Defining Concepts 3

Table of Contents

• Constitutive definition and directive definition
• The existence of concepts, Plato and Aristotle, truth and correspondence
• Confirming midrash and creative midrash as a parallel
• Conventionalism, baptism, essentialism, and the analytic-synthetic distinction
• The example of repentance, forgiveness, reason and emotion, and value as a stopping point
• Science in the service of political correctness and emotional intelligence
• Back-and-forth movement between intuition and definition, and expanding the conception
• Mathematics, the empty set, Platonism, and Rabbi Zini
• Contemplating the ideas and conceptualizing the definition itself
• A halakhic example: giving a bill of divorce, the Ketzot and Kehillot Yaakov
• Critique of the deductive-nomological model of explanation and emphasis on the path
• Practical ramifications, critique of Brisk, and Rabbi Chaim
• Summary of the role of definition

Summary

General Overview

The text distinguishes between a constitutive definition, which creates a new concept, and a directive definition, which tries to hit upon an existing concept. It argues that the very possibility of arguing about right and wrong in definitions such as morality, Judaism, or democracy assumes that there is some truth outside mere linguistic usage. The text connects this distinction to the Plato-Aristotle dispute over the status of concepts, suggests a link between conventionalism and essentialism, and shows how in practice a definition works as a process of back-and-forth movement between intuition and formal definition. The examples taken from multiple intelligences, moral repentance, and the analytical process in Jewish law lead to the conclusion that a sharp definition is almost never “the thing itself,” but rather a means of building intuition and judgment, and that a literal reading of definitional bottom lines creates mistakes.

Constitutive Definition and Directive Definition

A constitutive definition creates the concept by declaring what the concept will be, and therefore there is no point in arguing about it beyond questions of convenience or accepted usage. A directive definition tries to characterize an existing concept, and therefore truth and falsehood can apply to it, and one can conduct weighty arguments that are not merely lexical. The text argues that disputes such as “who is moral” or “who is a Jew” are perceived as arguments about right and wrong, and therefore hint at a point of truth outside us, to which the definition is supposed to correspond.

The Existence of Concepts, Plato and Aristotle, Truth and Correspondence

The text presents Aristotle as seeing concepts as categories or forms through which we view objects, and Plato as seeing concepts as ideas—abstract objects that exist in the world of ideas. The text explains that a term is the linguistic item, and a concept is what the term expresses, and that attributing truth to a definition means comparing the definition to something outside the speaker. The text argues that the assumption that directive definitions exist implicitly assumes a Platonic view, because only then can one say that the definition is directed toward fitting something that exists outside us, whereas in a constitutive definition there is no correspondence, and therefore no truth or falsehood.

Confirming Midrash and Creative Midrash as a Parallel

The text compares the distinction between directive and constitutive to the distinction in the study of Jewish law between confirming midrash, or supportive midrash, and creative midrash. Confirming midrash anchors an already known Jewish law in verses through the tools of interpretation, while creative midrash produces a new Jewish law through those tools. The parallel serves the claim that there are processes in which the definition or formulation anchors something that preceded it, and by contrast processes in which the formulation itself is what creates.

Conventionalism, Baptism, Essentialism, and the Analytic-Synthetic Distinction

The text presents conventionalism as the view that concepts are created by social agreement, similar to what Kripke calls baptism, in which a word is attached to a concept the way a name is given to a baby. Opposed to this is essentialism, which tries to hit upon the essence of the concept and is not satisfied with agreement alone. The text distinguishes between the logical dimension of analytic versus synthetic and the epistemological dimension of convention versus essence, and argues that although in practice “they usually go together,” there is no logical necessity to tie them together.

The Example of Repentance, Forgiveness, Reason and Emotion, and Value as a Stopping Point

The text presents two people asking forgiveness: one who feels nothing but apologizes because he understands that it is the right thing to do, and one who is full of guilt and apologizes in order to calm himself down. It prefers the first as a morally “purer” penitent. The text describes the first model as Kantian, acting out of moral law rather than emotional reflex, and casts doubt on the neurological claim that morality necessarily depends on empathy connected to the amygdala. The text uses the Eglei Tal and its distinction between enjoying study and studying for the sake of enjoyment in order to illustrate the difference between an accompanying motive and a decisive motive. It connects this to Leibowitz’s position in the article “Detachment from Instruments,” according to which values cannot be grounded essentially, because if there is a reason for a value, it becomes a means and not a value, and so the chain of “why” stops at a moral axiom.

Science in the Service of Political Correctness and Emotional Intelligence

The text describes how the idea of emotional intelligence strikes him as a move of “political correctness,” whose goal is to make everyone come out a “genius” through multiplying types of intelligence. The text describes a methodology in which one distills essential features out of the concept of intelligence, builds a definition from them, and then applies it in such a way that figures like Maradona are included under intelligence alongside Einstein. The text argues that if this is a directive definition, then the result is supposed to preserve correspondence with the original usage of speakers, and if suddenly the definition includes people whom speakers would not have called intelligent, that is a sign that the distillation was not done correctly—not necessarily that a plurality of intelligences has been discovered.

Back-and-Forth Movement Between Intuition and Definition, and Expanding the Conception

The text proposes a “second token,” according to which there is a circular process in which one begins with an intuitive concept, defines it analytically, applies the definition in a way that expands the picture, and then returns to the speakers and changes their conception. The text argues that if the speakers are persuaded, this is described as discovery and not invention, because the definition reveals to them what was already latent in their conception—“it was in the heart, but not revealed to the mouth.” The text compares this to studying geometry, where the axioms are understood, but sophisticated theorems such as the sum of the angles of a triangle become “self-evident” only after an analysis that reveals what was latent in them.

Mathematics, the Empty Set, Platonism, and Rabbi Zini

The text brings Rabbi Zini’s story about opening set theory with the definition “a set is a collection of elements,” and then saying “the empty set is a set with no elements,” and emphasizes that the students do not notice the logical tension in this. The text raises the question whether mathematical concepts exist or are created as a continuation of the dispute over Platonism in mathematics. It suggests that one can understand acceptance of the empty set as a process similar to this back-and-forth movement, in which the concept of “set” changes so that it includes the exception as well, and it raises the question whether this is invention or discovery.

Contemplating the Ideas and Conceptualizing the Definition Itself

The text explains that “contemplating the ideas” is not sensory observation, but rather repeated inner examination of the fit between the definition and the intuition that is trying to hit upon the idea. The text argues that this fit is achieved by returning the definition to the intuition, correcting the definition, and continuing the cycles of conceptualization and intuition at ever higher levels. It applies this also to the concept of definition itself, and argues that understanding its role is built through the process and not only through a bottom line.

A Halakhic Example: Giving a Bill of Divorce, the Ketzot and Kehillot Yaakov

The text describes how in the Talmud there is no definition of giving a bill of divorce, but rather a large collection of cases, and that among the later authorities there are definitional proposals. The text brings the Ketzot, which suggests viewing the giving of a bill of divorce as a transfer of ownership, and rejects this by means of the case of “if it was written on items from which benefit is forbidden, it is kosher,” because according to some medieval authorities (Rishonim) there is no ownership over items from which benefit is forbidden. It also rejects a definition of mere physical giving by means of the case of a bill of divorce in a courtyard transferred to the woman, without any physical movement of the bill of divorce, and describes a search for a common denominator such as “transfer of domain,” which is still not sharp enough. The text describes Kehillot Yaakov as piling up qualifications until the definition becomes ad hoc and does not help in issuing halakhic rulings in new cases, and suggests that the central value of the process is building halakhic intuition through the back-and-forth movement rather than creating a formal formula.

Critique of the Deductive-Nomological Model of Explanation and Emphasis on the Path

The text presents Hempel’s deductive-nomological model, in which one explains a particular case by means of a general law from which the phenomenon is derived, and compares this to the analytical attempt to derive laws from a definition. The text argues that in many fields the formal theory covers the cases already seen but does not help regarding the next case, whereas participation in constructing the theory builds an intuitive understanding that allows future judgment. The text compares this to a historian who explains the past, but whose bottom-line formulation will not predict the future, whereas going along with the process of thought will build a “sense” for identifying new patterns.

Practical Ramifications, Critique of Brisk, and Rabbi Chaim

The text presents the value of the “practical ramification” and the tendency to establish sharp dichotomies in the style of Rabbi Chaim, and argues that “in general, a Brisker distinction of that sort is never actually correct,” but it is “always useful” as a working tool. The text argues that the mistake is to take the definitions as final and binding for mechanical work, and emphasizes that Rabbi Chaim and the Brisker method should be read primarily through the path and not through the result. It illustrates this with the analytical inquiry into damages to property—whether the obligation is negligence in guarding or “my property caused damage”—and argues that clearly there is “some of this and some of that,” and that the dichotomy is meant to build understanding, not replace judgment.

Summary of the Role of Definition

The text argues that a definition is not only constitutive or directive, but a tool that tries to aim at a concept that exists intuitively yet always misses to some extent. The text presents definition as a process of approximation that sharpens intuition, opens horizons, and then returns again to correct both the definition and the intuition in a back-and-forth movement. It concludes that the alternative—working only with intuitions—does not lead anywhere, and therefore it is vital to carry out this movement of conceptualization and return even if one never arrives at a sharp and final definition.

Basically, I spoke about two kinds of definitions: a stipulative definition and a targeting definition. A stipulative definition is a definition that creates a new concept, and a targeting definition is a definition that tries to characterize or define an existing concept. Now the question is how exactly one arrives at a targeting definition. That is, with a stipulative definition we don’t arrive at anything; we simply produce a concept by defining it and declaring to everyone what the definition will be. But when we’re talking about an existing concept that we’re trying to define—and we said that there can be arguments, I think we talked about this, right? About who is moral or who is Jewish; did I mention that? I don’t remember anymore. Yes, I think so. Once there are arguments going on about definitions, I said that one of the proofs that there are targeting definitions is precisely that there are arguments about the definitions, because there is nothing to argue about with stipulative definitions. Meaning, whatever you defined—that is the concept. Let’s just see which concept is most convenient to use, which concept better—I don’t know—fits the accepted intention. Fine, yes, that’s a kind of dictionary dispute. Meaning, what do people usually mean? Fine. But I think the arguments I’m talking about—arguments like who is moral or who is Jewish—are usually not understood as arguments about dictionary meaning. Rather, there’s some dispute here over right and wrong. Meaning, what do you mean, this is Jewish, that isn’t Jewish—not just in the accepted usage, not only in the accepted usage. And then the claim is that there is some objective something here, and we can hit the truth if we define it correctly or not. And therefore there can also be arguments over how it is correct to define the thing, or not.

Now we need to understand what exactly that means. What this really means, or implicitly assumes, is that the concepts we are arguing about, or trying to define, actually exist prior to the definition. Right? That’s the claim. We’re trying to define an existing concept. Now in what sense do they exist? If we understand it as a dispute over accepted usage, like Arik suggested earlier, then people are arguing about how one usually uses the concept. But if we are arguing about a concept not in terms of its dictionary usage, its linguistic meaning, but about what is right and what is wrong, then that means there is some point here that lies outside of us, and we are trying to hit it. In other words, it seems to me that if I enlist Plato and Aristotle for this purpose, then there is some dispute between them over how to relate to concepts.

Aristotle sees it, for example, that when we speak about properties of objects or something like that—every property of an object is a concept, right? This object is red and square and tall. So red, square, and tall are concepts; they are not objects, right? They are descriptions of objects, carried out in terms of concepts. Now Aristotle sees these things as a kind of category, meaning forms of our way of looking at objects. Plato, by contrast, sees them as ideas. “Ideas” means some abstract objects that exist somewhere, in what he calls the world of ideas, or the world of universals, the world of species—there are various names for it. But horseness exists there somewhere in the world of ideas. For Aristotle, horseness is only an abstraction that we make when we see horses. But there is no such thing as horseness; meaning, we abstract from a collection of horses that we saw and build some fictional concept called horseness. For Plato, we contemplate the concept of horseness; we do not construct it. Meaning, the idea of horseness exists in the world of ideas, and somehow through the concrete horses we try to contemplate that idea. We are trying to hit something that lies somewhere outside us. It’s not something we produce, not something we constitute, but something we try to hit—and therefore, as I said before, it can be true or false. There can be arguments about it, because usually—what is the notion of truth or falsehood? I think we talked about this once—it is usually a comparative notion.

Right? When I say, for example, “It’s dark outside now,” what does it mean to say that this sentence is true? That there is a correspondence between the sentence and the state of affairs in the world that it describes—that it really is dark outside now. So the sentence is true because there is some correspondence. And therefore, when we usually speak of truth and correspondence—it suddenly occurs to me that this is, yes, correspondence. I should have made some kabbalistic quip about that. But in any case, when I attribute the concept of truth to a definition, say, then again that basically means there is some sort of comparison here. Meaning, this definition needs to fit some thing outside me. Because a stipulative definition cannot fit anything—it produces the object; it isn’t supposed to fit anything. So truth or falsehood simply doesn’t apply to it.

So what that means implicitly is basically a Platonic view. Okay? Because only in a Platonic view can a concept—or really, a term—try to hit something outside itself. A term is a linguistic thing. A concept is the thing that the linguistic term expresses. I say “red,” so there is the word “red” and there is the concept red. The word “red,” r-e-d, that’s the word, the term. Why do you need to claim that? What? I’m claiming that the proposition “the apple is red”—let’s take that—you say that means there has to be a red outside us or an apple outside us. No, I didn’t say such a proposition must—I didn’t say that. Aristotle also made such claims and thought there was no such thing as red really outside us. No, I wasn’t trying to prove the Platonic view. What I claimed is that if I say there is a targeting definition and not only a stipulative one, that presupposes a Platonic view, right? Now you can accept that or not accept it; you can be Aristotelian too. But I’m saying: if we arrive at the conclusion that there is a targeting definition, then that means we are implicitly assuming some sort of Platonic view, that we are directed toward something outside us. What is that thing outside us? Yes, it is that very point—perfect ideas.

“Targeting”—is that the new concept in your definition or the existing concept? Targeting and constituting are two kinds of definitions. A constitutive definition is a definition that creates the concept, constitutes it; it is built on the definition. Exactly. The concept is built on the definition. It has no existence outside it; the definition constituted it. “He made you and established you.” By contrast, a targeting definition is a definition that tries to mean something that already existed beforehand. It’s a bit similar to what researchers of Jewish law or of Talmudic thinking call a sustaining midrash versus a creative midrash. A supporting midrash, a sustaining midrash, or a creative midrash. A supporting or sustaining midrash is a midrash that takes a known Jewish law and tries to anchor it in biblical verses through exegetical tools. A creative midrash is one where the Jewish law is created by those exegetical tools—we didn’t know it before; the exegetical tools produced it.

But still, why must it refer to something outside us? Why not to the shared conception that exists in our consciousness? That’s what Arik said earlier. Meaning, of course one can also argue over what the accepted usage is. Meaning, yes—and then that does not presuppose a Platonic view. But I said that I think the arguments—the arguments I mentioned last time, what is a democratic state? What is a Jew? What is moral?—those arguments are too emotionally charged to think they are merely about what the accepted meaning is. When you argue about whether a certain act is moral or not, do you see that as a linguistic dispute? Is it proper to call it moral? After all, we are arguing about what morality really requires—whether it requires such an act or its opposite. So that means the concept of morality is not constituted by us. There is such a thing, and I condemn you for doing something not in line with my definition. I’m not saying, “You’re simply not using the concept of morality correctly; let’s find another concept that fits better.” That sounds too neutral for these kinds of arguments.

So I’m saying: there are concepts that are constitutive, where the definition there is constitutive, and there the argument really will be about usage. But I think there are also concepts where the role of the definition is a targeting role and not a constitutive one. Is it the same principle, that whoever holds of the targeting definition must assume Platonism—must he hold the same thing also in all the disputes about the synthetic-analytic distinction, about philosophy of science? Is there a force of gravity or only a law? And if I hold that there really is a force, is that the same—an implication of the same dispute? Yes. I connected it to the analytic and synthetic in the book, although I explained that it’s not exactly the same. Meaning, it could be, for example—actually maybe I’ll define another pair of concepts and then come back to that point.

There are conceptions of concepts as conventions—meaning, a concept is a convention. I’m describing the same distinction I made earlier, just again, with another pair of concepts related to this issue. Convention means that we agree among ourselves to define some concept in a certain way, and that is how it is created. What Kripke—I may have mentioned this—what Kripke calls baptism. Just as you baptize a baby and give him a name, a Christian baby—you baptize a baby and give him a name—so too with a concept: you baptize it and attach a linguistic term to it, a word. A concept is the thing the term describes, as I said before. That is conventionalism. And then there is essentialism—the view that says that a concept has some existence not by virtue of baptism, not by virtue of a social agreement that we all agreed to use this word in that sense; rather, I am trying to hit the essence of the concept. Convention is not enough here. Okay?

Now, this goes back to what you said earlier. In the book I said that analyticity and syntheticity, in their pure form, are really logical conceptions. They are connected to logic. Meaning, whether you accept only valid logical arguments as admissible arguments, or whether analogies and inductions and things that are not valid logical arguments also count—something softer. Here, though, I am not speaking about logic but about epistemology, which is something a little different. Right, in practice they usually go together. Someone analytic in the logical world is usually a conventionalist in the epistemic world. That is the bitter reality. Someone who plays only with logic and is unwilling to do things that are not absolute and not certain naturally doubts concepts like ideas that nobody sees, so he says no, that’s fiction—you are really just dealing with convention, simply defining something, and it basically comes from within you, not from something outside. Okay? Therefore I think that in practice it really does go together, but I’m saying that on the logical level one can separate the two. Meaning, you can be a conventionalist and synthetic, or the reverse. I don’t think there is a logical necessity to attach those two things to one another.

Okay, now I’ll try to show an example that illustrates this point. There is science in the service of political correctness. How does that work? By the way, that penny also dropped for me in Sde Boker, at that famous meeting. A lot of pennies dropped for me there. A meeting with Ben-Gurion? No. I once lectured on tolerance and pluralism and said that the penny dropped there—what the difference is between them—at that meeting in Sde Boker with the folks from the midrasha. And this penny also dropped there. Because they invited me to speak during the Ten Days of Repentance with the students. Not the university lecturers there, but a different meeting—with the students in the environmental school, an environmental high school, very good kids, an excellent school. And they asked me to come and speak during the Ten Days of Repentance about atonement, apology, forgiveness—about that whole conceptual world, not in the religious sense, not in a religious context. To speak about the concepts, their human significance, their moral significance, without any connection to religious matters. That’s what they asked of me.

So I began with a question. I said to them: suppose someone hurt his friend and went home, and he understands that he hurt his friend. His heart doesn’t ache, he doesn’t care about his friend one bit. He doesn’t care about him at all. But he understands that he did something wrong, and he goes to apologize. Intellectually he understands that if you did something wrong, you should apologize. That’s one character. The second character hurt someone else and feels guilty; he has stomach pains, and then he goes to make peace with the other person, to ask forgiveness. Which of them is the real penitent? A moral penitent, not a religious one. The real one. The first one—do you accept his request for forgiveness? I asked them. The first one, who feels nothing and doesn’t care about you at all? And everyone said, of course not. I said: I accept only that one. Why? Because the second asks forgiveness in order to calm his own stomach pains. The first asks forgiveness because he understands that it is right. Because he understands. What, do I have a problem with the fact that he is autistic? That he doesn’t have the feelings that are supposed to arise in a normal person when he hurts another? In us certain feelings arise—what are called pangs of conscience. In him they do not. He is autistic, fine, his amygdala is damaged, so what? But in the end he understands that he did something wrong and he comes to ask forgiveness. It seems to me that this is the finest penitent one could imagine. The second, in my view, is someone who is really doing the act for himself, not for me. Because he has stomach pains, and to calm them he asks forgiveness.

Anyway, from there we started developing in the direction of intellect versus emotion. Because the first one—it’s not that… he did the act not for you but for the moral law. Yes, not for me, but solely for the moral law—that is what I appreciate, I accept that. Meaning, not that I meant “for me” in the personal sense, but rather not for himself, but because that is what is right. A kind of Kantian thing, meaning he does it because the categorical imperative requires asking forgiveness. Fine, I very much appreciate someone like that. I think that is the purest request for forgiveness there is, in my view. On the contrary, someone who does it out of feelings—it may be that this too is a genuine and proper apology, everything may be fine—but it’s hard to know, because maybe he’s doing it merely to calm himself down.

Sometimes it’s like the Eglei Tal in the introduction—I may have mentioned that too once; I’ve mentioned everything once. He says that there are those who stray from the path of reason and think that one must not rejoice when studying Torah, one must not enjoy studying Torah, because then the study is not for its own sake. And there is no greater mistake than this. We bless and ask every morning, “Make the words of Your Torah pleasant in our mouths, Lord our God.” The fact that you enjoy it is perfectly fine. On the contrary, he says even more than that: the essence of the commandment is to enjoy it, because then you connect more deeply to the things, understand them better, internalize them more. But afterward he adds something that people know less well. He adds there and says: yes, but someone who does it because of the enjoyment and joy—that really is study not for its own sake. If you enjoy and are happy that you are studying, excellent, perfectly fine. But are you studying for the sake of the enjoyment and joy? That really is study not for its own sake.

This is exactly the same phenomenon I’m speaking about here. It may be that when you ask forgiveness—if it’s also… that’s already a topic at the beginning of tractate Zevahim, you know, “for the sake of Passover” and “for the sake of peace-offerings,” meaning when you have two intentions, does that count as “for its own sake” or not count as “for its own sake.” At first he does it incidentally, he enjoys it, and afterward already out of enjoyment. Could be. But I’m saying there are complex situations. Right now I’m speaking about the two extreme models. Fine—one does it this way, and one does it that way. So the question is, who is the one who studies for its own sake? If he does it for both, fine, that’s a mixed case; there is room to discuss it. But what happens if he doesn’t do it for both? He does it for the sake of Heaven, but he enjoys it. He would study even if he did not enjoy it, but he does enjoy it—does that disqualify his study? Certainly not, right? Because in the end he is doing it for the sake of Heaven. But if he is not doing it for the sake of Heaven but for the sake of the enjoyment—not that he enjoys it while doing it for the sake of Heaven, but he does it for the sake of the enjoyment—that is study not for its own sake. That is what he claims there further on, and it sounds very reasonable to me.

So the same thing here as well. You ask forgiveness because you feel guilty—it may still be that you are asking forgiveness for the true reasons and this is a pure request, everything is fine. And together with that, you also feel guilty. The question is whether that is the case, or whether the guilt is what leads you to ask forgiveness because of it; you go ask forgiveness not because you truly understood the mistake you made, the wrong you committed, the injury to the other person. Can one exist without the other? I think so. Many brain researchers claim not, and I don’t think they’re right. They claim that once you lack the capacity—when the amygdala is damaged, as I said earlier—you lose the capacity for empathy and no longer feel the other person. And once you do not feel the other person, you cannot understand that you hurt him. So where would guilt come from? He has no guilt. Someone whose amygdala is damaged has no guilt. That is the person, the autistic person I spoke about earlier—the autistic one.

What do you mean? He has guilt? Yes, that’s how we are built: after we hurt someone, we feel guilty. And why does the first one ask forgiveness? The first one because he thinks it is right. What do you mean he thinks it is right? It is right to ask forgiveness after I hurt someone. Why does he think it is right? Just because it is right. What do you mean, why? If I explained why through some other principle, you’d ask “why” about that one too. At some point it stops, right? That is a moral axiom. He says: if you hurt someone, you should ask forgiveness. Kantian. A Kantian principle. There are always starting points such that if you ask me why, I won’t know how to answer, but it begins there—it is self-evident—and from there I can begin to reason about things. So I’m saying: values begin the chain of reasoning. They cannot be grounded. Values. We spoke about this once on another occasion with Leibowitz here, with the “disconnecting from instruments.” Yes, Leibowitz’s essay “The Disconnecting from Instruments,” where the claim is that one cannot fundamentally rationalize values. If there is a reason for a value, then it is not a value—it is a means. Essentially, the value is the thing that justifies it, grounds it; the thing you are grounding is really coming to achieve the thing that grounds it, so the grounding thing is the value, not the other one. When you reach the value, that cannot be grounded. And the value is that when I hurt someone, I ask forgiveness. That is an internal moral value, not because I am relieving difficult feelings inside me, but because this is what is right. In my eyes that is an amazingly pure act.

Not sure it’s pleasant to live with such a robot—that’s another question. The problem also is that if I am autistic, I don’t know whether I’m hurting him. Exactly. That is what I started to say before, that brain researchers tend to think that once the amygdala is damaged you cannot behave morally, cannot exhibit moral behavior, because they hang moral behavior on empathy. Only when you understand that you have hurt someone else can you respond accordingly—that is, first of all, only then can you refrain from hurting. You understand that such a thing hurts him; afterward you can go appease him, ask forgiveness, and so on. But that can be a convention. What? That he knows that if someone does such a thing, then there is a convention that he should go… No, so that is what I’m saying. It can be a convention, but I am not satisfied with that. Of course it can be. There was even once a TED talk by some neurologist, a TED lecture, by a neurologist whose brain was damaged—something like split-brain or something after surgery, I don’t remember exactly what was there—and she described how she nonetheless manages to function within society without feeling everything that we feel. A stroke, I think. I think it was a stroke in the left side. And she described how she still manages to function within society without feeling everything we feel, but she understands that this is how one should act, so she…

It’s like—I was thinking about this a lot today, I’m wandering—thinking about Nash, when I read the book or saw the film A Beautiful Mind. It’s amazing, at least as the movie presents it. I think that’s somewhat simplistic, but the movie presents it this way. The first half of the movie I enjoyed, until I went out at intermission and went home. It looked like some bad thriller about agents attacking him, Russians and all sorts of things. So I didn’t get the point. Then after the intermission, suddenly you understand that all those agents never existed; it was all in his mind. You understand? Now Nash, because he had Nash’s intellectual ability, apparently managed somehow to understand that although it was obvious to him there were agents and everyone else were idiots because they couldn’t see them, somehow he managed… From his website—I read it—he writes there that his feeling was like being on a strict diet. He wants to do such-and-such, but he thinks about it, and this he won’t eat and that he will eat. No, but the miracle is that he managed to understand that he was the one who was wrong and not the others. That’s impossible. How can you understand such a thing? You are convinced that you see Soviet agents here. Everyone else doesn’t see them—all those complete blind idiots. I see them. Fine? And now I need to decide that the fact that I see them is the illusion, and all these blind people are actually the ones who are right.

Maybe it’s similar to vertigo… Vertigo, where you need to trust the instruments… trust the instruments, exactly, rely on other people. But I know I’m a smart person and they’re all idiots, so what does it mean to rely on all these idiots? This point is very hard to understand—how did he…? Yes, I’m crazy. Exactly. That’s Rabbi Nachman’s story. If I… no, if I… the grain… the wheat that they wrote for themselves, they wrote for themselves… “I am sane.” Ah, they wrote “I am sane” or “I am crazy”? No, “I am sane.” Why? Everyone else will say about them that they are crazy, and they wrote down, to remember: “I am sane.” That’s how… Maybe the opposite in the story, actually… It doesn’t matter, it’s the same idea, the logic is the same logic. In the version of the story I remember, they said: if we don’t eat from the grain, and we go mad—yes, but if we don’t eat, we won’t be able to live. How will we live if everyone is crazy and we alone are sane? So we’ll go mad too, we’ll also eat, we’ll also go mad, but we’ll make a sign to remember that we are crazy. Okay, fine, I don’t remember. So maybe I don’t remember the story. That’s how I remember it, but in any event… There are probably several versions.

In any case, I’m saying that with Nash you could say: so what did Nash do? You could say that Nash followed conventions. He didn’t truly understand that they were right; rather, he understood that in order to function within society, you need to be in discourse with the rest of the members. Then it’s just a convention. He didn’t really understand that they were right and he was wrong; rather, he understood that only this way could he function in society, otherwise everyone would see him as crazy. So he had no choice; he adopted the mistaken point of view as the price he paid in order to be part of the group, of human society, meaning to be able to communicate with other people. But one can understand it differently: no, he really understood that he was wrong. It’s not a convention—that’s why I brought the example. It’s not a convention. I understand that I’m wrong.

Now similarly, a person can detach from experiences—that’s the point—and operate his intellect in a way that is not fed or controlled by emotions, experiences, things that don’t really come from him but are somehow imposed on him. Fine? They come to him without his control. And in this sense too, I think a person can understand that this is the right way to behave morally. Of course, he needs to understand that he hurt someone—that is certainly true. Because if he doesn’t understand that he hurt someone, then he doesn’t understand what he did. He simply doesn’t understand. Only after he understands that he hurt someone, when he goes to apologize, then he can do it instinctively—because I have empathy, I understand that I hurt someone, and immediately this request for forgiveness comes out of me. Or I can understand: no, now I understand that I was wrong because I have the capacity for empathy with the other person, and now I ask forgiveness because I think it is right to ask forgiveness. Not as some reflex that passes through me. It is my decision. It is not something that happens through me, okay? Both those things are possible. Moral behavior, it seems to me at least, is supposed to be of the second kind.

Anyway, that’s not the point. Afterward, as things continued, they started talking to me about emotional intelligence and non-emotional intelligence and yes, De Bono’s six hats and all these things, and that’s how they managed to annoy me there, and then the penny dropped for me. That whole story was leading up to this penny. And then they said to me: “What do you mean? There is emotional intelligence. Not everything passes through the intellect. The heart also has some kind of intelligence. A different intelligence.” I told them that in my eyes this was just political correctness. You want to comfort stupid people, so you tell them, “You have high emotional intelligence,” meaning people who have no intelligence. I told them: how does this work methodologically? How does science now work in the service of political correctness?

You basically want to make everyone come out okay—that’s political correctness. Everyone should be a genius like Einstein, fine? So what do you do? Usually when we look, we say Einstein is a genius and others are not. So what do we do? How do we make everyone geniuses? We want to produce other intelligences. We say: “They have been endowed with intelligences of another kind”—which Einstein perhaps didn’t have, or maybe he did too, doesn’t matter—but they too are geniuses in another context. How do you do that? So how was this notion of emotional intelligence actually produced? Later more pennies dropped for me; I’ll add them in a moment, but this was the first penny. How is it done in practice? I take the concept of intelligence as people understand it, and try to distill from it its essential characteristics. This is really the meaning of observing the idea. I try to distill the essential things to this concept and clean away what is non-essential, okay? And once I succeed in distilling the essential things, the set of those essential things is the definition of the concept. Meaning: take all the features, extract from them the essential parts, and then I have a definition of the concept. Okay? Now that is what they did there, and they came, I think, to five parameters or something like that that define intelligence. Fine?

Now, not “someone just casually says, let’s call that intelligence.” No, no, no. There is organized work here. People make a living from this. There is organized work, with, I think, five—I’m no longer one hundred percent sure, but I think five—features that define the concept of intelligence. And now you look at Maradona and say: wow, he too is intelligent, not just Einstein. And also, I don’t know, someone who knows how to function well in social-emotional settings and so on—emotional intelligence, motor intelligence, this intelligence, that intelligence, lots of intelligences. Okay? And everyone comes out intelligent. Wonderful. What’s the bug? The bug is that it seems this is a targeting definition, not a stipulative one. Right? After all, I took people’s intuitions about what intelligence is, and from that—how did I start?—from that I distilled the five features. Right? I have to start somewhere. Unless I invent the features, and then the definition is stipulative. Right? But if it is a targeting definition, then there has to be some input. Meaning: on what am I basing the definition, and against what am I checking it to see whether it is correct or not? Right? A targeting definition is checked to see if it’s correct. So I check it against what people generally call intelligence. Okay? And then something very strange comes out.

Because before I started the work, ordinary people called Einstein intelligent and not Maradona. Fine? I distilled the features out of what people say. And then suddenly I arrived at a situation where Maradona too is intelligent. What is the conclusion? That there are multiple intelligences? A feature is missing. Right. The conclusion is that I distilled incorrectly. After all, if I distilled correctly, then the definition should match how people see the concept of intelligence. Why? Maybe… one second. If people see the concept of intelligence in Einstein and not in Maradona, and I am trying to understand what they are doing—not teach them, not innovate a new definition, but aim at a concept that already exists prior to the definition—well then I failed. I failed to hit it. Because when I defined, when I extracted the definition, when I distilled the features and built the definition, it suddenly turned out that it does not give me the same results that people ordinarily attribute to the concept of intelligence. So what does that mean? That the definition does not fit people’s use of the concept of intelligence.

Who said Maradona isn’t intelligent? What? That’s what they said? Intelligence… that’s what the multiple-intelligences people say. They say there is motor intelligence. That’s the move, that’s the move. But motor… yes. It doesn’t go in one breath with intelligence. No, no, all of them are intelligences. There is only… all of them, all the intelligences satisfy the five features. He also has intelligence in dexterity with his hands. No, again. Let’s sharpen the move better—it’s subtler. What we call intelligence is not that. No, no. If it’s not that, then it’s not that at all. I’m saying this is an important point. What are the five features? I don’t remember. There are five features that define the concept of intelligence. Fine? Now motor intelligence is also intelligence. It has additional features that emotional intelligence doesn’t have. Fine? That is what distinguishes it. Emotional intelligence has its own features, and it is emotional intelligence. What? No, it has the five features of intelligence. It has a sixth feature, which determines the species within the genus. The genus is intelligence. What? No, there is nothing wrong except that it’s inconsistent.

Why? If he has those five features, then that also works in the legs. Fine—but he has those five features, right? Apart from the fact that the legs… I’m saying, apart from the legs he has those five features. Right? Did they check that? I’m saying Maradona is an example; I’m not fixated on Maradona. Motor intelligence is also intelligence. Put more sophisticatedly. I didn’t understand. When they distilled and came to five parameters, yes, did they then go and check whether they are found also in people who are not defined as intelligent? Yes. And the whole purpose of the move was… and they found that yes, of course. The whole purpose of the move was to expand the concept of intelligence and put an end to the arrogance of the wise in their own eyes, who think they are intelligent and others are not, or that all of us think they are intelligent and others are not. Let’s educate the public: everyone is intelligent. How do you do that? Distill the features from the concept of intelligence, distill the features from the concept of intelligence, and suddenly discover that it really applies to many more people than we think.

Don’t those parameters involve quantity? What? Don’t they involve quantity? No, these are types. That’s why I say quantity doesn’t matter. Maradona may be quantitatively as intelligent as Einstein, just in another domain. Say Einstein has the same quantities in all five parameters? Not in all… yes, in the five parameters yes. Not in the sixth. The motor one—Einstein, I assume, was a less talented soccer player than Maradona. Though one could… So in what was Einstein superior to Maradona? In intellectual intelligence. I don’t know, I don’t want to offend you, but maybe Einstein had more intellectual intelligence than the other side. What? Can’t we say that Maradona is motorically gifted and that’s not intelligence? No, no—again, I repeat: they did say that. I’m not talking right now about measurements; measurements are secondary, even though they do measurements too. I’m talking about the principled move.

In the principled move, whenever we define intelligence, anything that has an adjective attached to it—as in the Talmud—emotional intelligence, motor intelligence, what does that mean? That first of all it is intelligence. One, two, three, one, two, three, four. Exactly. That first of all it is intelligence, and those are the five features that everyone has in all the types, besides there being additional features that define the species. But what seems difficult to me is how it can be that Einstein and Maradona both satisfy one, two, three, four, five. Why not? Gardner—he returned to the same point. We’re all, leave aside the word intelligence, we’re all human beings, except one is a coal miner and one is a carpenter. What? So you… you’re too broad, that doesn’t help. He’s going to demand his own solutions; the difference here is… There is no point arguing, since I don’t remember the five features. One has to read the relevant books or relevant articles and see. I’m speaking now about the schema, the logical schema.

Do the five features also vary from person to person? Meaning, there is a person who in the fourth or fifth of the general five features is better, as it were? In the five features, in terms of intensity, I think—though truly I’m not an expert in this field. In terms of intensity, if there is such a thing at all, I think you then already need to talk about the type; you need the sixth feature in order to determine intensity. Understand? It’s like someone who has traits. Not saying which traits—good traits or bad traits. Whether he has many traits or few traits—that is not relevant. First tell me what kind of traits he has, and then I’ll tell you whether he is very kindhearted or only slightly kindhearted. I think there too the measurement has to appeal to which intelligence you are talking about. There is no measurement of intelligence, it seems to me, of abstract intelligence. Okay. Even in character traits it doesn’t work as you say. What? Because a person who has one-sixty-fourth of pride has pride, right? A lot. And a person who is arrogant also has pride. Of course—but a lot. And we say that this is good and that is not good. Well, of course, because this is little and that is much. What do you mean? It works exactly like that.

In what was Einstein better than the carpenter? I didn’t say he was better; I said he was more intelligent. And in what was he wiser? He knew how to formulate the theory of relativity and the carpenter didn’t, and neither did I, to my shame. What? There are differences between people. Of course there are differences. No, it’s “different but equal”—that’s the whole idea here. The lawyers shouldn’t hear this; it’s forbidden. Because what they want to say is that Maradona is equal to Einstein—not in the sense that he too knows how to formulate the theory of relativity. That simply contradicts the facts. The stupidity doesn’t go that far—I mean the stupidity of the researchers. What they mean is that Maradona has abilities fully equivalent to Einstein’s, in another domain. The fact that the crowd gave him the… the hand of God… Yes, exactly. Right, and they didn’t even whistle him for it, yes? So… the hand of God… hand… hand… not basketball, soccer. In soccer if you touch with your hand they should whistle; in basketball you need to touch with your foot for them to whistle. Not legal but not proper. He scored a goal with his hand. Fine. In any event, don’t think I understand like Menachem… It sounds like the secrets of insiders; I know a little… that I have no such motor intelligence.

In any case, the point is that when you try to distill the five basic features, okay? then assuming you are really doing a targeting act and not a stipulative one, the product should stand in correspondence to the starting point from which you began—the way human beings use the concept of intelligence. Now it turns out that the correspondence doesn’t work, because those five features are also found in Maradona, while the very people from whom I distilled those features did not call Maradona intelligent. So what does that mean? It means that I did not distill correctly. It does not mean that Maradona too is intelligent; it means I did not define the concept of intelligence correctly. They are searching for a concept, yes, trying to point here to something, trying to point to something specific, to aim at it, but they don’t have the concept. The closest thing that seemed suitable was ordinary intelligence, the intelligence we know, and then he expanded that concept, called it intelligence-plus by analogy from the concept of intelligence in order to describe something. If that is so, then we’ve come back—and that’s why I bring this example—then we’ve come back: if so, this is a stipulative act. Entirely stipulative. But stipulative… stipulative in… a stipulative act is not research… because until now we didn’t call Maradona intelligent. Until now we didn’t call Maradona… But scientific work is supposed to be targeting, not stipulative—we’re not philosophers. Yes, but it’s not that simple, because it did use another concept in order to look… What? So I created something out of nothing—so what? Does that make me a scientist? A scientist is supposed to describe what exists.

There is ordinary intelligence… there are concepts one can use to describe it… To describe what exists, you define concepts… No problem. But in the end you can define whatever you want; the science is not in the definition. The science lies in what you do with the definition. Take the definition and now check whether Maradona satisfies it—that is scientific work. No problem. But the definition itself you created through a stipulative process, not a targeting one. It is entirely targeted, entirely targeted. There is an ability—intelligence—from the capacity for discernment, I don’t remember the Latin word, from the capacity for discernment. There is a capacity for discernment in the mathematical areas where Einstein is strong, and there are people who have emotional discernment. Now there is something there; it is directed toward that. You can argue that the use of the word intelligence perhaps was not successful and they should have called it emotional discernment. Okay, so I… that’s the next penny. I said I’d get to the next penny. I completely agree. The first penny dropped, but it was clear to me that there was some terribly basic failure here.

But in the end, since I do believe that when people speak about concepts, these are usually targeting concepts, concepts that exist—and the fact that this thing was accepted, meaning multiple intelligences, and people speak about it, and it is also apparently fairly fruitful in those fields at least—so that is the second penny, which basically says that I was not right before. In the end there is some process of back-and-forth between the stipulative and the targeting, and this connects to the question of the types of definitions. I essentially begin with a concept, and this is indeed scientific work—some hybrid stipulative-targeting work. I begin with an intuitive concept. Everyone uses the concept of intelligence, and more or less understands what is being talked about. This is intelligent, that is not intelligent, this one has a lot of intelligence, that one has little intelligence. Fine? Now I ask myself: what exactly do they mean? So clearly my starting point is what they say. But afterward I find some definition, distill a definition. At the next stage I say, wait a second, I can now expand this definition. Maradona too is intelligent, not just Einstein. Now I go back to the original group and say to them: friends, Maradona is intelligent too; you were mistaken. And suddenly they are convinced.

And if they are convinced, that means I discovered something new; I did not create something new. If I had created something new, then when I came back to them they would say to me: define another concept, use it as you please, but I will not agree that you say Maradona is also intelligent. But if I go back to the original speakers and say to them: friends, I am taking the concept you use and defining it in a certain way. Do you agree to the definition? Now I use that definition and I see that actually it is much broader. Why don’t you also relate to him as intelligent, and him as intelligent, and so on? Then if I gain agreement, and if they suddenly grasp it, then I have expanded their understanding of something that was already inside them before; I have simply pointed out an error to them.

Very often this analytic path, the attempt to distill, to make an analysis of a concept and provide it with a formal definition, helps us think about things that we in fact already know. Only it has not become explicit. We do not use concepts that are actually known to us, but we do not use them correctly. We once talked about geometry, right? A teacher teaches geometry to a child. Now all four axioms of geometry are known to every child. Everyone knows that between two points there passes one straight line, that two parallels do not meet—simple things. But no child would arrive on his own at the fact that the sum of the angles in a triangle is 180 degrees. Almost no child; he would have to be very talented for that. The teacher helps. Now what does it mean that the teacher helps him? Does the teacher invent? No, the teacher reveals to him that within the axioms, which he too understands, within those axioms, if you dig in them properly, if you analyze them properly, you will discover the theorem that the sum of the angles in a triangle is 180 degrees. After I reveal this to him, he will find it within himself. Meaning, after I make this mathematical move, the person will understand that it is self-evident that a triangle has 180 degrees. It’s obvious. It was latent within the axiom. How did I not see this before? Fine, it’s understandable how I didn’t see it before, but in principle I could have seen it before too, because it was really something I knew implicitly beforehand. The analytic process exposed to me something I was not aware of.

Now if I understand the analytic process of the intelligence researchers in that way, one can also offer it a targeting meaning rather than a stipulative one, and it will still work. I think that is basically what you meant to say. I go to people and say to them: look, you think Einstein is intelligent and Maradona is not. I claim that you are mistaken. You are mistaken even according to your own definition of intelligence. And let me show you. Let us go together and try to define the concept of intelligence. Look at what you think about Einstein; try to define the concept of intelligence. We defined it. Then I say to them: okay, let’s see—those five features all also exist in Maradona. Fine? So what’s the problem? Why do you think he isn’t intelligent? And then the person slaps his forehead and says, wow, you’re right, he’s intelligent too. And what does that really mean? It means that I exposed an error that he had been living in. He was simply living in error. The intuitive concept he used was indeed the correct concept that I distilled. When he used it, he used it incorrectly.

Just like in a moral argument. When I convince someone about a certain act that it really is moral or really is not moral, and he thought otherwise—suppose I convinced him. Does that mean I changed his moral concepts? Usually not. Usually I take his moral concepts and try to show him that such behavior does not fit his principle. Because if it fits my principles but not his, I won’t be able to convince him. He’ll say: that’s your morality. My morality says otherwise. When I convince him, that means that within his own moral system it is not right to behave that way. So why did he behave that way? That’s a sign that I didn’t distill his moral system correctly—when I tried to show him what his moral system is, I didn’t distill it correctly. No, that’s not true. He didn’t distill correctly. I distilled correctly, and if in the end he agrees, then it is entirely possible that I distilled what was inside him better than he himself did. Okay? And that is why I convinced him.

Now of course this is a very delicate thing, because it depends somewhat on analytic abilities and intellectual abilities. I can fool people. There are people who are not sensitive to this nuance: whether the definition is stipulative or targeting. And then you can fool them, because people don’t catch this catch, which really is just a catch. You take a person and say to him: look, you use the concept of intelligence, you say Einstein is intelligent and Maradona is not. And suppose that in fact his concept of intelligence applies only to Einstein and not to Maradona, for the sake of discussion. Now I do this trick to him, I distill five features, and here, you see, Maradona is intelligent too, and he is convinced. And maybe he is convinced because he is a fool, not because he discovered something else within himself, but simply because he isn’t smart enough to understand that I fooled him. So indeed, then it really is a catch, a serious catch. Exactly. Then indeed, he probably has emotional intelligence. So I’m saying: in such a case, that really is science in the service of political correctness.

Is the empty set a targeting definition? What? Is the empty set a targeting definition? Not the empty set—every set. Why are you asking about the empty set? The concept of a set itself—what is it? A collection of elements. Fine, but is that a targeting definition or a stipulative one? I can define a set; I can say even the empty set is either targeting or stipulative. That is the dispute over Platonism in mathematics. The question is whether mathematical concepts exist—whether you are Aristotelian or Platonic. Do they exist in the world of ideas, or are they merely forms of my way of looking at things and categories? But you can’t accept a definition that contains a contradiction and still insist that the definition I understand is stipulative. Why? Who said it contains a contradiction? If it’s a set, it’s a collection of elements. This is Rabbi Zini in his famous article. No, in Rabbi Zini’s article it was when he taught set theory. Rabbi Zini wrote an article in the book Higayon, where he says that he was teaching set theory at the Technion—I don’t know if he still does, I don’t know. He says there that he opens the first class by saying: a set is a collection of elements. Naive set theory, of course; today we don’t define it that way. A set is a collection of elements. And immediately after that he says—what does he say? He starts talking, and then says: the empty set is a set without elements. And everyone writes this down enthusiastically and with holiness, all trembling with holiness as they write his words, and nobody notices that if you say a set is a collection of elements, and then define the empty set as a set devoid of elements, then it is not a set! Because a set is a collection of elements! Just as zero is not a number, yes? It’s that same sensitivity. Fine? So nobody asks, nobody even blinks.

He says this is exactly like when you hear ideas from a rabbi or, I don’t know, in the religious world—then all the intellectual students mock those who accept things without asking questions. You accept your rabbis in exactly the same way. That is what he basically wanted to say there in the article. Yes? So I’m saying there too—but there could be basic concepts that have no definition. What? Right! They have no definition, but do they exist? Yes! Exactly. Then he is a Platonist. Right? The concept of a set is not a collection of elements. You simply erred in the definition. Rabbi Zini was wrong, not they. It’s not true—a set is not a collection of elements. Most sets are collections of elements. At least one is not. The empty set is not. In any case it is somewhat similar, but it is not that. We approximate it with the definition “collection of elements,” but we understand that a set— in what sense is the empty set also a set? Especially after we already invented zero and zero is now considered a number; we’ve gone through a lot of processes, and now we understand it. We have enough capacity for abstraction to live with this thing, and now the concept of set is different. Did we invent it? That is the same question. Is this a stipulative definition? Did we really create the concept of set out of nothing? Or is this a targeting definition?

We managed to hit the concept of set, even though in the past, if you had asked people, they would have said: the empty set? What’s that? That’s not a set. A set is a collection of elements. But if you do the process, like with intelligence—distill what a set is and succeed in showing them that the empty set is also a set—then they might say, wow, we were mistaken, the empty set is also a set, and this fits our intuitive concept of a set, even though it doesn’t fit into the formal definition. Fine? And I spoke about Pirsig in the previous lesson or the one before that, about Zen and the Art of Motorcycle Maintenance, where he says that at some point he wakes up and says he is chasing after the concept of quality. How to define the concept of quality. He says the Greeks messed up our minds because they put into our heads that anything we haven’t defined doesn’t exist. When he speaks of the Greeks, he means Aristotle, of course. Aristotle, not Plato? What? Actually Aristotle, I think. Plato is the opposite. Fine, but he says things exist; they are not contingent on your defining them. For Aristotle, the concept doesn’t really exist; once you define it, that constitutes it, it doesn’t target it. No, because with Plato you begin with there being lots and lots of human beings, then they mention some concept, and then he says to them: what do you actually mean? Yes, yes, of course. That depends on what meaning you assign to the Socratic process. Does he mean to confuse them and basically show them they understand nothing, or does he mean to teach them? Is it simply a Socratic way of teaching?

The conclusion of the early dialogues, at least, was that they understand nothing. Could be, I’m not sure. But it seems to me that the goal of the Socratic process was not to show them they understand nothing, but to show them what they understand, better. That is exactly the same thing, exactly the same claim I made here. Just like the goal of defining intelligence is not to show you that you understand nothing because you saw Maradona as intelligent, but to try to make you understand better what you in fact understand deeply or implicitly already. Once you conceptualize it, define it, then it becomes a kind of interplay between our intuitive perceptions and the definition. The definition helps us understand more intuitively, but it is not obligated to match exactly… You wanted to say here that this is a matter of back-and-forth, something circular. Exactly. Meaning, I take the concept of intelligence, which is intuitive. Intuitively, all the while he was not using it correctly; he thought only Einstein was intelligent. And I say, okay, now let’s go to the analytic side, let’s analyze the concept and extract five features. Okay? Now, with those five features I’ll examine Maradona. Wait, Maradona satisfies those five features? Good. Now I return to myself and say, wait, I understand that these features captured the concept excellently. And if it applies also to Maradona, that means my intuition is not what I thought it was. I discover something about myself through this analytic process. This is not a defining process, it’s a targeting process. Meaning, it tries to target the concept of intelligence that exists within me, not define the concept of intelligence stipulatively. Therefore I say: this is simply excellent. That’s the second penny.

But by taking from the original intelligence this new shared intelligence, you created—you targeted a new concept. There are now two concepts here, because when I say Einstein is intelligent, or when I speak about intelligence, “intelligence,” these are already two different things. No, fine, but I exposed to the person that within the conceptual world of intelligence there are types and species. He was sure that the one species called intellectual intelligence, say—that’s how they call it there, whatever—the intelligence of Einstein, he thought that that intelligence is what is called intelligence. Then suddenly I opened his eyes and said: wait a second, there is a concept of intelligence that is broader, of which that is one species. There are other species. And all this after I defined it for him; he discovers it within himself. He really understands that before he was looking too narrowly. You found several new concepts and used names… meaning, you found several new concepts. No, that’s exactly it—I found, I did not invent. I discovered, I did not invent. I did not invent, you are extracting what exists in reality, but you found several new ones. What do you mean new? They were not new; they exist in reality. I did not create them. Yes, the terms. He also grasped it—the person grasped it—because if he hadn’t grasped it even afterward, the whole process wouldn’t have worked. So in the end he understands it because it was inside him; he simply used it incorrectly.

And this is a very important point for understanding the role of a definition. The role of a definition is very often to bring us precisely to this result—that it doesn’t fit our intuition. Because if it fit our intuition completely, then why make definitions at all? Usually we make a definition in order to sharpen our intuition better. But “sharpen better” means that there will be some difference between before the definition and after the definition. But if indeed the moment there is a difference I have failed in the process of definition, then there is no point in doing it. This idea of back-and-forth is the next stage. Meaning, I began with stipulative definitions, said there are also targeting definitions—which many people perhaps at first glance don’t even relate to as definitions, because it sounds like conceptual nonsense. Then I said, wait, but there is some problematic process here. Then I said yes, but there is back-and-forth. And this back-and-forth is actually a result of this Platonic conception of targeting definitions. There is a concept that exists. There is my perception of the concept. I perceive it correctly, but I just don’t use that perception correctly. Somewhere inside, if someone reveals it to me, I will find within myself a correct definition of the thing—if I need help from outside. But in my initial intuition I do not use it correctly. So what do we do? We go to the analytic side and define properly, even though that seems to move away from intuition; we try to capture the intuition. But of course one has to be aware that very often the definition does not succeed in fully capturing the intuition.

It does not fully capture it, but gives us a good approximation that opens new horizons. And after we have opened new horizons, we return to intuition and now use it differently. But that different use may again not fit the definition perfectly. That’s why I said it is back-and-forth, and the process continues. Until now I have spoken only about three stages: intuitive usage, conceptualization through definition, and return to the person with the intuition—in other words, correcting his intuitive usage. But it continues. After I correct that, I will go back again and define, and I will see that my definition also changed a bit. Meaning, we are always playing between one and the other. And thus, what I have described now is basically what is called contemplating ideas. We do not contemplate ideas with our eyes. I observe objects with my eyes. But how do I contemplate ideas? How do I define… right. The term “democratic state.” What does “right” mean? After all, I said that for something to be true, correct, there must be comparison, right? Comparison requires observation. I need to observe the concept “democratic state,” see the definition you are proposing, and understand whether that definition is correct. Correct meaning fitting the idea, right? But for that I need to observe the idea, to see the definition and see whether there is correspondence. What does it mean to observe an idea? It means to take the definition, bring it back inside myself, and see whether I find that definition within myself, or whether there are some changes I need to send back to my analyst, yes? So that he will do the additional analytic work and add another tweak to the definition, or cut away some feature, define it a bit better. And little by little the changes will surely become smaller and smaller all the time, but I always need to return to intuition, feed the conceptualization back into it, return again to intuition—and this is a process of back-and-forth, and that is how our concepts are refined.

We are basically endowed with an intuitive understanding of them, but that understanding is not applicable as long as it has not gone through conceptualization. Once it goes through conceptualization, I feed it back in, and then conceptualization of second order, intuition of third order, conceptualization of third order, and so on. It’s back-and-forth, and this can perhaps continue forever, I don’t know. Now I’ll bring an example to illustrate this. I hope the move is understood. I’m trying to explain from the question of what a definition is to the question of what one does with it, and in the end I’ll get to… I’ll do it in practice. I’ll take things and do this with them, okay? But first I’m trying to define what I’m going to do, because otherwise when I do it, you’ll be skeptical and won’t agree with everything I say. I need this introduction in order to conceptualize what I will later do intuitively. Even the concept of a definition itself can be grasped intuitively and can also be defined as a concept. The concept of definition itself. And there too there is a process of back-and-forth. That is what I am trying to do here.

You spoke about Aristotle, that he strives for the definition of things by means of concepts that themselves are undefined—about the difficulty of defining something through a definition that includes concepts not themselves defined. Quine spoke about that. What? Quine spoke about that. Maybe, but no—also on this point you spoke about back-and-forth, that it is circular. Right, Quine’s web. Quine argued that we grasp concepts not in a linear fashion—from the basic concept that defines the concept above it—but in back-and-forth. It’s a web. All concepts have some sort of relation to one another, and our understanding develops all of them together. We don’t fully understand one, and from it define… derive the second, then the third—or in several directions, whatever—but it isn’t a directional process. It’s circular. Circular, but in segments… You define “democratic,” then define something else, and then you go back: wait, is this really a democratic state? No, I need to define the democratic state differently, and then it will come out from there in such-and-such a way. Exactly. Back-and-forth. It’s exactly the same thing.

Now look, I’ll give you a halakhic example. This penny dropped for me even before the previous two pennies—or only now am I connecting it. Because good insights come together? Is it connected to “good insights come together”? No, “good insights come together” is just… but it is also circular. No, of course. I have lots of circles. I can give you lots of circles. I don’t mean examples of circles; I mean examples of this process of back-and-forth with a definition. Look, I once wrote an article about the definition of… it was on a weekly Torah portion, many years ago, when I was doing my doctorate. I wrote on the Torah portion Ki Tetze, where there is divorce, the section of divorce. When you look at the Talmud, how does it define the process of giving a bill of divorce? It doesn’t define it. Nowhere is there a definition. What there is, is a set of dozens and dozens of examples. Dozens already in the Talmud itself, even before the medieval authorities (Rishonim). Dozens. Right? There is no definition anywhere. It is the later authorities (Acharonim) who usually make the definition, a bit the medieval authorities, but mainly the later authorities.

The Ketzot, for example—his basic move—is to say: if giving a bill of divorce were an act of transfer, that’s the first proposal. Giving a bill of divorce means taking the bill of divorce that belonged to the husband and performing an act of transfer to the woman. It ends with the bill of divorce now transferred into the woman’s ownership. And that is the act of giving a bill of divorce. Like how we understand transfer in general. There are definitions of how not to give? What? Of how to give and how not to give. There are discussions there about all sorts of cases—whether this is valid giving or invalid giving. The Ketzot says this can’t be. Why? Because it says: if one wrote it on something from which benefit is forbidden, it is valid. If one wrote a bill of divorce on something from which benefit is forbidden, it is valid. Why valid? Because according to some of the medieval authorities, one cannot own things from which benefit is forbidden. According to some of the medieval authorities—or all of them? According to some of them, one cannot own things from which benefit is forbidden. So if you write a bill of divorce on something from which benefit is forbidden, and the definition were transfer, that can’t work. So here is an example that contradicts the Ketzot’s proposed definition. The definition that “giving a bill of divorce” means transferring ownership of the bill from the husband to the woman. That is a proposal, a hypothesis. We go back to the base, to the cases, and we test: does it stand the test, does it not stand the test? That’s the back-and-forth. So this is the “back.” I look and say: no, a bill of divorce written on something from which benefit is forbidden is valid. That can’t be.

All right, back to the definition. After all, that definition is not totally wrong. There are many cases in which giving a bill of divorce is indeed a transfer. For example, if he places the bill in the courtyard and transfers the courtyard to her—that is valid giving of a bill of divorce. Why? Here the act of giving was indeed just an act of transfer. I transfer the bill and transfer it to her through the courtyard, or by courtyard-acquisition. Through the courtyard—here it is through the courtyard. So it isn’t totally detached. The Ketzot didn’t invent it out of nowhere. There are many cases that point in that direction, that suggest that giving a bill of divorce really is a transfer. But it doesn’t pass all the tests. There are cases in which it doesn’t work. So you need to sand it down a bit. You need now to define something slightly different. So perhaps it is only the transfer from his hand to her hand physically? Now I’m going all the way, to the opposite extreme. Not transfer at all, nonsense. The act of physically moving the bill from his hand to her hand. That doesn’t work either, right? It doesn’t work because of transferring the field. He placed the bill in his courtyard and transferred the courtyard to her, and the bill is valid. The bill didn’t move physically. It moved legally, not physically. And that too is valid. So it’s not physical giving, and it’s not transfer. So what is it? One can always say either-or. But then it is no longer a definition. In a definition we are looking for what is common to all these instances of valid giving of a bill of divorce.

Then the Ketzot stops there. I don’t remember exactly, but it seems to me he doesn’t continue. The Kehillot Yaakov has two or three sections in tractate Gittin on this question. Read it—it’s fascinating. Every time he brings an example, and he sounds exactly like Gideon Ofrat on the question of what art is. He brings examples that negate every definition. Why assume there must be something common? Good question. Excellent question. We talked about that a bit in the first session. But that is usually the assumption. Then we begin to bring examples, and in the end what you see in the Kehillot Yaakov is that you wind up with a definition whose number of caveats is roughly equal to the number of cases. It gets you nowhere. A definition is supposed to show what the common foundation of all the cases is. Once the definition becomes either giving or transfer or this or that, then you haven’t defined anything. You have simply listed all the cases like a peddler. You’ve come like a peddler with your wares and times. Meaning, that is not a definition. A definition is an attempt to find what is common to all the cases. No, even if you reduce many cases to a few “or’s,” that’s also… But the feeling one gets from the Kehillot Yaakov is that you aren’t reducing much. You end up with some definition that somehow you don’t know what to do with, because it is ad hoc. Meaning, it fits all the cases I know, but when I try to discuss a new case, with this complicated definition I won’t get anywhere.

And my feeling at a certain point was that the Kehillot Yaakov didn’t really mean to define at all. He meant to produce intuition. How do we produce the correct intuition in a decisor or a judge regarding whether this giving of a bill of divorce is good or not good? Precisely through the process of back-and-forth. What he is saying is this: we always think in Hempel’s deductive-nomological schema. He says that scientific explanation means proposing a nomological law—nomos means law—a general law from which this particular case can be derived deductively. The deductive-nomological schema. Meaning there is a nomos from which, say, the tides—how do you explain that phenomenon? There is the law of gravity; that is the general law, the nomos. From it we derive deductively the particular case of tides: the moon, the water, both are bodies with mass, the rule is that bodies with mass attract one another, and therefore there are tides. That is a classic deductive-nomological schema.

So what are we really doing? Let me return to the conceptual Talmudic analysis. He is really saying: I am trying to understand what giving a bill of divorce is. It may be that I will not come out with a clear definition, because it is like Pirsig with quality. I don’t know how to fit it into a definition. So what do we do now? People always say this is simplistic. Very often when I propose some sharp definition of something, they say: that’s simplistic. And what is your alternative, as Shimon Peres would ask? We need to move forward. I agree that in the end I won’t remain with a definition. But the definition is an excellent tool for sharpening intuition. The approximate definitions, which come closer and closer and never quite arrive, nevertheless build my intuition. So now I begin with the Ketzot, who gives me a first proposal, totally naive: giving a bill of divorce is transfer. Now we go back. You can go back to the intuition regarding the Talmudic case—it doesn’t matter—but it’s still the same process of back-and-forth. In the Talmudic case, there is a written bill and something from which benefit is forbidden. Fine, so it’s not that. Let’s go to the other extreme: physical giving. No. He placed it in the courtyard and transferred the courtyard—that too is valid giving, and that too is not physical giving. But physical giving and transfer are both valid. How do I know? But neither is an exclusive condition. So what is common to physical giving and transfer? After all, there must be something common—why are both valid? There doesn’t have to be, but we assume there is something common. It’s a pathology of human thought that always thinks there has to be a common definition for all phenomena.

Apparently some kind of transfer of domain—not transfer of ownership, but transfer of domain—which is a somewhat vaguer concept. Transfer of ownership is legal acquisition, while physical giving is an actual physical transfer. So “transfer of domain” is some thing that perhaps tries to include both. Let’s see whether it really includes all the cases, and one can continue and derive from there, and so on. What do I come out with in the end? “Transfer of domain” is such a vague concept that if I stop there in the plain sense, I still won’t know how to decide in a new case whether it is a valid bill of divorce or not. If I now say to a student: listen, what is valid giving of a bill of divorce? Transfer of domain from the husband to the woman. That is valid giving of a bill of divorce. That gives him no tool at all to decide a case that comes before him—whether this is valid giving or not. He has to go through the whole process with me. I need to begin with him and tell him: look, let’s start by saying that it is transfer. No, I negate that because a written bill on something from which benefit is forbidden is valid. Let’s begin with physical giving. Ah, I negate that too, because a courtyard that I transfer is also good. Then transfer of domain is the common side to both. And if I go through that process with him, then his back-and-forth builds his intuition. Every time I negate something, he discovers it within himself.

At the end I am not left with the definition. That definition is worthless. It is vague and crooked and complicated, with lots of parameters. The definition is not the important thing; what matters is the road to the definition. Because the road to the definition built within me what people call “da’at Torah”; it built within me a kind of intuitive perception, a perception that says: now I can smell what valid giving of a bill of divorce is and what it isn’t. Even in a new case not found in the Talmud or in the medieval authorities, I already have some sense, because I went through this whole process, I wrestled with this issue, and now I can understand what valid giving of a bill of divorce is. If I had not gone through the process and I simply gave you the final definition at the end, it might satisfy all the tests of the Talmud—that final definition with all the parameters and vagueness and everything—but it would not help me at all. It’s like mathematics, something absolutely precise that doesn’t help me at all. Why? Because it is a complicated definition. If you take it formally, it won’t help you; it will help only in the cases you already knew, like Ben-Gurion said about historians—that historians are experts on the past, not the future. They’ll explain to you what happened, but never rely on them when they tell you what will happen.

So here too it’s the same. If the theory in its formal sense describes the cases I saw, not the cases I will see. But if I am a partner in the process of constructing the theory, in this whole complex back-and-forth process, then I have built within myself a certain conception that I can also work with in the future. As in history: if you read the historian’s article and take only the bottom line—wars are always caused by such-and-such motivations—then you will always prepare for the previous war, because the next war will be caused by something else. But if you went through the whole process with the historian and said: here, once we thought wars were caused by beauty, but wait, Napoleon did it differently. Ah, so apparently there is a more complex cause here. Then we said, okay, but Alexander the Great was something else again. Exactly the same process. And in the end I am not left with the theory. The theory won’t help me at all; the theory only covered the cases I saw, not the case that will come next. But if I went through the whole process of building the theory, then I built within myself a better historical understanding, and now I can try to sense whether a war will break out here or not.

In the end, that is my goal, not the definition. Because in mathematics one can progress with definitions. In other areas of life, definitions are a tool to understand the thing better, to build intuition. It is not correct to relate to definitions—and this is already the next stage—but a definition is neither stipulative nor targeting, it is neither this nor that. It is a process that helps me build intuition. It is targeting in the essential sense: it tries to target a concept that already exists in me intuitively; it does not create it out of nothing. It is targeting, though it does not succeed; it always misses. It aims like one aiming at the moon with one’s eye, but in the end I miss. Meaning, it tries to target; it does not quite target. That is basically the proposal I am making: a definition tries to target.

Now notice that I just carried out here a process of defining what a definition is—that is, this itself is a definition. And with this process too, don’t treat what I am saying now as a final bottom line, but rather think of everything we did along the way in order to understand intuitively. If we went through that path, then we understand, at least intuitively, what a definition might actually do. Now what this means—and with this I just want to finish, and then I really do need to start with examples. Until now the examples were just to make the point easier to hear. The point with which I want to finish is the practical implication. When you make a sharp definition, immediately there is a practical implication, and that is the advantage of the Talmud, which always asks “what is the practical difference?” because the Talmud wants to see what your definition really is in a precise way, to say that every conceptual inquiry is really about the practical implication.

And this is a feeling not only of mine but, I think, of many people: that there is a naive conception—the naive view of Rabbi Chaim’s dichotomy, this dichotomy of Rabbi Chaim, that it is either this legal category or that legal category, and then immediately there are practical implications and everything is wonderful and everything works out and everything is excellent. It doesn’t work anywhere, ever. Never anywhere. As a rule, a Brisker distinction is never correct. But it is always useful. Almost always—if it is done properly, then it is useful. It isn’t wise; it is useful. There’s a big difference, and I think that some of the Briskers don’t understand this. Some of the Briskers think that the definition they arrived at in the end is the binding thing, and from that point onward they work with the definition. Now that is a consequence. I’m saying: the road—how to read all of Rabbi Chaim—not the bottom line, because his method is very important. Not only Rabbi Chaim, but also those after him who refined this method, which he did in a relatively naive way.

When we go through that path, we build within ourselves a certain understanding that will help us decide what the Jewish law is in every situation—not by means of the definition with which we ended. After I investigated why one must pay for property damage—whether because of negligence in guarding, or because “my property caused damage,” that classic inquiry of the later authorities—it is obvious that it is neither this nor that. Everyone presents it as either this or that: practical implication, less payment, everything wonderful—and it doesn’t work. It doesn’t work. Clearly this is meant to tell you that there is something of both here, but it is not only this and not only that. Yet if I went through the whole process and understood that the end also didn’t work, then I’ve done enough back-and-forth to understand well, intuitively, when someone should be held liable for property damage. Then I can be a judge. But if I’m stuck with Rabbi Chaim’s definitions, don’t ever appoint such a person as a judge. Someone who really works with those definitions—that is a grave mistake. To go with those definitions and work with them all the way through, meaning to take them too seriously, is a mistake. What matters in the Brisker process is the path, not the final result. Because the path is what works on my intuitions. Of course I do this through creating definitions that become better and better if I do it right. But it is never really the thing itself.

We spoke about rules of language that try to approximate how we actually speak—it’s an approximation. But they never really succeed. Why? Because they are not the correct rules. They are the best approximation I can offer for natural speech, for proper speech. Okay? So Jewish law too is a kind of language, and thought in various domains is a kind of language. I cannot force it into the straitjacket of rules and sharp definitions. But it is terribly important to try to define, because without that the only other option is: okay, work with intuitions. If you just work with intuitions, you won’t get anywhere. You need to conceptualize and then return again—the whole process.