Platonism – Lecture 15

[Rabbi Michael Abraham] The motion of the train, but that’s not a force. The train carries it at that speed. Force… okay, fine. There’s room here to quibble a bit. The principle is this: if a body has—think about the planets revolving around us, okay? Those planets move in a circle all the time. Abraham our Patriarch asks: who turns the spheres? And from that he reaches the conclusion that there is God. Once in Yeruham, on Simchat Torah, Rabbi Blumentzweig brought this midrash, I think. So I told him that I never understood that midrash. You don’t need anyone to turn the spheres; that’s Newton’s first law. If they keep moving all the time at the same speed, then that simply means they keep going like that all the time; you don’t need someone acting on them for them to move at a given speed. Of course, you need a force toward the center for the motion to be circular, but on the fundamental level this doesn’t create any need for some external being to act on the system. It’s a system moving at the same speed all the time. In any event, for our purposes—now when I ask the question, fine, so that’s Newton’s first law. Now I want to measure it, right? To observe a body behaving according to Newton’s first law. The question is: how do I do that? And the answer is: there’s no way to do it. None. No body from the creation of the world until today has ever moved in uniform straight-line motion all the time. Why? Because there is no body in the world on which some force is not acting. However small its magnitude may be, some force is always acting on it. Therefore there really is no body moving in uniform straight-line motion. So what does that mean? Seemingly it means the law doesn’t deal with our world at all; it isn’t an exact law. Since it never really works. Okay? If I nevertheless want to observe it, at least approximately, I need to create some kind of laboratory. That’s what laboratory experiments are. I create a lab in which artificial conditions prevail. What does that mean? Conditions that somehow mask all the forces—no other objects inside the lab, some total vacuum, temperature zero if you like, nothing is supposed to interfere. In that almost hypothetical laboratory, a body that moves will move in uniform straight-line motion. If I manage to create such a lab—and it will never be exact, because there are always some effects of force, or friction, or the vacuum isn’t absolute, and so on—but at least it will be close.

Contrary to the common image, by the way, a laboratory situation does not come to imitate the world; on the contrary, it comes to detach itself from the world. Meaning: in the world itself, the laws of nature do not work, ever. When I want to see the laws of nature at work—and for the experiment to succeed as well, which never really happens—then you need to create a lab that is specifically removed from natural circumstances, from the ordinary natural state of the world out on the street. You need to create something that is sometimes very, very sophisticated, very, very artificial, with all kinds of things that neutralize phenomena that appear in the real world. You create a fictional world, a hypothetical world, a world unrelated to the real world, and maybe there you’ll succeed in seeing the law, the law of nature, in its purity—relatively in its purity; it’s never perfect, but relatively in its purity. Meaning: in order to see the law, you have to move away from the world. The law doesn’t explain the world; the law exists only in a reality that has nothing to do with the world at all—a Platonic reality, a different reality, a fictional one, unrelated to the world. Okay?

The same thing if I want to observe the effect of gravitational force, yes? We know that every two bodies—two objects with mass—exert on each other a force, gravity, Newton’s law, okay? Newton’s law of gravitation, not one of Newton’s three laws of mechanics. So two bodies with mass exert gravitational force on each other. How can I—and there’s a formula for this force, right? One over the square of the distance. How can I measure that law? There’s no way. Because whenever I check a real body in our world, all kinds of other forces will also act on it, not only the force exerted by that specific body that I want to measure. There are others. Think of the solar system. I want to measure what force the sun exerts on the earth. That will never be exact, because all the other stars also exert force on the earth. Therefore it will never really be Newton’s law of the sun versus the earth in its purity. And summing up all the forces from all the stars—that’s impossible. Therefore there is no real way to compare the results of the experiment with the theoretical statements, with the theoretical law. There’s no way. I can create a situation in which it is approximately true. If the sun’s influence is very strong and the others are weak, then I assume it’s more or less only the sun’s influence, and then I assume I’m more or less measuring the sun’s gravitational influence. But really, if I wanted to do it, I would have to remove all the other stars, leave only the sun and the earth, remove the air and all friction and all the other things, and then take measurements. Maybe at zero temperature too, and only then take the measurements. Of course, that can never be done. And therefore, in the real world we are always condemned to such approximations. Meaning: to some situation in which the laws of nature do not really operate in their pure form.

Until now I’ve talked about laws in physics, but this is also true of laws in other fields. Let’s take the one law that exists in the social sciences. Right, this is the joke I always tell in these contexts. It’s not a joke—it’s a report from my sister. My sister studied criminology at the university. She told me that every course began with an introduction on what science is—falsifiability, Popper, and so on. I told her: I don’t know, I studied physics, and no course dealt with the question of what science is. Meaning, none of the lecturers cared. Which of course means that there are fields where you need excuses to explain that they are scientific, and there are fields where it’s self-evident. But another story she told me: she said her lecturers would try, as it were, to talk about some topic, and then they’d say they were trying to demonstrate some law, right, a law in psychology or criminology. Then they’d say: let’s take, for example, the law—and then they’d pause to think which law to focus on. For example: frustration and aggression. The relationship between frustration and aggression. But it was always frustration and aggression. Meaning, there was no other law. He’d sit there thinking as though he had thousands of laws he was teaching: oh, you know what, let’s take the law about frustration and aggression. But it was always that one. There was no other law. It was the only law there.

Now think about that law. What is that law? That law basically says that a frustrated person tends to behave aggressively. There is a connection between frustration and aggression. Of course, this does not mean that a person who is not frustrated won’t react aggressively, and it also doesn’t mean that a frustrated person always will. Sometimes a non-frustrated person will react aggressively, and a frustrated person will not react aggressively. There can be exceptions in both directions. Fine? So in practice it’s very hard to see the appearance of this law in the world, because in the world itself, suppose the person was frustrated and you saw that he didn’t behave aggressively. Do you throw the law in the trash? The answer is no. It could be that something else intervened and he decided to restrain himself and not behave aggressively. That does not mean that the law establishing a connection between frustration and aggression is wrong. It means there are other influences in the world that can interfere with the appearance of this law. Okay? Just like in physics. The law of gravitation is true, but there are other influences—other gravitational fields, or laws, electromagnetic forces, or whatever, friction and so on—that can interfere with the appearance of the law, and therefore the law does not describe reality accurately, because in reality there are all sorts of other influences besides the factor the law deals with.

So with frustration and aggression, for example, a person who was brought up well—even if frustrated—is not aggressive, or is less aggressive, because education is also a parameter. Frustration alone does not determine aggression. Education also has an effect; that’s friction. The parallel to friction in physics is education in the world of psychology. Just replace the first letter. So the claim is that the scientific law, the general law, does not accurately describe the world. Ever. Now, many people draw the conclusion from this description—or before that: meaning, there too, if I wanted to see the law in its purity, I would need to create a supposedly clean laboratory situation, to raise a person with no education. None. From the moment he leaves his mother’s womb, give him no education at all. Let him meet no people, let him do nothing. And then measure him with no other influences, nothing. Make sure he’s not tired and not irritated for other reasons and nothing else. Take him, frustrate him for some reason, and then see whether he reacts aggressively. There maybe one could test the law that links frustration with aggression. Of course there are other ways to do this—you take many people and assume that in a large group the other influences cancel out, and then what remains is only the effect of frustration. Right, there are various ways to get around this. But in any situation you see in the world, the law never appears in its purity. The law does not describe the world correctly; it is a kind of approximation.

That brings me to the next stage. Many people think, because of these descriptions, that the reason the law doesn’t describe the world exactly is because the law is not exact. The law is approximate; it is not an exact law; we cannot arrive at exact descriptions of… But the law of nature is absolutely exact. Again, under the optimistic assumption that we have arrived at the correct law of nature, because maybe we made a mistake. But in principle, the fact that the law does not accurately describe reality in the world does not mean that the law is not exact. It only means that in our world there is a combination of several influences, or several laws of nature, and what happens in the world is the result of all of them together. Each of them is completely exact. It’s just that in our world a single law of nature never appears alone, without the influences of other laws. Therefore it’s not because the law is wrong, but because reality is complex. Complex reality means a reality whose circumstances are governed by a system of several laws, not just one law. So besides Newton’s first law there is also friction. And besides the relation between frustration and aggression there is also education. And that too is a law of nature: someone who undergoes such-and-such education will behave in such-and-such a way. And there too, of course, there can be criticism, because education doesn’t always work deterministically. But there too you can explain it: yes, because there are influences besides education. Bad company, good company, classmates, trying to impress, whatever—various other reasons; not only education shapes a person. So you see it’s the same idea.

Meaning, there too I can say education shapes a person, and the science of education is an exact science. Everything is completely exact. Why in reality is it much more complex and never seems to work? Because in reality there are all sorts of other laws, each of them completely exact, but when they work together, none of them appears in its purity. And therefore we can’t really measure theoretical laws of nature—our theory—in reality. What do we do in order to measure them in reality? We build a Platonic world. In scientific language that’s called a laboratory. A laboratory is basically building Plato’s world of ideas. And what does that mean? I build a world in which there are no other bodies, no friction, zero temperature, no air, absolute vacuum; there are only the two bodies that interest me. Or a world in which there is no friction, no society, no environment, nothing—only frustration, and I want to see whether aggression emerges. And so on. In a world of that kind—which of course never exists in our world, it’s some hypothetical world—in that world the scientific law is exact. It ought to be, if it is true. If it doesn’t come out exact, then apparently the law is wrong and should be thrown out. But assuming the law is a correct law, then in the laboratory, in the Platonic world of ideas, it will work exactly. That does not mean that in our world it will work exactly; on the contrary, it usually won’t. But the criterion for whether a law of nature is right or not is not the experiment in our world—sorry—it is the experiment in the lab, the experiment in an abstract, pure, hypothetical Platonic world. There I check whether the law of nature is exact. If it is exact there, then it is exact. And now we have to see how we apply it to our world.

Why am I interested in laws that deal with Platonic worlds? Because in the world—Platonism here, and Aristotle too—this is not the difference between Aristotle and Plato, because at the methodological level Aristotle too would say the same thing. The law deals with a Platonic world. Aristotle does not recognize the existence of an actual Platonic world, and therefore he would say this is a world that doesn’t really exist; we merely create it in our imagination because it helps us analyze our world. What does that mean? Our world is complex. It has all kinds of aspects. You can describe it as some point in a coordinate system. That point has a projection on each of the axes. Think of a Cartesian system of three perpendicular axes: x, y, and z. There is a point somewhere in that space. That point has a projection on x, a projection on y, and a projection on z. Okay? Each of those projections is a projection on one axis. The point itself is not on the x-axis, not on the y-axis, and not on the z-axis. It has three components. It is somewhere in space, or at least can be. So it has three components. Likewise, every situation in our reality is a situation in which all kinds of laws of nature are operating. You can see it as a system of several axes describing our situation, and our situation combines various laws of nature. This law of nature and this law of nature and this law of nature together—their joint effect produces the behavior of what actually happens in the world.

But in order to understand the x-axis separately, the y-axis separately, the z-axis separately, you need to create a fictional world that is one-dimensional, not three-dimensional—a world in which there is only the x-axis. In a world where there is only the x-axis, the x-law will work in its purity. In a world where there is only the y-axis, the y-law will work in its purity. What happens in a world where there are three laws, three axes? Then there will be a combined effect of the three laws. By the way, if it is linear, as in mechanics, then you really can analyze each component separately: the x-component acts separately, each Newtonian law works on each component separately. In the end, though, you need to describe all three components in order to describe the motion in space. And there are situations that are non-linear, and then the x-component affects the y-component and vice versa. You can’t separate variables. Once you can’t separate them, all the components operate together, and then something non-linear—chaos—can emerge in such systems, and so on. That’s much more complicated. But on the principled level, the combination of each of the theoretical laws of nature—the pure, abstract ones—in our world will give us the behavior in our world. Each such law of nature by itself describes behavior in the Platonic world: pure, abstract, in which a certain form appears in its purity and nothing else interferes with it.

Think about horseness, right? The concrete horse is a horse that sometimes limps a bit, and isn’t perfect, and is a little too fat, and is missing part of an ear, all kinds of things like that. The perfect horse—the idea of horseness in the Platonic world of ideas—that is horseness itself, in its purity. In our world, beyond the fact that you are a horse, you also live in a certain environment, and there is also a tiger there that tore off half your ear, and all kinds of things of that sort. Therefore horseness will not appear in its full purity in a concrete horse. In our world, the ideas always appear flawed. But that says nothing about the ideas; the ideas themselves are perfect, and one can understand them beautifully. The value of this, at least methodologically, is that the ideas are projections or components of our reality. In our reality there is a brown horse-object. So I need the idea of brownness, the idea of horseness, and the idea of being preyed upon—he was also preyed upon. Okay? And if I understand each of those separately, I can try to analyze what is happening to the concrete horse before me. Dealing with complex reality itself is usually very complicated, and there are no laws that truly govern it directly. I need to break it down into its components, discuss each component as though it exists alone in some Platonic world, find the law of nature that governs that component, and then return to our world, put all the components back together, and try to understand what happens in the real world—which is always a combination of all the influences. Then, of course, we are never fully exact, but that is the general direction.

So in short, in order to understand a situation in the real world, we have to break it down into its components. For each component, we perform some kind of abstraction, take it into a Platonic world, understand it separately. After we have understood each of the components separately in the Platonic worlds, we bring them back here and try to understand what happens now in our world when all of them together affect the situation. Meaning, the laws of nature do not deal with our world. They deal with pure Platonic worlds. Aristotle will say that this is a theoretical abstraction; there are no actual Platonic worlds. We perform an abstraction and discuss some world in which there are only two bodies and nothing else—zero temperature, no friction and nothing. That is an abstraction we perform; there is no such world. Plato claims there is a world in which the law of gravitation appears in its purity—a world of gravitation. The idea of gravitation appears in a world that is a two-body world, that’s it, that is all there is in that world, and there it appears in pure form. Therefore, the difference between Plato and Aristotle is the question whether this world exists. But Aristotle too, on the methodological level, agrees—or ought to agree—that the way to understand our world is by way of Plato. Meaning, I need to construct laws that deal with Platonic worlds, and only afterward return to our world. The dispute over whether Platonic worlds really exist or do not really exist is a different metaphysical philosophical dispute, but as for the methodology of science, there ought not to be any dispute. Platonists and Aristotelians will grasp it in exactly the same way.

Now, I want to explain this a bit more: what does the transition to the Platonic world mean? Think, for example, about a horse. Right, let’s go back to our horse. This horse has many properties. It has legs. It has, of course, four legs, a head, two ears, a certain brown color, height, weight, who knows what, beauty, all kinds of parameters, age, all kinds of parameters this horse has. Now if I want to clean away the irrelevant parameters and talk about the ideal horse, about horseness, okay? Later on I’ll say more about the difference between an ideal horse and horseness; they are not the same thing. The idea of horseness is not an ideal horse, but for now I’m ignoring that. That created paradoxes; for Aristotle it created a paradox regarding that identity. That identity is mistaken. In any case, the claim is: how do I get there? I’m supposed to strip away from it all the irrelevant properties of that horse. For example, I’m not interested in the fact that it lives at such-and-such an address; that contributes nothing to its being a horse. It’s not a different kind of horse, the horse that lives at this address rather than that one. Its height too, at least within some range, is irrelevant. Horses have a certain range of heights—fine, this horse has one height, another horse has another height. Height contributes nothing to the idea of horseness. The idea is a collection of components—yes, I spoke about this, I’m obliged to.

The idea is basically the equivalent of a definition. What is the definition of an object? The definition of an object is taking only its essential characteristics, the characteristics without which it would not be what it is. For example, I can define a Jew as a person who wears pants, has a nose, and is also born to a Jewish mother or converted according to Jewish law. But that is not really a successful definition. Why? Because inside that definition there are properties that are not essential to his being Jewish. He wears pants, he breathes—every person is like that, not specifically a Jew. In the definition of the concept Jew, I need to include only those characteristics that are essential to his Jewishness: born to a Jewish mother, converted according to Jewish law, something like that, okay? So the definition gathers the set of essential characteristics. In order to get from the specific Jewish person standing before me to the Jew in his ideal definition, to the idea of the Jew, I need to strip from him all sorts of properties that are concrete: that his address is here, that his father and mother had such-and-such names, that he is such-and-such age, that he has a certain disability or doesn’t, that he looks this way or that way—all that is irrelevant. It has nothing to do with his being Jewish.

By the way, one of the common mistakes—and it always irritates me—is that all kinds of self-righteous people ask why in the conversion process we don’t also test the moral dimensions of the convert’s behavior: that he doesn’t murder, doesn’t steal, honors his parents. Why only that he eats kosher and keeps family purity? What is the meaning of this emphasis on ritual commandments and neglect of moral commandments? The answer is very simple—and that is exactly how it should be done. Why? Because when I want to check whether the convert really wants to become a Jew, or has become a Jew, I need to check the aspects that are essential to his being Jewish. To say that we should check that he doesn’t murder is irrelevant; every person is not supposed to murder, not only a Jew. To check that he honors his parents—every person should honor parents, not only a Jew. So I cannot define a Jew as a person who honors parents and does not murder. True, he should honor parents and not murder, just as he also wears pants. But wearing pants is not a parameter that belongs to his Jewishness; it belongs to his humanity. Therefore, if I want to test the definition of his being Jewish, I need to take those norms, those commandments, that distinguish him as a Jew, that a gentile is not supposed to do: that he eats kosher, family purity, things of that kind. There his Jewishness is measured.

And again, not because eating kosher is more important than murder, or because eating non-kosher is more severe than murder—certainly not. Murder is one of the prohibitions about which one must die rather than transgress. It’s not a question of severity; it’s a question of uniqueness and essentiality. The question is whether it is essential to his being Jewish or not essential to his being Jewish. Whether it is important or not important is a completely different question. Therefore, when I test the convert in the conversion process, I will test him on eating kosher and family purity, and not on murder and honoring parents. Not because murder and honoring parents are less important, but because murder and honoring parents are less specific, less essential to his being Jewish—or not essential at all to his being Jewish. If he is a Jew who murders, then he’s not a human being, not that he is not a Jew. So it is irrelevant to test him there. I am not coming to check whether he is a human being; I am coming to check whether he is a Jew when I test the convert. Therefore this claim simply fails at the logical level. It is not a dispute in worldviews about how I understand morality and all sorts of things of that kind, as often… That is how it looks. These criticisms always come from the left, right? Why are you busy with family purity and eating kosher and not with morality? And the answer is: this has nothing to do with left and right, it has to do with logic. The left is generally a bit weak in logic, if I may remark—but that’s only a wicked little aside in parentheses.

The point I want to make is that a definition is the set of essential characteristics of a thing. It has other characteristics; they are non-essential characteristics. They do not enter into the definition. Now when I want to take a horse and abstract it and arrive at the horse—to the idea of horseness—I need to strip away from that horse all the non-essential characteristics. Try to look at a horse as though it has no color, no height, no age, nothing. What does it have? It has only the structure essential to a horse: four legs, two ears, the ability to gallop, I don’t know, however you define the essential properties of a horse. That is what creates the ideal horse or the idea of horseness. I need to perform an act of abstraction. Why is this called abstraction? Like taking off clothes. I need to strip away from it all the non-essential features, all the garments, and be left with horseness itself. The concept of abstraction, as we’re used to it, is exactly like undressing; it is stripping away properties.

Now understand what such a process of abstraction really means. In information theory there is a tradeoff, or uncertainty principle, between the amount of information and the size of the set: a constant product. Think, for example, of Ben-Gurion. Fine? Suppose I say: Ben-Gurion was the first prime minister of the State of Israel. I have described Ben-Gurion. What happens if I abstract away the property of Israel? The first prime minister of a state, not necessarily of Israel. You understand that I am now talking about more people, not only our Ben-Gurion, right? Meaning, if I remove a certain characteristic, what remains refers to more people. Right? And if I remove another characteristic: the first prime minister—not of a state, just a first prime minister, maybe of a city, an island, a continent, I don’t know exactly what—not only a state. So I abstracted away not only Israel but also state, and then it becomes first prime minister in general. Now I abstract away first. I am left only with prime minister. So of course that means even more people, right? Every time I abstract away another property, what remains fits more people. Then I say: he is a head, without government. He is the head of some body, not necessarily a government—still more. Then: he is a member of a body, not necessarily the head of that body. You understand that you can continue this process of abstraction quite a lot.

What happens in this process of abstraction? The amount of information keeps decreasing. As I remove more and more items of information, more and more characteristics, I am left with less information. Once I am left with less information, it is relevant to more entities. Right? If I speak about the head of some body, that’s many people. If I speak about a prime minister, that’s fewer people. First prime minister—fewer still. First prime minister of a state—fewer still. First prime minister of the State of Israel—that is already one person only. Okay, so the more information I add to the idea or the definition, the more I narrow the set of people to whom this definition is relevant. Therefore the scientific process, by definition, since it is interested in general laws and not laws dealing with some specific individual or object or some specific situation, but rather wants general laws—by definition I have to perform abstraction. When I look at a body moving before me, I do not look at that particular body in those particular circumstances. I look at a general body that has some essential characteristic—say, it has mass. That’s it. I don’t know its shape, I’m not interested in its environment, nothing. I abstract away all those properties. You understand that I now have much less information about the body; I am left only with the relevant information, that it has mass. I removed all the irrelevant information. But you also understand that I am left with a huge number of bodies—all bodies with mass. Everything I now say about this body, I have in fact said about all bodies with mass.

But of course in every concrete body, besides the fact that it has mass, it has all kinds of other properties too, and therefore there will be deviations from what I say about those bodies. In every body, in every situation, the deviations will be different, depending on the body and the situation. But what I say about the pure Platonic body, the body that has only mass—it is not round, not square, it is a point mass—you know the joke: physicists want to understand how a donkey works, so they begin with a point donkey. Let’s assume the donkey is a material point, that’s it. It has no legs, no hands, no weight, nothing; it’s a point mass. I start with that. Afterward we’ll grow it legs and a tail and hands and age and height and weight and color and everything, and little by little maybe we’ll succeed in understanding how a donkey works. But you have to start with a point donkey. Fine, that’s a physicists’ joke, but it’s true—that’s how it’s done. When you want to understand a concrete situation, a real situation from the real world, you have to abstract. You say: the body before me, A, has mass. B, it has color. C, it has electric charge. D, it has a round shape. E, it is located in an environment with other bodies around it, there is friction, there is air, it is going down a slope, various forces are acting on it—many, many things. I don’t know what to do with all these properties; it’s too complicated. I don’t know how to describe the behavior of such a body. So what do I say? Let’s take a body that only has a mass of two kilograms. Other than that it has nothing. It has no shape, no material, no body and no likeness of a body. Fine? But it has a weight—mass—of two kilograms. A point body. That’s what you always study in mechanics. That’s what’s done; it’s not a joke. That’s how mechanics is studied. All of mechanics that one studies is mechanics of a point mass. Well, not all of mechanics—the beginning of mechanics. The mechanics of a point mass.

Now, there is no point body in the world. Every body has some volume. Okay, but still, we speak about a point body, because our laws of nature deal with a point body. There is no such body. Fine. But the property of having mass—I want to separate it from its volume. Let’s ignore its volume and address only the fact that it has mass, and let’s see what that means. So you understand that what this thing says, it says about Platonic bodies in some abstract world, not in our world, because in our world bodies always appear with many other characteristics beyond simply having mass.

So on the one hand, the law of nature says something about a situation very far from our world. The purer the law of nature is, the farther it is from our world. One must abstract away far more concrete properties and remain only with one abstract Platonic property. Abstract point mass. That is a Platonic body; there is no such body, only in the world of ideas does it exist. Okay? On the other hand, this law of nature speaks about all bodies as such, in the dimension of their mass, while ignoring all their other characteristics. The more I abstract away properties, the more bodies I speak about. Therefore, if a law of nature wants to be general, it must be abstract. This is a point people don’t understand. There is a connection between the generality of the law and its being abstract. You have to—there’s no way around it—you cannot state a general law about non-abstract objects. Non-abstract objects are particular objects. Each object stands on its own; it does not belong to a group. There are no two objects that have exactly the same set of characteristics. If you want to say something about a group of objects, you must abstract. You must take a group of objects that share a certain set of properties. They have other properties too, but those I abstract away; they don’t interest me. I want to discuss this. Therefore the process of generalization is inherently tied to the process of abstraction. They are two sides of the same coin. If you want to say something general, you have to say it about something abstract. That is the point I want to make, and that is the Platonic process of scientific generalization.

One second, just one more sentence and I’ll finish the scientific introduction—it took too much time. The way back is of course illustration. Illustration is the opposite of abstraction. Abstraction is taking off the clothes; illustration is making it tangible. Not turning it into something abstract, but turning the abstract into something tangible. Illustration always means inserting more parameters. Therefore, for example, when I give you a parable, when I give you a parable about something, people always say: wait, wait, but in the parable it’s like this and like that—and that is always a mistake. Because a parable, by definition, contains parameters that are not similar to the thing it represents. If it were identical to the thing it represents, what value would the parable have? I want to give you a parable that resembles the represented thing in the relevant parameters I want to discuss. Don’t get hung up on the other parameters that are in the parable, which of course can influence things—but leave them aside, ignore them, because they only interfere. The move from the parable to the represented thing is exactly abstraction. The move from the represented thing to the parable is illustration. Illustration is adding parameters; abstraction is removing parameters. Abstraction involves generalization—it reaches more bodies. Illustration is always going back to one concrete body. One body standing before me that I want to understand.

And science began to advance when it started to understand that we are supposed to deal with abstract bodies, not the concrete bodies standing before us. But if I want to conduct an experiment, an experiment is always done on a concrete body. So I have to create some sort of laboratory envelope so that the experiment will nevertheless resemble a Platonic world. But basically I am talking about the Platonic world. The laws of nature deal with the Platonic world, not with our world. In our world it is always a mixture of many things, and in order to arrive at the laws of nature one has to perform abstraction, which is also generalization—the other side of the coin. Therefore, when someone accuses me, say, of making a generalization—people say, well, that’s a generalization. Here is a very common accusation. Of course it’s a generalization. Every attempt to understand a situation involves generalization. That is how situations are understood. When you offer an explanation for a situation, it will always be an explanation by way of generalization. Therefore, accusing someone who comes to explain something of making a generalization is simply a lack of understanding. To explain means to generalize. Not only is generalization not a flaw in an explanation; generalization is the very essence of explanation. I am making a generalization. True, after I have made a generalization, one must understand that in reality itself, that generalization will not always work. Very often there will be other parameters that interfere with it. Fine. That is indeed a valid criticism. Anyone who takes the Platonic theory and applies it as-is to the world—that is a mistake. But arriving at the Platonic generalization—that is how things are understood. That is how science works. And the moment people understood that, science began to advance. But it is not an accusation. Now look, I’ll give you an example so you can see how this leads us back to ukimta.

[Speaker D] Rabbi, Rabbi. Yes. According to this, does it come out that some law of nature of Newton, or of someone else, was ever exact and operated in the world exactly as it is? No. It never operated, because there were other parameters.

[Rabbi Michael Abraham] Reality in the world didn’t change in that respect; it was always complex.

[Speaker D] If it was correct—if it was ever actually correct even once in reality.

[Rabbi Michael Abraham] No, no. It’s not a question of the time axis. It was correct just as it is correct today. It is correct in the Platonic worlds, not in our world.

[Speaker D] But if, say, an infinite number of other parameters are involved—infinite, not something finite—then basically it was never correct, because if you add all the parameters…

[Rabbi Michael Abraham] Again, again. The number of parameters is unrelated to the time axis; those are two unrelated things. What does “never” have to do with it? If there are infinitely many parameters, then usually what science does is isolate the central relevant parameters and tries to claim that there are many other parameters that are less relevant. If there are infinitely many relevant parameters, you’ll never understand the situation. There is no way to understand it.

[Speaker E] I think it’s more accurate to say not that it is never correct, but that it is never exclusive. Right, exactly. That’s the point. No, but you keep using “it was never correct,” and that creates the misunderstanding that it was never correct. It’s not that it’s incorrect—it is correct. It’s just never exclusive.

[Rabbi Michael Abraham] Agreed.

[Speaker D] No, but that’s what I wanted to ask—that it’s not correct. If there are infinitely many additional parameters, then it was never correct either.

[Rabbi Michael Abraham] Again. Incorrect—no, not “was.” Leave “was” aside; the time axis is irrelevant. If there are infinitely many parameters, then you won’t manage to understand it. But the law that deals with each parameter separately can be completely correct. If it were—

[Speaker D] If it were alone, but it isn’t isolated.

[Rabbi Michael Abraham] Fine, obviously. The law does not deal with our world, but with the Platonic world. That is what the law deals with, not our world. Its correctness is measured there, not here. That is why the concept of statistical science arose. Because statistical science takes into account that there are all sorts of other parameters, and therefore the probability that the law will hold is such-and-such. It’s more delicate, because statistics, simply put, is mathematics, not science. Yes, but—

[Speaker F] It doesn’t deal with the world.

[Rabbi Michael Abraham] You can use statistics to explain things in the world, but statistics is not a claim about the world; it is a branch of mathematics, not of science. Just like algebra or arithmetic—it is mathematics, not science. Even though if you add oranges to a basket, two plus three will come out to five. But the statement two plus three equals five is a statement in mathematics, not in physics.

[Speaker F] Yes, but it explains—the statistics explains what we are talking about.

[Rabbi Michael Abraham] The explanation of the world by mathematics and statistics is a scientific claim, not the mathematics and statistics themselves. They themselves are mathematical. Fine, but that’s a different discussion. So if I return to our topic, what I really want to argue is that the laws of nature are actually dealing with Platonic worlds. Now look, let me show you an imaginary Talmudic passage that I wrote—actually, this is from an article of mine about ukimtas. I wrote a Talmudic passage there. Right? Sears-Zemansky, the mechanics textbook we studied for matriculation exams—today they probably study different books. Look. The book is written in Talmudic style. Mishnah: Every body with mass that is under the influence of another massive body feels a force proportional to the product of the masses divided by the square of the distance between them—yes, Newton’s law of gravitation. Now an Amora comes and raises a difficulty: But many bodies have electric charge, and therefore the force acting on them is completely different from what is described in the Mishnah. The force will not be gravitational force; they are also affected by electric fields in the environment. And there is another difficulty: in our real world there is friction, which also changes the force and acceleration of the body. So in fact the Mishnah is not correct. The Gemara says: ukimta. What are we dealing with here? A body with mass and no electric charge, located in a completely empty world, with no air and no other bodies or force fields. A crazy ukimta. Rava’s ukimta about a bound slave is a joke of interpretation compared to this ukimta. Do you understand? You tell me every body with mass feels a force proportional to one over the square of the distance. What are you talking about? You’re talking only about bodies that have only mass and no electric charge, no environmental influences, no friction, no air, no temperature, nothing. That’s the body I’m talking about. But that’s not what you wrote. You write that every body under the influence of another massive body feels such a force. Every body. So he makes an ukimta. Do you understand why an ukimta is a sensible thing? When we read a physics textbook, nobody even imagines raising this difficulty. This difficulty, right? And therefore there’s no need to make an ukimta, because it’s obvious to everyone that we’re talking about Platonic worlds. There’s no need at all to make the ukimta here; the ukimta is built in. Right, so now Tosafot do ask: And if you say that this is a simplistic generalization unrelated to the real world—where is there a world empty of air and of every other object besides one massive point-object? And furthermore, in Psalms it says, “The whole earth is filled with His glory.” Right, I’m joking a little here. That’s the question people always ask. Now notice, this is exactly the structure of the discussion about ukimtas in the Talmud, except that the ukimtas in Sears-Zemansky are a thousand times wilder than the Talmud’s ukimtas, and nobody bats an eye or says there’s anything illogical here. But in the Talmud everyone tears their hair out in panic that it makes no sense to make an ukimta. I had an argument with my son about—Rabbi

[Speaker D] But there is a difference,

[Rabbi Michael Abraham] Rabbi, but there is—just a second, I just want to finish for a moment. I had an argument with my son about ukimtas. He came with complaints: what do you mean, it’s not logical, what is this, they make an ukimta and so on. In the middle of the argument he made an ukimta to me. I challenged him with a question and he said: no, no, I meant this—he made an ukimta. I said to him: aha, you see? You just made an ukimta. Meaning, we don’t even notice how much the ukimta is an inseparable part of rational, sensible discourse. There’s nothing illogical about it. When I say—just one sentence to complete it, to close the circle so we don’t leave things hanging—let’s return to Rava, for example. Okay? Rava with the bound slave. Fine? Now what I basically want to argue is this: he makes an ukimta on the—right, maybe one more difficulty, sorry, before Rava, another difficulty that Rashba raises. Right, but the Mishnah teaches “every body.” Why are you telling me this only means a point-mass body with no other masses around it and in an empty world and so on? That doesn’t fit the language of the Mishnah. Right, exactly what we ask against ukimtas in the Talmud, correct? Does anyone even think to ask that about Sears-Zemansky? No. Nobody writes the ukimta; nobody is bothered that an ukimta is being made. It’s obvious: Sears-Zemansky is talking about an abstract world, about objects that live who-knows-where—not in any actual place, in the Platonic world of ideas, in Plato’s feverish mind. That’s where they live. That’s what Sears-Zemansky is talking about; he’s not talking about our world. But nobody is bothered by it. And when they come to the Talmud, everyone says it’s illogical—what do you mean, ukimta and all that, disagreeing with Tannaim and so on—nonsense. The Gemara does exactly what Sears-Zemansky does. What do you mean? And here, just one example to finish—we’ll come back to this next time. Rava says that if one places a bill of divorce in the hand of a woman’s slave, it is considered as though I placed it in the woman’s courtyard, and she is divorced. The Gemara asks: yes, but the slave is asleep. The Gemara asks: yes, but then it’s a moving courtyard? So he says: no, the slave is also bound. Ukimta. What does it mean, the slave is also bound? What I really want to tell you is the general principle. The principle says that the slave is the courtyard of his mistress, and therefore one implication is that you can place a bill of divorce in the hand of a slave and that is considered as though I placed it in the woman’s courtyard. The Gemara asks about laws that are not really connected to the slave and his status? That is the Talmud’s novelty. The novelty is the relationship between a slave and his master. And the claim is that a slave is like his master’s courtyard. That is what they wanted to tell us here. They express it through a law, but what they really want to tell me is a principle, a Platonic law of nature. And that law says that the slave is the courtyard of his mistress or his master. Okay? They say it not in the form of a general law but in casuistic form, through a case. Whoever puts a bill of divorce in his hand, the woman is divorced. But they are not coming to tell me a law in the laws of divorce. They are coming to tell me a general principle about the relation between slave and master: that a slave is his master’s courtyard. The Gemara asks: yes, but in property law a courtyard does not acquire if it is a moving courtyard. The Gemara says: fine, leave me alone with your nonsense right now. I’m talking about a bound slave—what do you want from me? I’m not talking here about property law. I’m talking about the question whether a slave is his mistress’s courtyard. And the answer is that he is his mistress’s courtyard even if he is not bound. For property law it’s not enough that he be a courtyard; he has to be a non-moving courtyard. That’s because of property law, but I’m not dealing here with property law. The property laws serve me in order to tell you the general law of nature, that a slave is like his master’s courtyard. That’s the law. This law is true for a sleeping slave and a non-sleeping slave, bound and unbound, and whatever else you want. You don’t need ukimtas for that. The law is always true for every slave. It’s true that in terms of the implications I now want in Jewish law, the application in the world, in a concrete situation—where will this law of nature find expression? For example, that you can put a bill of divorce in his hand. Wait, wait, wait—you’re talking about property law, and in property law a slave is a moving courtyard, so that doesn’t work. Fine, so I’m talking about a bound slave. When I say ukimta, what I’m telling you is: stop confusing my brain. That’s what I’m telling you. Why are you confusing my brain? You don’t understand what I’m talking to you about. I’m talking to you about the relationship between slave and master, not about property law. In property law we know that it has to be a non-moving courtyard—the fact is that you challenged me from there. You know, there is another source that deals with property law. I’m not dealing with property law. I’m dealing with the relationship between slave and master, and that relationship is always true for every slave, bound or unbound, asleep or awake. He is always his master’s courtyard. As for applying this general law of nature to property law—can he acquire by courtyard-acquisition for his master? There he needs to be bound. So if you ask me how this appears in the world—after all, in property law it has to be non-moving—then the slave is bound. Leave me alone now. But in the final analysis I’m coming to tell you a statement that is true for every slave, not only for a bound slave. So there is no room to ask: if you want to tell me a law about a bound slave, why do you speak about an ordinary slave? Say that you are talking about a bound slave. No, because I want to tell you something about every slave, not about a bound slave.

[Speaker G] What did we actually want to say?

[Rabbi Michael Abraham] That a slave is his master’s courtyard. For what matter? What does it mean that he is a courtyard? He’s flesh and blood—what does it mean to call him a courtyard? For what matter—that is already the application question, that’s exactly the point. If you ask me, for property law, then indeed other parameters will appear—that’s already a real-world situation—and they will affect the situation. For example, for acquisition it’s not enough that it be a courtyard; it has to be a non-moving courtyard. But for example, if there is leavened food in my slave’s possession, does that mean I have violated the prohibition of leavened food? A different practical implication. The answer is yes, even if he is not bound, because that is my courtyard. So the determination that the slave is his master’s courtyard is not connected to property law; it is a general determination. The Gemara has a style in which it does not state general laws; it works casuistically, it speaks about cases, about incidents. So in order to tell me that a slave is his master’s courtyard, what it actually says is that if you put something in the hand of the slave, his master has acquired it. That is just a way of saying it, really. But it is not talking here either about property law or about courtyard law. It is only saying: what is the relationship between slave and master? And that is true for every slave, so there is no need to tell me this specifically about a bound slave. As for the application—you want to tell me how he acquires? Ah, there’s a problem, how does he acquire? After all, this is a moving courtyard. So the slave is bound; leave me alone. The moment I said the slave is bound, I removed your difficulty and left the law of nature appearing in its purity. But the law of nature is true not only in this particular case where the slave is bound. I am talking about slaves in general. Neutralize the fact that he is bound; the fact that he is bound is, from my perspective, not an important parameter. It matters for acquisition; it does not matter for the question whether the slave is a courtyard. And a law of nature deals with the question whether a slave is a courtyard, not with the technological applications of the law of nature—whether he also acquires or does not acquire—that is already technology.

[Speaker H] But in the Mishnah there is no hint of any of this.

[Rabbi Michael Abraham] In the Mishnah there is an assumption here—and I’ll get to this next time—that when the Gemara reads the Mishnah, it is clear to the Gemara from the outset that even when the Mishnah brings a case, it really means to bring a general law and not a case. The case is only an example through which the Mishnah presents a general law.

[Speaker H] Okay, but again, I’ll return to it: there is the Mishnah “one who placed the jug.” The Mishnah says that the one who was walking is exempt. In the end there is another approach—no, the Mishnah really is not an ukimta. So there is a dispute whether there is an ukimta or there isn’t an ukimta, and that is exactly the opposite law from what appears in the Mishnah.

[Rabbi Michael Abraham] Correct, right, right, but the law of nature will remain. The general law will remain.

[Speaker H] Every single passage in the Mishnah confuses us.

[Rabbi Michael Abraham] I’ll bring the additional examples I mentioned, two more passages involving ukimtas. I’ll explain it there, and there you’ll see it in a better way. After that I invite you to bring me—to challenge me with—ukimtas from various passages, and usually what people have asked me, I’ve managed to explain all the ukimtas in all the passages.

[Speaker H] I’ll ask next time about “one who placed the jug.”

[Rabbi Michael Abraham] Okay, okay, but just let me present the overall move with the examples so it will be clearer, and after that I think it will be possible to discuss it. All right, at this point we’ll stop here. But—

[Speaker D] If Sears-Zemansky had said it, had spoken in casuistic form, and had said: the sun and its relation to the moon is according to such-and-such a law, then people would have said to him, but that’s not true. Then he would start neutralizing every important detail. In other words, the difficulty is not that there is some misleading simplification here, but that there is really a kind of deception as it were—you’re not saying the main point.

[Rabbi Michael Abraham] I’ll get to that next time, because there is a difference between physics and the Gemara in that sense. In physics it really makes more sense to present the general rule, while the Gemara presents the general rule through a case. Or the Mishnah presents the general rule through a case. And I think that’s not accidental. There is some explanation for it because of the difference between the fields, but we’ll talk about that. All right, okay, Sabbath peace.

[Speaker B] Sabbath peace, thank you,

[Speaker D] Thank you very much.