocity. So that’s a fanciful indication—but never mind—of the idea that velocity is a quantity that exists at a point, but we don’t know how to work with that. Our senses don’t work that way. Therefore the brain does some sort of integration of the senses and creates dynamic processes. We do not know how to grasp dynamic processes. In quantum theory, whoever knows this, by the way, there is a distinction between the momentum picture—the velocity—and the position picture, and they don’t talk to each other; they are orthogonal. Fine? The position picture is basically looking at the world in the way of a camera. Every time you take a picture, you see where each thing is. But a camera doesn’t know whether objects are moving—think of a camera with exposure time zero. Then it captures the state; it has no idea which object is moving and which isn’t. It only knows that it is there. Since exposure time is never really zero, you see a trail if the object is moving. But if the exposure time were zero, then we wouldn’t see whether the object was moving or not—we’d only see where it is, right? Now let’s imagine an ideal movie camera. An ideal movie camera is one that sees the velocity of every body, but has no idea what its position is. We can’t imagine this because our minds work with cameras. Therefore we need all the movies with the frames and so on. Okay, but in principle we can speak of such beings. Beings equipped with a movie camera would see velocities and not positions. Beings equipped with cameras would see positions and not velocities. And the uncertainty principle simply says that a person cannot look at the world through a camera and a movie camera simultaneously. Either you look through a camera or you look through a movie camera. You can’t see both together. That is basically the uncertainty principle. Okay? So what does this mean? That we as human beings have difficulty grasping dynamic processes. I have to define them through static states. When I want to know what is happening dynamically at a certain point, I must create an interval, know what happens on one side of the interval and what happens on the other side, and make some kind of interpolation between them in order to see what the dynamic quantity I’m interested in actually is. Okay? Now think—let’s return to giving a get, because in the end this connects there too. I want to argue that if we wanted to define giving a get, since giving is a dynamic action, our definitions will always be through the state before and the state after. For example: it belonged to the husband and afterward he transfers it to the woman, meaning that in the end it belongs to the woman. Or: it moves from the hand of the husband to the hand of the woman, meaning that before the giving it is in the husband’s hand, after the giving it is in the woman’s hand. All these definitions are definitions that try to grasp a dynamic concept through static endpoint states. And you can’t do it. That’s exactly the point, because we are talking about something dynamic. The endpoint states can at most give some perspective on it, but in the end that will never really be it. We will have to remove it by inscribing through hollowing out. We’ll have to remove all the definitions through states, because definitions through states are static definitions. And when I want to define what a valid giving of a get is, I am trying to capture a dynamic process. A dynamic process cannot be defined by means of states, which are static things. So therefore what we do basically is we try to define the state at the beginning, the state—derivative, yes?—and then Zeno’s paradox comes and says, wait a second, but it can’t be that the derivative is the definition. Because if the derivative is the definition, then what is the velocity at a point? For velocity you need an interval. And then I say—ah, suddenly I understand that this is only a tool that helps me calculate something, but when I want to speak about the thing itself, I have no way to speak about the thing itself. I need to remove this tool, the derivative, the static states, and understand what remains after I have removed them. And that is exactly the study of inscribing by hollowing out. Therefore I think it is not accidental that it appears precisely in topics of giving a get. It appears in topics of giving a get because we are trying to define a dynamic process. And to define a dynamic process is always done through static states, because that is how our thinking is built. But you cannot define a dynamic process through static states. At most that is an operational definition, but it doesn’t give me the thing itself, as with velocity. Right? Think, for example, about a factory. Many times people say that change in a factory helps it. It refreshes people; they make changes in the processes happening in the factory. Now notice, the content of that statement is very interesting. Because if you make a change in the sense that it simply increases output—meaning, you streamlined some process—that is trivial. Of course, we all know that if you increase output then you have made the factory more efficient. That’s no great insight. When people say the statement I said earlier, they mean something else. The very fact that you make a change, even if you didn’t increase output, has done something to the factory. Now do you understand that this basically means that the change you made is not measured through the state of the factory before and the better state after? Right? The very fact that I am in a dynamic process, regardless of where I came from and where I end up, itself does something good for the factory. Now regardless of whether that’s true or not, I only want you to notice that that is what this sentence says. And that sentence basically says that I measure the benefit to the factory not through the state before and the state after, but through the very being in a dynamic process. The very fact that the arrow is at a point in time—it is there in velocity, it has some other quality—even though at a point in time you won’t see it changing position. But it has some other quality. Standing and being there are not the same thing, even at a point in time. Fine? And the way to become aware of this is only through inscribing by hollowing out, only through negative attributes. Because we have no way to grasp the dynamic process positively. Exactly like in film—we actually create the dynamics through hollowing out. We say: static, static, static, static, at a very, very high rate, and we understand that it’s not static; we remove the static dimension, and what remains for us is actually some kind of dynamics, even though what was presented to us was nothing but a collection of static things. This is basically creating dynamics by inscribing through hollowing out. Okay, that’s the claim. Okay, so we’ll stop here at this stage.