Simplicity, Lesson 1

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[Rabbi Michael Abraham] What is a mah matzinu—is it an analogy? Yes. A mah matzinu is an analogy, but it’s not an abstraction. A mah matzinu is an analogy between two things. This feature here and this feature here are similar. Right. But that’s not abstraction. Maybe along the way we do make an abstraction, but I’ll still talk about that. Now therefore, these are the abstract concepts we’re talking about here. Say, for example, creating the concept of money—that too is a kind of abstraction. So let’s say, how did it begin? It began with trade as barter, say, between one commodity and another. Slowly people saw that the market really couldn’t function that way, and then it became necessary to identify that inside an economic market there sits some very, very abstract kind of thing called value. And in fact, you exchange tomatoes for chairs according to some criterion that determines a basis for comparison between them. How many tomatoes is a chair worth? How can you compare that? How can you compare tomatoes to chairs? Right, it’s like asking what there is more of—water in the ocean or kindness among human beings? That’s not even a question you can answer; it’s not a well-defined question. Those are two kinds of things that are incommensurable, with no common measure. You can’t compare two such things. So how do we compare tomatoes and chairs? We’re not comparing tomatoes to chairs; we’re comparing the value of tomatoes to the value of chairs. But for that—and suddenly you need to understand that there is such a concept called value. Once you understand that there is such a concept called value, and that it stands behind very many phenomena that on the surface look completely different—yet behind each of these totally different objects there sits something called value—once you put your finger on that thing, an entire world opens up. Because now you say, okay, let’s create money. What is money? Money is a concretization of the concept of value. A hundred-shekel bill has no intrinsic meaning; it’s just conventional. Purely conventional, the hundred-shekel bill. But that bill is a concretization—it’s the opposite of abstraction, by the way—of the abstract concept of value. In effect, you quantify that concept, you define it, and you create objects that are its representations. And now you can play with them, and buy and sell and use them, once you’ve understood that thing. So in the end it’s a double process. You made an abstraction and understood that there is this concept of value, and then you concretize it. Concretization: you turn it into something concrete. That is, you translate this value, or break it down into coins or bills that are in fact the expressions of that abstract concept.

The primary categories of damages—that too is a kind of abstraction. The Talmud at the beginning of tractate Bava Kamma talks about the primary categories of damages. So what is “horn”? You would say: horn is when the animal comes like this and gores—that’s horn. The Talmud says, what are you talking about? Horn is something that intends to damage and is unusual; it has two characteristics. Okay, that is the concept of horn-type damages. In other words, you take something concrete and make a certain kind of abstraction out of it. You say: from my point of view, horn is not an organ in an animal’s body; rather, horn is a type of damage. And suddenly, when a dog bites, that’s called horn damage. What connection is there? Would anyone ever think of calling a dog bite “horn”? What’s the connection? You understand that horn is a type of damage; you abstract from the goring. You no longer see the goring as the physical act of an ox goring a donkey; rather, the goring is some kind of damage that intends to cause harm, or that is unusual, not ordinary damage. Is horn specifically a concretization? But you move out from the concretization and abstract from it. You didn’t start from the abstract thing and say horn is such-and-such. The Torah speaks about horn: “If one man’s ox gores the ox of his fellow,” so you start from the tangible thing and abstract from it. You say: in fact, horn is only an example of an abstract concept. So horn becomes one of the concretizations? Exactly. Meaning, along this axis of concretization and abstraction we always move back and forth. Because in the context of money, first of all we made an abstraction and understood the concept of value, and then we concretize it—we say, fine, so money will represent the concept of value. That’s why very often someone who talks about money sees it as an abstraction. But that’s not correct; it’s a concretization of another concept, which was the abstraction. That other concept is value. Okay.

Very often in everyday language, when we talk about someone who made an abstraction, we’re actually talking about something very concrete. It’s just that that concrete thing could not have come into being unless beforehand someone had made some abstraction that this concrete thing represents. What is abstraction in the internet? An abstraction of the concept of space. The concept of space as you know it—you’re to my right and I walk from this room to that room—so we have concepts of space. Now, it’s not at all a trivial invention to speak about the internet world in the terminology of spaces. Cyberspace? Yes. Isn’t that just borrowed language? It’s not just a matter of language; that’s exactly the point. The language is already a concretization of that abstraction. Why is it abstraction? It’s abstraction because suddenly you understand that space doesn’t have to be specifically the space we know. Also in mathematics, when people talk about spaces. The question of—no, that’s what I’m saying. Borrowing is too weak a concept. It’s true that there was borrowing; that’s how I opened. Borrowing is too weak a concept. Because this isn’t figurative usage; it’s really the same thing. When they built the internet, did they think in terms of—was that a concept they used, or did they do what they did and afterward say, “oh, we can use that terminology”? Exactly, that’s what I’m saying. No, I think not. I’m not sufficiently expert, but I think not. At first they didn’t talk in that kind of language. No. After they understood what they had, suddenly you experience it, you understand that it’s actually like a space. Then you go back to the concept of space, abstract it, and say: wait, once I abstracted it, now I can use the terminology that exists there in the internet world as well. So in fact this involves some kind of abstraction, and maybe afterward also a concretization of that abstraction, or another concretization.

All spaces in mathematics are abstractions. You talk about vector space, this kind of space, another kind of space, Hilbert spaces, all sorts of things of that kind. Essentially, you take the concept of space as we know it here, abstract it—or make different abstractions from it; there are all kinds of abstractions—and you give them names. And after that, of course, every such theory has what’s called a model. The model is basically a certain context in which the theory can be realized. It realizes the theory; it obeys the laws of the theory. Okay, so we say that this thing constitutes a model of such-and-such a theory. Okay, so the model is a concretization of the theory. The theory is an abstraction that comes out of some particular model. Okay? Those are basically the processes I’m talking about here. We use them in many contexts—we’ll come back to them; I’m just using examples here to sharpen the point.

“Do not cut yourselves into factions”—I think I already mentioned this. “Do not cut yourselves into factions,” so “do not form separate factions,” that is one of the rabbinic interpretations of this verse, and the intention is that there should not be two religious courts in one city, and things like that. The dispute between Abaye and Rava—Maimonides, for some reason, rules there like Abaye: that there is a prohibition of “do not cut yourselves into factions,” and one does not make two religious courts in one city, and so on. What does “in one city” mean? Today there is no city that doesn’t have two synagogues in it. So what about the Jewish law that forbids this? Courts. No, also synagogue—it’s the same thing. Religious courts are only like the minor who went and was born—religious courts are commanded to separate him. Who are “religious courts” there? “Religious courts” there means everyone. The religious courts that upload the recordings are simply commanded. “Religious courts” means the public. Here too, by the way, another abstraction. In Jewish law, in many places when it says “religious courts,” it means the public. You don’t make two publics in one city—that’s what “two religious courts in one city” means. And therefore this prohibition also applies to synagogues; the prohibition is explicit in the halakhic decisors. The prohibition also applies to synagogues, to everything. It’s forbidden to do this. Also as for religious courts, by the way, there’s more than one in one city, but also synagogues—and it’s forbidden; it’s explicit in Jewish law, forbidden to do this.

So how do people do it? Because today it’s clear to us that the concept of city that appears in that context is not really the geographical city as we know it today. We’re speaking in a virtual world. Our world is so mobile today and people move from place to place, so the concept of city or community—for example, communal customs. What is a community? Once, a custom was the custom of the place. There was a place, and it had a custom in that place. Today, custom is not determined by place. Even though very often we use the jargon of “the custom of the place,” that’s not what is meant. It means the custom of the community. And today community is something ethnic, not geographic. Because of the world’s dynamism, because people change places. Once a person would be born in a certain place and generally also die there, and he and his sons and grandsons too. The world was more static, so they spoke in terms of place. What do we do? We make an abstraction. We basically say, wait a second, the place spoken of there was really only a concretization of a more abstract concept, a concept that defines a community. Today, when the concept of community is not characterized by a geographic place but by something else—maybe by origin, by something ethnic—abstraction is created by the constraints of reality. Same thing, as you said before. Right, but there is still an abstraction here. And when we encounter a different reality, we identify components in it that are different but also similar to another reality. Is “the custom of my ancestors” an abstraction? I follow the custom of my ancestors. Of course that’s an abstraction. If I’m careful about certain customs, that’s not abstraction—my ancestors were physical people. No, your ancestors aren’t an abstraction; you were born from someone. I’m not claiming your ancestors are an abstraction. What I’m claiming is that the custom of your ancestors was not an abstraction. Obviously. But what I’m claiming is that “the custom of your ancestors” is an abstract concept, because in the Talmud “the custom of your ancestors” means the custom of the place. And if you moved to another place, you would adopt the customs of the other place, not the customs of your ancestors. But today it isn’t like that. Right, “in a place where they had the custom.” But today no. Today, when you move to another place, you continue the ethnic custom of your ancestors; you don’t join the custom of the place. Why? Because you understand that even back then, when they spoke about the custom of the place, they didn’t really mean the place. Why? If they came to Petah Tikva in its time, they took on the custom of Jerusalem—not Jerusalem’s ethnic custom, but Jerusalem’s local custom—and both Ashkenazim and Sephardim practiced that in Jerusalem. Listen to what your own mouth is saying. When they take Jerusalem’s custom to Petah Tikva, that’s not the custom of the place. Because in fact they attribute it to the place. The custom of the place in which there will be a custom. Good, so what does that mean? It means that the criterion was the custom of Jerusalem—so what difference does that make? It was also the custom of Moshe-Yankel. The point is that precisely place is not the determining parameter. You’re taking it from place to place; that itself means it isn’t a local custom. By the way, Rabbi Ovadia disagrees with you. He claims it’s the authority of the local master, and he himself also doesn’t exactly relate to this, but that’s another matter. I’m saying fine, you can argue—we’ll talk about “do not cut yourselves into factions.” I’m bringing it as an example that there are meanings in Jewish law that…

What? Today does this Jewish law still have significance? In a place where this Jewish law applies, that there not be two religious courts in one city? Then it applies. Look, the flexibility is such that you can work around anything, but there is still room, say, to claim that where there is an Ashkenazi prayer quorum, one does not establish another Ashkenazi prayer quorum. That is an application of “do not cut yourselves into factions.” People aren’t especially strict about this today. If the synagogue is full, then fine, then yes, by all means, they’ll establish another synagogue. But if the synagogue is not full, in principle if you establish another synagogue in the same place you are violating “do not cut yourselves into factions.” If it’s the same liturgy belonging to the same community—that’s exactly the point. The place doesn’t determine it; the community determines it. But even two synagogues with different liturgies? I’m saying something reasonable; I don’t know how to bring you some proof from the Talmud. But the logic says that the contemporary application of “do not cut yourselves into factions”—after all, it’s prohibited in the Talmud and in the halakhic decisors, it’s prohibited. So why do people do it today? The explanation I give for this is because the concept of place has undergone abstraction. Essentially what people understood is that what was spoken of in the Talmud as place was from the outset an ethnic concept. Except that at that time, place in practice characterized ethnicity, because the ethnicity always remained in the same place; the world was not dynamic. Today, when the world is dynamic, we essentially understand that when they spoke there about place, they really meant an ethnic matter. That’s the interpretation we at least propose here. And if they didn’t mean that there, then that’s what we mean today. But it is the replacement for what was once called the custom of the place. There too, by the way, they talk about “the custom of your ancestors remains in your hands,” there in the chapter “In a Place Where They Had the Custom.” Yes, the people of Beit She’an who wanted to go and so on—“the custom of your ancestors remains in your hands.” But in that context it’s clear to everyone that this means the custom of the place. Your ancestors who lived in that place—this was their custom, which was the custom of the place. And today, no: we take it literally, it’s the custom of the ancestors even if it’s not in the same place.

By the way, the custom of Petah Tikva is like the custom of Jerusalem—why? Because people from Jerusalem founded Petah Tikva. Yoel Moshe Salomon. Meaning, in fact, it’s not determined by the place but by the people. And that’s exactly the point, exactly reflecting the fact that it’s not the custom of the place. Because “the custom of the place” means that if Jerusalemites moved to Petah Tikva, then it’s a new custom, the custom of Petah Tikva. It has nothing to do with the customs of Jerusalem; Jerusalem’s customs apply in the territory of Jerusalem. That’s the criterion of place. Take place and you get a gap. Yes, like “the stringencies of the place from which he went” and “the stringencies of the place to which he went,” all those rules—those are still leftovers from the ancient concepts of local customs. Also the extra festival day observed in the Diaspora when you arrive abroad, and so on. Why? Because there the applicable laws really still cling to place. For some reason—and one needs to discuss why and when not. And once the applicable laws or customs are attached to place, then anyone who arrives in that place takes upon himself the stringencies of that place or the customs of that place. And that really is a remnant of that period when customs truly followed place. But in very many things we no longer do that. Right, liturgical customs no longer work that way. There have been Ashkenazi and Sephardi customs in Holland for hundreds of years already, right? There are communities of Menasseh ben Israel, the community of Maharam Hagiz—sorry—there are various Sephardi rabbis who established magnificent Sephardi communities in Europe. Right, so therefore place does not obligate. Once the world becomes more dynamic, place stops—or at least becomes less significant; I don’t know if it stops entirely, but its significance decreases. Okay, so that too is a kind of abstraction.

This issue is discussed a lot by the later authorities. In Spain, communities moved from place to place, and they establish a community of people from Ioannina in Greece. That is a result of the fact that the world becomes more dynamic. There, by the way, it was dynamic against their will, but it was dynamic, and this raised the question: wait, so how exactly do we preserve the concepts that existed in the new reality that exists today? And very often such a thing requires some kind of abstraction. And we abstract the ancient concept because it cannot be applied as is. Right, this is like “derive from it and from it, but set it in its own place”: you take something from one place to another, but apply it according to the circumstances of the other place. But in order to do that, you need to understand in what sense you are still preserving what was there, because after all everything you are doing here is to preserve, not to change. You claim that this is the correct preservation of what was there. In what sense are you preserving it? Because you say that what was there underwent abstraction, and that abstract thing is in fact what I am doing here according to the circumstances here. Therefore that is really the way to preserve it; the change is the way of preserving what was there. But in order to understand why this different thing is the correct way to preserve, you have to do… abstraction. You basically have to understand: so what is similar in these two different things? There is something abstract that really was preserved, even though on the concrete level it looks completely different. But there is something abstract here that is still similar. It is still the same thing.

Actually, when we talk about—and we’ll see more examples; I’m just bringing a few examples here to define the topic—we’ll eventually get to halakhic examples too. Not today, but we’ll also get to several halakhic examples and discuss them in greater detail. So in order to understand the process of abstraction, we basically have to enter a bit into the question of how one deals with concepts. Say we have some concept defined by a set of characteristics. So first of all, there are two levels at which one can relate to abstraction. First of all, the very creation of the concept. That is, the formation of concepts is a very complex process. A lot of analytic philosophers deal with this. Take, for example, a democratic state. A concept. Okay? Now there are also states that are democratic states. Those are more concrete creatures, although a state itself is a concept, so I don’t know how concrete it is. A state. A land is an object. A state is a concept, not an object. Okay? And between the State of Israel and the Land of Israel—today we perceive the State of Israel as concrete and the Land of Israel as abstract. It actually works the other way around. The Land of Israel is the concrete thing, and the State of Israel is abstract. A state is an abstract thing. Okay? It’s so present in our lives that we understand it as something very concrete from our point of view. Like people who live on the internet—for them, a site is a website; a site on a trip, they don’t even know what that is. What do you mean by abstraction? The borders of a state are a very, very concrete thing. What? The borders of a state are very—when you mark them, it’s very concrete. Right, right. But that’s a decision. What? There is nothing natural there that you can point to and say, ah, that’s the border. It’s a decision. So states decide where the border passes between them, and now it can also be marked. Once you mark it, there is a concretization of that abstract thing called a border. It has no root in actual reality. There is a geographical border, say a river—that’s a geographical border—but a political border is a result of convention. It’s an agreement between different societies or between states, and therefore it is fundamentally an abstract thing. And you plant it in the ground and turn it into something tangible.

Again, the processes of abstraction and concretization always come together. Almost always together. You make an abstraction—and why do you make an abstraction? You make an abstraction in order to see that if we make a different concretization, that concretization is of the same thing as the original thing. So abstraction is always done for the sake of concretization, and vice versa. That is, through many concrete things you rise to something abstract. And from that abstract thing you create another concretization or a different concretization.

Take the concept of a democratic state, for example. We know, we are familiar with a collection of states that we tend to call democratic states. At some stage—and that comes afterward—we ask ourselves, wait, what exactly is democracy? And it’s not so clear whether there will be disputes about this, or whether not everyone will agree on all the characteristics. And therefore “the enlightened states” often serves as a substitute for the point. You want to claim that this is how a state ought to be run. A democratic state must be run this way. How do you know? That’s exactly what I’m disputing. I claim that a democratic state should be run differently. Ah, fine, so let’s go to the enlightened states. The states we all agree are democratic, and therefore it is clear that this is how a democratic state should be run. But there is something problematic here, because if we have a dispute over what democracy is, how will you bring me proof that you are right and not I? We are arguing over an abstract concept. You can point to certain states that we all agree are democratic and show from there that democracy should function this way and not another. But if I argue, then maybe I also won’t agree that those states are democratic, or I’ll think there are other states that are also democratic and you think not. There is really no way to decide such an argument. Very often such an argument is demagoguery, because you are assuming the conclusion. You assume what democracy is, and then you determine: these states are democratic states, and now look—every democratic state, yes, all the great sages of the generation say such-and-such, as is well known. Meaning, you come to someone with claims: after all, all the great sages of the generation say such-and-such. Wait, but that Jew over there says something else. Obviously—he’s not one of the great sages of the generation. Why isn’t he one of the great sages of the generation? Because he says something else, so he’s not one of the great sages of the generation. Very often it works like that.

Now, this is not—understand—usually done innocently. It’s not done maliciously. It’s done innocently because there really is no independent way to define it. How would you define independently what democracy is? We don’t have a yardstick. In Greece? What existed in Greece? Who says I owe anything to Greece? What? Separation of powers is also part of it. You can disagree with that. Okay, this is democracy and that is democracy. But I’m asking—no, someone will tell you that without separation of powers it’s not democracy. So you think he’s wrong, and he thinks you’re wrong. Now how will you prove it to him? Because in Greece it wasn’t there. So what? So then they weren’t democratic? Maybe it’s possible to be. Okay, maybe, but another person will tell you no, that’s not possible. A state without separation of powers is not a democratic state. You can hear that, by the way, from many people, some of them judges on the Supreme Court. We don’t act at all like Greece. Of course not. Something from Greece was taken, but it went through many interpretations and expansions and elaborations and everything, and today it is understood in a way that is not Greece. Today there is a set of characteristics without which many people will tell you: you’re not democratic. For example, a Jewish and democratic state—so if a state is Jewish and democratic, people will tell you there is no such thing as a Jewish and democratic state. If it’s Jewish, then it’s not democratic. Now you claim no, and you argue. Okay, how will you prove it? Because in Greece they weren’t Jews? How will you prove it? There is no real way to prove it. Your proofs will always depend on assuming the conclusion. You’ll go to other states that you assume are democratic and bring proof from them, one way or the other, doesn’t matter. And then they’ll tell you: no, those states are not democratic—what proof are you bringing from them? Here’s a nice bit of pilpul. In East Germany, say, they called it the DDR, Deutsche Demokratische Republik. Any sensible person will tell you that’s not democracy because not… And there are millions of sensible people who lived there in East Germany who would tell you it is democracy. Not true, but fine. What do you mean fine? Prove to them it isn’t. Can you prove it to them? The fact is, their vote wasn’t received. So what? Who said you have to vote in order for it to be democracy? Who said? Maybe, I don’t know, some other characteristic? I’m just defending something I agree with, but I’m only saying—you have no way to prove it. You’re assuming assumptions that I may agree with, but what are you looking at in order to prove that it’s correct? At concrete examples? Then they’ll tell you those don’t concretize the concept in question. That itself is the argument. It’s a very simple thing. Democracy—do you count heads or do you count feet? Yes, exactly. So here there are several aspects. This can be democracy and that can be democracy. Yes, both are democracy. What are you talking about? The second isn’t democracy. Ask today, right, they’ll tell you no. Why on earth should one vote be given to a wise man and two votes to a man who picks tomatoes? Exactly, that’s not democracy. And at the time of the revolution every one… In any case, majority rule is democracy. What’s called a unanimous decision. Yes, we reached a unanimous decision—only my mouth. And that’s among those with voting rights only. In Greece only… Who will define those with voting rights? In Greece only the upper aristocrats had voting rights, only ten percent. Those sitting in the bouliasts—they were the voting-rights holders in Athens. Athens, the democracy of Athens, had ten percent with voting rights. Yes, unlike, unlike—no military rule, no king. It’s rule of the people, that’s democracy. Now one can define that “the people” includes women, doesn’t include women, starts at age 18, age 20, age 30. Are we having a dispute about facts? I mean, there are people who will claim that a state that doesn’t give voting rights—and most people—that a state that doesn’t give women the right to vote is not democratic. That is what they will claim. Now you think not. Fine. In Switzerland, until 1974, women did not have the right to vote. No, and it was a democratic state, and that was to its credit. And it was clear to everyone that it was a democratic state. But today it’s clear that such a state would not be democratic. Now again, maybe you think they are mistaken. Do you have a way to prove them wrong? How will you prove it? Will you tell them that in Switzerland in 1960 women didn’t have voting rights and it was still considered democratic? No, then he’ll tell you: what are you talking about? I’m telling you that Switzerland in 1960 was not democratic. The nineteenth century, the twentieth century—this is circular.

In logic, in general, we define concepts in two ways—or sets, basically can be defined in two ways. Concepts too. You can define them by extension—extension and intension. You can define by extension. Say I want to define the democratic state, so I point to a set of states that are democratic states. That’s one way to define. A problematic way, because the moment a new state is born and you ask yourself whether it is democratic or not, you have no way to answer. Right? If the definition is by listing the items that make up the set, then it isn’t. But to all of us it is clearly a democratic state. And you have no way to decide. Exactly. So the alternative definition—that is, the alternative—is to define it by content, intension, by the meaning of the concept democracy, where the extension is only the result. After you understand that the concept is defined this way, now go through all the states and see which ones meet this definition, and then the extension will emerge as well. You don’t begin with the extension; you begin with the idea. Now, more than that: when you define a concept by extension, behind it there is always an idea. Yes, it’s a façade, an illusion—people who think you can define things by extension. Because why are you gathering exactly this collection of states and defining them as a set? Why these specifically? Suppose I now take Finland, Zimbabwe, and Belgium. I claim that this is a popopop state, okay? Let’s say I claim that. Now, I can define such a thing. Nobody on earth would ever define it. Why not? Because when you gather a set of states or a set of objects into a group, behind it there is always something that distinguishes or is common to all those items. Otherwise there is no point in defining it.

I once mentioned the story by Borges, the Argentinian writer—“Tlön, Uqbar, Orbis Tertius.” A brilliant story, in my opinion, and the guy was a genius in general. There he talks about some planet called Tlön, inhabited by idealists, idealist philosophers. Idealist philosophers are people who do not believe in the existence of an external world—solipsists, if you like. In other words, people who think that all that exists is only inside my consciousness. The external world does not exist; there are only perceptions within me. And he describes that planet there—literarily, of course, but in my opinion it’s a brilliant essay on idealism. A brilliant philosophical essay, although written as a story. And he says there, I’m shortening it, that in the dictionary of one half of that planet—I don’t know, the northern half, I don’t remember—there are all kinds of collections of characteristics that produce an object, arbitrary collections of characteristics, simply arbitrary, that represent an object. For example: the cry of a distant bird and the color of the sun at sunrise together with the number of tiles in this room. That concept is called Mosheleh, okay? The concept is the collection of these things. Why? Because basically in an idealist world there are no objects. Right? So what is there? There are collections of characteristics. Therefore, for example, he says there, you can’t say that the moon rose over the river, because there is no moon and no river. What you can say is that it mooned above the ongoing flow. There are only phenomena; there are no objects, because there are only perceptions that I experience. The objects aren’t really something that exists. Okay? So it’s a literary expression of that strange mode of thought, and more than that—any collection of characteristics can be a concept.

Now, to us that sounds completely absurd. Say “state”—I’ll create a concept, okay? States whose area is over eighty thousand square kilometers and whose population is up to three and the sea next to them is green. Let’s call that category yakumporka, okay? That’s the category. So what? You can define such a thing; the definition is fine, and maybe there will even be several states that fit into that definition, maybe, I don’t know. And that will be a set and everything will be fine. Why does it sound strange? It sounds strange because there is no reason in the world to gather those states into one set. Of course you can gather infinitely many sets and unite all kinds of collections of states or collections of objects in any way you see fit. Why do such a thing? When you do such a thing, two things need to be present. First, there has to be something similar in all the elements that define the set—but that exists in the set I just defined. All of them have a green sea beside them, eighty thousand square kilometers, and three inhabitants. They are similar. Beyond that, the collection of characteristics they share must constitute some single whole. That is, there is no reason in the world to gather objects that are similar to one another—all of them have a green sea beside them, eighty thousand square kilometers, and three inhabitants, okay? They are similar; there is similarity among the objects. Why gather that under the heading of a concept? The reason is that that collection of characteristics does not come together into something meaningful. Why should I care whether this state has both three inhabitants and a green sea beside it? It’s uninteresting. It’s nonsense. Okay. But if, for example, I gather states in which citizens have voting rights, and there is separation of powers—judicial, executive, legislative, and so on—and civil rights, and all sorts of things of that kind, and a free press, freedom of speech, I don’t know, things like that, and for all those states I define them as a set—this set I call democratic states. Here it makes a lot of sense to define such a thing. Why? Even though it’s a collection of characteristics, and every state in that set has that collection of characteristics, so in that sense it’s like the green sea and the three inhabitants. Why is it sensible here and not sensible there? Because here the collection of characteristics comes together into a meaningful whole. This collection of characteristics creates some kind of organism—an intellectual organism, of course. In other words, there is logic to saying that a state ought to be run this way; there is a conception underlying these things. Therefore it makes sense to gather all these characteristics together and call them by one name, and define a set of democratic states or the concept of a democratic state.

Now, clearly—how does this actually happen in practice? In practice, I look at various states that seem to me to be operating in a way that sounds interesting or proper, okay? And I say: okay, let’s gather them all into one set, and invent some name for it, democratic state. I still haven’t defined what a democratic state is, but of course I already have some intuition behind it when I put all these states into one set. Then political scientists begin trying to think about how to define that set. What does it actually mean to be a democracy? Then they give characteristics and explain why those characteristics should be joined together, or why there is logic in joining them together, and perhaps even offer criticism: one characteristic yes, another no, maybe change something. You can begin discussing it after you make that abstraction. Of course you can then make an abstraction and a concretization. The abstraction, in a certain sense, was already made when you gathered those states, because behind your consciousness, when you gathered them, you already understood a bit what a democratic state is. Otherwise you wouldn’t have gathered those states into one set. Then you begin to clarify: what exactly is this elusive idea standing behind my consciousness? And you begin to define: a democratic state is a state with freedom, with civil rights, separation of powers, yes, voting rights, things like that, freedom of speech, all sorts of things. Okay. Then you are in effect breaking down into small change that same abstract idea that stood behind your consciousness. But all of this is still abstraction. It’s all abstraction. And now, of course, you can create a state that would be an ideal democratic state. No democratic state is really ideal. Democracy does not appear there in its purity in any state; there are always problems. Now you can try—utopias are created this way. Utopias are always the result of abstraction. After you make an abstraction, you try to concretize it. That is, you try to produce something tangible that will realize the abstraction you have thought about, which usually leads to disasters. But that’s what people do. So abstractions are always made for the sake of concretizations. You produce another tangible object that will realize the abstraction you made beforehand. So you take tangible objects, derive an idea from them—that is a process of abstraction. You discuss the idea itself, thus refining your abstraction, and then you try to produce some concretization. Right, that’s basically how utopias are born.

Okay. All the disputes over “who is a Jew”—the same kinds of disputes, right? There is the halakhic definition, but there are those who say, what are you talking about? There is a secular Jew, there are secular cultural definitions of the concept Jew. You tear your hair out in front of such people; you have no way to argue, no way to prove it. Right, like Greece. Let’s go to Judaism as it once was. Once everyone agreed that a Jew is someone who converted properly or whose mother is Jewish, and the rest was marked off. Meaning, something has to begin somewhere; otherwise the definition is incomplete. But today no. Today people will tell you, what are you talking about? Someone who speaks Hebrew, reads Amos Oz, serves in the army, and I don’t know what, and is productive and moral—fine, that’s what is called a Jew. Strange definitions of that kind. And go argue with those people. It’s clear to me they’re talking nonsense, but you can’t argue. How can you argue about a definition? He defines it one way, you define it another. I’m only asking why this is even an argument. We already talked about this. Why is it an argument at all? Who said we’re talking about the same concept? So let’s part ways: you call it kompomkan and I’ll call it Moshe-Yankeh, and everything will be fine. Why do we need to use the same word? We’re just taking two different concepts, using the same word, and calling that an argument. It’s not an argument. It’s just stubbornness about a word instead of parting as friends, each choosing his own word, and everything would be fine.

So why do we nonetheless see this as an argument? And there is an argument here. Anyone who thinks one can part as friends over semantic tools is mistaken. There is a real argument here. And the real argument is indeed who is a Jew, because the concept Jew is an abstract concept. And there are those who claim that its concretization is the halakhic concretization—halakhic, whether his mother is Jewish or he converted properly, or whatever the halakhic definition is. Others say, what are you talking about? This abstract concept—maybe once that was its correct concretization. Today the correct concretization is to build the institutions, pay taxes, serve in the army, and speak Hebrew. Okay? That is the concretization of this concept. Right, of course it’s clear to them that this wasn’t true once. Anyone with eyes in his head will not deny that it wasn’t so once. What do they claim? They do exactly the same processes I spoke about before. They say that once the definition was halakhic because that really was common to everyone, but today there are many Jews—and they are Jews—for whom that thing is not common. Therefore the definition has to change. But changing the definition is not creating a new concept; it is continuing the previous concept. This is its true realization under the new circumstances. Redefining the term. Yes, redefining the term, but the claim is that it is the same term—you can define, you can say what it means to define—no, it is the same concept. No, not the term, the same concept. And my claim is that the concept Jew is the same concept, and we have a dispute over what things characterize it. This is not a semantic question; it is not only a question about the term in language. It is a real dispute. We can’t simply part: you take the concept Jew, I’ll take the concept Israeli, and everything will be fine. That won’t help, because we have a dispute over who is the true continuation of Abraham our forefather. That is a real dispute. How to govern the Jewish people. Fine, the same dispute. My point is that there is a real dispute here. It is not a matter of definitions. Why? Because there is some abstract concept called Jew or Judaism over which the dispute is taking place. The definition tries to capture it. But the definition is not the thing itself. The definition tries to capture or hit upon the thing. But the thing is abstract. And he proposes a different definition for that same abstract thing, and therefore we have a real dispute. It’s not that I think he is right and I am right too. I’m not making a pluralistic claim here, that we are all right. What I’m claiming is that we are all trying to hit the same target. We have an argument; I think I’m right and he is wrong, but we do have an argument. You can’t separate on a semantic basis. We’ll choose separate words and everything will be fine. Because that would mean the claim is that this is a linguistic convention. You’ll call it Jew—fine, so why get confused? You call it Jew, I’ll call it Israeli, and everything will be fine. No, because we are talking about the same thing. We are talking about how the people should be run. That’s a consequence. That’s not an abstract thing; it’s concrete. No, no, which steps I take. Again, you’re returning to the same thing. No, it’s an abstract thing. It’s an abstract thing with concrete implications, and that’s exactly the point. The dispute doesn’t begin with the question of how to run the people; the dispute begins with the question of who is a Jew. Once you define the concept Jew, then you will run the Jewish state according to your method on the basis of that definition. That is already the concretization. Concretization always comes after abstraction. In the background of concretization—again, not chronologically afterward, but in its background—there is some abstraction. Fine, that’s the point.

And this process of abstraction is literally what the word suggests, like taking clothes off. What is abstraction? It is taking a concept or an object, stripping away certain characteristics, removing certain characteristics from it, and remaining with what seems to me like the essential skeleton of the thing. If that thing also appears in another context, then no problem—the other context too deserves to be called by that name. Community, ethnic group, as we discussed earlier, horn-type damage, all the examples I brought before. A dog that bites can be called a goring by horn. Someone who doesn’t know the context would have you hospitalized if you said such a thing. “This dog caused damage by horn”—say that out on the street and they’ll hospitalize you on the spot. A dog causing damage by horn—have you ever heard of such a thing? Why? Because you abstracted the concept of goring by horn. You say: something whose intention is to damage and that is unusual—that is called horn. So for me the concept horn has undergone abstraction, and a dog bite too is horn. Okay?

Now, this abstraction, if so, is not—on the one hand it is some kind of analogy, but not exactly analogy. Because analogy comes after I have already reconcretized that abstraction. That is, I’ll show—let me show how it works. Suppose I take two chairs and say: this chair, it’s a chair, and that too is a chair. This chair has four legs. That chair I can’t see; it’s far away. But if it too is a chair, then probably it also has four legs. I’m making an analogy between the chairs, okay? Just as this one has four legs, that one also has four legs. It could be untrue, but analogy can also be wrong sometimes. Analogy is not a necessary argument. But we use analogy. Why do I make that analogy? Because behind the scenes it’s clear to me that for the concept chair, this characteristic of four legs is probably an essential characteristic. By contrast, if this chair is green and I infer that the other chair is also green, people generally won’t accept that. There is no reason to assume that color is essential to the concept chair. So when I abstract the concept chair, I take a concrete chair and generate from it an idea of chair. That idea is not made of plastic, or wood, or iron, or anything. It is abstracted from matter. It is not—one second—it is not material at all. Rather, it has certain abstract characteristics. I remove all the irrelevant or less relevant characteristics, leave only what I think at least remains essential, and in that I have made an abstraction. And now I say: in that object too there should appear the characteristics that I abstracted from this object, therefore I make an analogy. That is, analogy basically works on the same plane, from chair to chair. That is not abstraction. But behind the analogy there often sits an abstraction. Because you basically say: these two chairs are different—this one is here and that one is there—so where is there room to compare? Because place is not an essential characteristic of a chair. It can be here, it can be there; that doesn’t matter, it does not characterize the chair. What does characterize the chair? That it has four legs. Now, if it is a chair, then probably it also has four legs. So I made an abstraction. And at the foundation of the analogy lies an abstraction. Therefore very often analogy looks like abstraction and abstraction looks like analogy, but one has to understand: these are two different things.

I’ll say more than that. What is more similar to abstraction is not analogy but actually induction. Induction is generalization. Say you take a certain chair and say: this chair is a piece of furniture. Now, a table is also a piece of furniture. So in a furniture store, if they sell this chair, they probably also sell tables. They sell furniture there. Or you say: this horse is mortal; it may die, it will die eventually. So probably all animals are mortal, or all horses are mortal. Fine? You made a generalization. Not an analogy. You took an individual and applied what you know about it to an entire group that contains it. That is not analogy from individual to individual, but movement from the individual to the general. Okay? Now here it is clear that there is an abstraction, because the moment you broaden the scope from a limited number of elements to a larger number of elements, how is that broadening done? There is always this trade-off. The more you reduce the number of characteristics, the more you increase the number of objects. In information theory, right? In information theory, the more information there is, the smaller the set. If you say “the first prime minister of the State of Israel,” there was only one such person—Ben-Gurion. Or “the first prime minister of a state,” not necessarily Israel—that’s already more, right? Or “the first prime minister,” not necessarily of a state—maybe there are governments that aren’t states. More. A prime minister without being first, just a prime minister, bigger still. The more you remove information, the more you enlarge the number of objects in the relevant set. Right? Abstraction means removing elements of information. Usually it means removing elements that seem to us irrelevant, and remaining with the elements that are relevant. That is what is called abstraction.

But this abstraction is often basically the shadow or image of generalization. Because abstraction means removing some elements, some characteristics, and remaining with part of the characteristics that in my eyes are the essential part—and it is a big question how one defines what is essential and what is not essential. And once I remain only with part of the characteristics, then clearly the definition will fit more objects. More objects will fall under the definition, right? So that’s how generalizations are made. When you make a generalization, you say: if this horse is mortal, then all horses are mortal. Why? Because you assume this is a characteristic of horseness. Then someone comes and says: what are you talking about? All animals are mortal—that’s broader. Why? Because this is not a definition of horseness at all; it is a definition of being an animal. A horse is only a particular case. Broader still, right? The more abstraction you make, the larger the group you refer to. Because greater abstraction means removing more characteristics. The greater the abstraction, the farther it is from the source, but it is also more refined. That is, it represents the source in a purer way than the source itself. Because in the source itself there are many properties that are secondary, not essential to it. When you speak about a concrete person, that concrete person also has height, skin color, clothes he wears—that is not at all relevant to the concept of human being. But if you speak about the idea of the human being, it has no clothes, no skin color, no anything. What is there is only the collection of properties that are essential to the concept of human being. So you have made an abstraction, and this abstraction moved you from one concrete human being to a group of human beings, in all of whom these characteristics will appear along with various other characteristics that are less important to me, in which there will be differences among the individuals. Therefore abstraction generally goes with the concept of generalization and not with the concept of analogy.

Only what? Only that between analogy and generalization there is also—and with this I’ll finish—there is also some interplay. Not psychologically but logically. Logically. Yes. A question of psychology is a factual question; I’m speaking here about the principled philosophical question. Look, ostensibly analogy is the basis and induction is the result. Why? Because when you take one horse and generalize to all horses, you are basically making an analogy between one horse and every other horse, and then you get a generalization to all horses. Right? So in fact analogy is the basic tool and induction is simply a collection of analogies. But that’s not correct. Why? Because when you make an analogy between one horse and another horse, you assumed that their both being horses is enough to liken them. So in fact you already assumed this about all horses, even though you did it with one object. Therefore induction is actually more fundamental than analogy. In every analogy there is a hidden induction; we just don’t put it on the table. Very often we go straight from this horse to that horse without noticing that we have actually assumed something about all horses, without saying it, because we assumed nothing about that other thing except that it is a horse. So why do we assume this characteristic exists in it? Because in fact it exists in everything that is a horse—it’s just that we spoke about one particular thing, but essentially we made a generalization. Therefore the generalization is ostensibly more fundamental than the analogy.

And that brings me to the distinction with which I’ll perhaps open next time, because we really have to stop already—the distinction between induction and abduction. And abduction is what will lead us to a better understanding of what abstraction is. Let’s finish with that. We’ll stop here.