Defining Concepts 1

Table of Contents

• The difficulty of defining right and left, art and poetry
• A critique of postmodernism and the distinction between a technical failure and an essential failure
• Definition as mapping from the world into a conceptual system, and the problem of the margins
• Composite definitions and litmus tests: Religious Zionists and Haredim, psychiatry and medicine
• Disease as an ideological definition, the DSM, and homosexuality
• Intersubjectivity, colors, veterinary medicine, and the patient’s will
• A definition refers to concepts, not objects, and definition itself uses concepts
• A circular network of concepts: Quine, the brain as a neural network, and analogies from physics
• The Aristotelian definition: genus and species, significance and uniqueness, and the labors of the Sabbath
• Borges, Tlön, conventionalism, and essentialism

Summary

General Overview

The text presents an attempt to clarify what a definition is, why it is important to define things, and why it is hard to define concepts like right and left, art and poetry, while criticizing a postmodern move that infers from the difficulty of definition that the concept has no real content. The speaker proposes distinguishing between a technical failure to formulate a sharp definition and the stronger claim that “there is no such thing” as the concept, and argues that in at least some cases there is an objective meaning that one can aspire to capture in a definition even if it is complex. At the same time, he raises the possibility that there are concepts of a different kind, like “disease,” which are mainly ideological categories dependent on goals and desires, rather than a purely professional description of reality. He suggests thinking of definition as a projection of a multiplicity of objects and features in the world into a limited conceptual system, as an act that requires deciding between the essential and the secondary, and as a process that operates within a circular network of concepts rather than within a linear chain of definitions.

The difficulty of defining right and left, art and poetry

The speaker describes right and left as an especially difficult example to define because of historical reversals and changing usages, and attributes to Zisser and another scholar whose name he does not remember the claim that these concepts have become “fairly empty of content” and remain only as historical leftovers. The speaker compares this to a book by Gideon Ofrat on defining art, in which definitions are proposed and then rejected by means of examples of works that everyone agrees are art but do not fit the definitions, until reaching the conclusion that art is “whatever is displayed in a museum.” He adds that the concept of poetry also suffers from vagueness, and gives as an example his irritation at not finding an entry for “poetry” in the Hebrew Encyclopedia and his feeling that the humanities avoid the work of definition.

A critique of postmodernism and the distinction between a technical failure and an essential failure

The speaker presents the extreme postmodern claim as saying that not only do we lack the ability to define, but that the concept itself does not exist and is “just some subjective hallucination.” He proposes a more moderate position, according to which there may be a meaning understood by speakers, but it is difficult to translate it into a small number of sharp sentences, and he connects this to the sense that some people are good at definitions and that when they offer a definition for a difficult concept, others recognize that “they did it well.” He argues that he has no proof of the ability to distinguish between the essential and the secondary, but he sees the success of good definitions as an indication that in many cases the problem is more technical than essential.

Definition as mapping from the world into a conceptual system, and the problem of the margins

The speaker describes definition as a projection of a large set of objects in the world into a limited conceptual system, illustrating this with the concept of a “chair,” where there is a clear core and broad margins of borderline cases that provoke dispute. He notes that vagueness at the margins does not require us to conclude that there is no definition, and distinguishes between cases of conceptual metamorphosis, where there is a clear basis that can be expanded or softened, and multidimensional concepts, where the difficulty lies in the question of what the “basic concept” is at all, and not only in how to handle the edges. He suggests that dealing with complex concepts requires a kind of “observation” that distinguishes the essential from the secondary, even if it is hard to justify formally why that choice is not arbitrary.

Composite definitions and litmus tests: Religious Zionists and Haredim, psychiatry and medicine

The speaker illustrates a similar difficulty through the distinction between a Religious Zionist and a Haredi, and argues that almost every feature one proposes is not by itself necessary, while the overall combination may define the matter more sharply. He presents the possibility of a complex definition in which not every detail is necessary, but the collection creates a distinction, and offers an analogy to diagnostic methods in psychiatry in which “three out of five” features are required in order to establish a diagnosis according to the standards of professional associations. He argues that this raises suspicion regarding whether this is a real concept or a definition designed for practical, legal, and institutional needs, and he distinguishes between the need for a definition and the justification for saying that it reflects something real.

Disease as an ideological definition, the DSM, and homosexuality

The speaker argues that there is no professional way to determine what counts as mental illness and what does not, and presents the removal of homosexuality from the DSM in the 1970s as a social and value-laden process, not as a new scientific finding. He claims that the decision whether homosexuality is a “disease” depends on an ideological stance of legitimacy or disqualification, and that this works “in reverse” from the narrative according to which science discovered that it is not a disease. He compares this to kleptomania, which remains classified as a disease because stealing is perceived as bad, and extends the claim to “disease” in general, including in the physical realm, as depending on the desire to live, not to suffer, and to prolong life expectancy, where the doctor functions as an expert only after the patient defines the goals.

Intersubjectivity, colors, veterinary medicine, and the patient’s will

The speaker uses the example of the color red to present a distinction between the objective and the intersubjective, and argues that certain concepts do not exist in the world itself but in the shared consciousness of human beings. He explains that the concept of “disease” appears objective because most people want to live, and so we skip over the subjective question, but in his view the will is always there in the background. He illustrates this through the treatment of animals, where the veterinarian is actually serving the needs of the human being who defines what he wants from the horse, thereby reinforcing the claim that the one who defines the “disease” is the one who sets the goal, not the object in itself.

A definition refers to concepts, not objects, and definition itself uses concepts

The speaker states that one cannot define an object, only a concept, and when we say that an object is a chair, what this means is that it is a concrete realization of the concept chair. He criticizes mathematical definitions in the style of Russell, which define a number as the set of all sets having a given number of elements, and argues that this is not a philosophical definition of the concept but a formal mechanism convenient for mathematical construction. He emphasizes that a definition always uses words and other concepts, and therefore a problem of infinity or circularity arises, and he concludes that in the end one must rely on concepts that are not themselves definable.

A circular network of concepts: Quine, the brain as a neural network, and analogies from physics

The speaker attributes to Quine the idea that understanding and definition function nonlinearly, as a network of concepts in which concepts define one another through different paths, so that the focus moves from point to point until an understanding of the whole fabric emerges. He argues that the goal of definition is an intellectual goal of clarity and distinction, not a purely logical goal, and he gives analogies from solving problems in nonlinear circuits by means of assumption and consistency-testing, and from iterative methods. He tells about a course on diagrams with Boris Shapiro and describes a physical approach that changes the order of calculation even when there is no full mathematical justification, relying on the fact that in reality there are no infinities, and he compares this to the idea that understanding can stabilize through consistency in the network even if the path is not “cleanly linear.”

The Aristotelian definition: genus and species, significance and uniqueness, and the labors of the Sabbath

The speaker attributes to Aristotle a conception of definition as a combination of “genus and species,” such as man as a “speaking living being,” and interprets this as the need to show to what genus the thing belongs and in what way it differs from other species within that genus. He argues that definition involves deciding which properties are essential, and suggests a distinction between the significance of a change and uniqueness in relation to other categories. He gives an example from the labors of the Sabbath, with a quote from the Talmud at the beginning of Bava Kamma: “That which was significant in the Tabernacle is called a principal category; that which was not significant in the Tabernacle is called a derivative category,” and explains that “significance” can be interpreted both as importance and as uniqueness, in a way that parallels the genus-species structure.

Borges, Tlön, conventionalism, and essentialism

The speaker brings Borges’s story “Tlön, Uqbar, Orbis Tertius” and describes an idealist world in which there are no nouns, only verbs like “it mooned” and “it dawned,” and in another dialect in which “objects” are formed as arbitrary clusters such as “the cloud flying in the sky together with the bird’s cry in space.” He uses this to ask why a certain collection of features creates a concept like democracy and not other collections, and formulates two approaches: conventionalism, according to which concepts are useful fictions imposed arbitrarily, and essentialism/Platonism, according to which a definition tries to uncover a real idea and hit upon an existing essence. He presents Kripke as formulating the idea of stipulation in a definition, like naming a baby, and connects postmodernism to an anti-essentialist position which claims that there are no essences and therefore there is no point arguing about definitions, whereas he himself argues that there are good and bad definitions and that there is room for dispute over whether a definition is correct.

Basically, at the end of last time I tried a bit to define left and right, or to move toward a definition of left and right. And while doing that I thought maybe we should talk more generally about definitions: the importance of definition, what a definition is, the problems involved in defining things. Left and right are the first example you might try to deal with, but it’s a hard example. It’s a hard example, and therefore if I were starting a whole series on definitions I wouldn’t start with it, because it challenges in a very non-simple way the ability to define those concepts sharply. I think I mentioned the book by Zisser and someone else, I don’t remember anymore, about left and right—maybe some political scientist from Bar-Ilan, maybe Ellinger? I don’t remember anymore—Zisser and someone else, who try to describe these phenomena of left and right across the short history in which they’ve existed, and it turns out they went through so many changes and reversals that their basic claim is that these concepts are pretty empty of content. They’re historical leftovers of concepts that were perhaps once more distinct, but today they’re completely mixed up. To my mind that book is an example—maybe one day I’ll bring it so we can follow it a bit—because in my opinion it’s an example of the failure of the humanities and social sciences. Meaning, they don’t do serious work. And I also mentioned another book in the past—I don’t remember whether I mentioned it this time—a book by Gideon Ofrat that tries to define what art is, and there too he shows that basically it’s a concept that cannot be defined; it’s too rich, too complex, too unclear. In the end he offers definition after definition, each chapter devoted to a different proposal, and he rejects the various definitions simply by means of examples. He tries to bring examples from the history of art of works that nobody disputes are art, but they don’t fit the proposed definition. And then by elimination, in the end he eliminates all the proposals and is left with nothing. And that is a wonderful expression of the postmodern way of thinking, because the last chapter of the book basically concludes that art is whatever is displayed in a museum. In other words, there is no definition, okay? And in a certain sense that’s very parallel to the move made by Zisser and the other one, I don’t remember who, in their book on right and left. There too they try to offer all kinds of characterizations, and everywhere it suddenly flips and changes and gets mixed up and there isn’t any, so basically the conclusion is that there is no such thing as left and right. These are concepts that have changing uses, undefined and vague, and in short not really concepts you’re allowed to use if you want to be careful. And I mentioned a third example, connected somewhat to the issue of art, and that’s the example of poetry. The concept of poetry itself also suffers from the same complexity and vagueness, and therefore, as I once mentioned, when I had to speak about poetry and looked up the entry for poetry in the Hebrew Encyclopedia to see what it was about, it turned out there was no such entry. And I got really angry about that—or even angrier. I was already angry at the humanities anyway: these idlers, what are they doing? I mean, it’s time they also did something for the salary they get—at least define the field they don’t know how to engage in. Is there an entry? There is, yes, but inside it there’s some kind of definition, some sort of attempt to relate to poetry. I tried to define it in a more systematic way. That’s one of the examples I’ll try to talk about. It’s not a problem of defining in general, like the Talmudic text the Rabbi brought then: the moment you want to define, it’s like making a rule, and in reality there are no rules. And if there are no rules, then there are no definitions. Okay, the same line of thought, the same line of thought. I may also have mentioned before—I think on various occasions—the book by Pirsig, Zen and the Art of Motorcycle Maintenance, which was a cult book, I don’t know, from when I was in the army. So there there’s some rhetoric lecturer named Phaedrus who goes on a motorcycle trip across the United States with his son, and basically it’s a kind of pursuit of the definition of the concept of quality. He tries to define how to grade his students’ papers—by what criterion does he determine that this is a good paper and that’s a mediocre paper and that’s a bad paper; how do you assess the value of a paper? For that you need to define the concept of quality in the context of a paper, but more generally too. And he has all kinds of philosophical essays there along the way; it’s a very interesting book. And at some point in the book—I flipped through and tried to find where it was, because I use it from time to time as an example, and I didn’t find it; one day I’ll have to do it in a more orderly way—he comes to some insight that the wicked Greeks messed up our heads. Why? Because they got us used to thinking that if a certain thing has no definition, then it doesn’t exist, or that everything that exists must have a definition. And that’s not true. Again, I’m laying out the move, I’m just bringing it from all kinds of places—and that’s not true. In fact, there is no definition for the concept of quality. But of course that raises the question: so does it also have no meaning? Or is this only a technical problem, that you can’t define it? Is this our lack of ability? Or is there something in the concept itself such that it really isn’t one concept—not that we aren’t managing to capture its essence, but that there really is no such thing, it’s just shifting uses like the color brown? It depends on the context. Meaning, maybe it has no meaning at all—not that we’re in a hopeless chase because we can’t manage it because we lack the ability, but that no such ability exists, it can’t be done, there is no definition. That is hard to accept. The postmodernists want to make that claim—or the extreme wing among them, the terrorists. That claim basically says we’re using a concept that doesn’t exist, not that we don’t know how to define it. That’s completely different. So there is a situation where I say: look, I have a sense of what this concept is, I just don’t know how to pour it—or cast it—into organized systematic vessels; I don’t know how to present it in a closed, clear way, in a finite number of sentences, a small number of sentences. Fine, that’s a technical inability, but the concept itself has meaning. When I use it, I understand what I’m talking about, and the listeners, I hope, understand what I’m talking about too. That’s a more moderate claim. The postmodern claim says not that I have a feeling and just don’t know how to translate it into words, but that there is no such thing; it’s just a subjective hallucination, there is no such thing. Okay? That’s a much stronger claim. And all these examples I brought earlier—at least the smell that rises from them, though by the way I’m not sure the authors always mean this, but sometimes they do, and in any case the postmodernists always take it all the way and turn it into an ideology—there is no such thing, not that we don’t know how to do it, there is no such thing, just hallucinations. I think that before you take concepts that are hard to define, like left-right and creation, the very attempt to define things—what is it, really, to make a definition? It’s to perform a kind of projection from a very large set of objects that exist in the world into a much more limited system, which is our conceptual world. Take for example the concept of a chair, supposedly trivial. No. In the world there are tens of millions of chairs, objects used for sitting, and about some of them there will be a dispute whether this is a chair or not a chair. Things with a different angle and slope and strange color—is it a chair? not a chair? How do you know? So at the margins there will be disputes. No, but exactly—I’ll get to those problems too, to the problems of vagueness. Maybe it’s simply a case where the margins are very broad. Okay. No, I’m saying, that’s another example, but there let’s say regarding a chair I doubt anyone would say there’s no definition at all. They’d say, look, as you say there are margins, but at the core I can define what a chair is: four legs, an object used for the sitting of a single person, let’s say, something like that. Now fine, there are things that will challenge that definition a bit, but it seems to me there is a pretty clear core that does satisfy it, and around it there are always margins—our world is complicated, there are always margins. That’s still a relatively easy case, and I’ll deal with—I mean I’ll try to touch on—examples like that too, for instance examples of the heap paradox, where does it stop, conceptual metamorphoses, and all kinds of things like that. But I’m talking even before metamorphoses. Metamorphoses are relatively easy, because there is a clear definition, and little by little you can soften it a bit or broaden the meaning a bit, or move between two poles and do interpolation between them and define a sum, weighted sums of those two poles. You can create such metamorphoses. But at the base there are definitions. Here, with concepts that are more complex or more multidimensional, it isn’t just two that you run between but some kind of thing that’s more dispersed, and there it challenges us on a much more principled level—in the question of whether there really is such a thing at all, not only the question of whether I know how to define it and whether it will also fit the edge cases. Here there is no concept that is a core before the edge; the question is what the basic concept is at all. And by the way, really—and this is one of my goals—to try to demonstrate or show that the way to deal with such complex concepts involves… an operation that many have related to as a kind of speculation, whereas I see it as a kind of observation, what’s called observation. Meaning, it’s not speculation but an attempt to distinguish between the essential and the secondary. Now I don’t know how to define why this is essential and that is secondary. I chose to throw out certain elements in order to remain with a sharp definition and then to bring them back in some way—I’ll show this in examples—but I’m just trying to explain the topic. And everyone will ask me, wait a second: why did you decide those are the main things and those are marginal? I could just as easily decide that what you call marginal is the core and the core is the margin. Who decides? Okay. Now I don’t really have a way to explain it. But I have a feeling that what I’m saying here is not subjective, but rather that I’ve hit upon a real point—and the fact is there are people who are good at definitions and people who are less good at definitions. And when people who are good at definitions offer you a definition of a concept you had difficulty with, you understand that they did it well. Meaning, although—you know, the skeptic will come and say, who says? I could also define another definition and it fits another part of the set of chairs, let’s talk about chairs or poetry or whatever, and I see that as the core and the rest as the periphery. I have no way of telling him why he’s wrong. I don’t know. In that sense it is a lack—I want to argue that sometimes there is a technical inability. I’m willing to accept that there is a technical inability. It’s hard for me to accept that there is no definition at all. So I say that if someone is better on the technical level and manages to try to offer me a definition, I will often find myself agreeing. And for me that’s an indication that the problem is more one of technique than of essence. Now I don’t know how to prove that; I’ll just try to demonstrate it with various examples. The examples I mentioned earlier, I’ll try to work on them and try to offer a definition. Right and left are a good example for this. Because right and left really are a pair of concepts that differ from one another in many aspects, and in different places maybe sometimes this also changes a little. There is some connection, a feeling that there is a connection. But when you try to put it in black and white, to define what the litmus paper will be so that when you answer yes you are right-wing, and when you answer left you are left-wing—it’s very hard. Or what will be the difference—yes, we once talked about Religious Zionist versus Haredi. Seemingly these are two clear concepts; there’s a difference, everything is fine. But try to define what the litmus paper is and it will be very hard. Maybe, I don’t know, the chapters of Psalms once a year that are said on Independence Day—you understand, these are definitions that don’t really exhaust the concept. That may be a symptom, but it doesn’t really exhaust the concept. And when people try to define the concept itself, then almost every characteristic you raise here—and I also talked about this once—almost every characteristic you raise here is not really a binding characteristic. Meaning, that characteristic, as a characteristic of Religious Zionists, could also appear among Haredim or vice versa, and they would still be defined as Haredim and they as Religious Zionists. The collection of characteristics defines the group better, but each of the characteristics is not—it’s not strict. So that’s confusing. So in many cases you need—and these are some techniques of how to arrive at a definition—you can say that each characteristic separately really isn’t necessary, but the collection defines unambiguously. That too is a definition. Whoever fulfills requirements A through T is a Religious Zionist. Now it could be that A, B, C, and G will also appear in some Haredi person, but he doesn’t fulfill all nine, and therefore he is not a Religious Zionist. You can also offer that kind of definition. It’s a complex definition, but it doesn’t have to be connected to what we talked about in the previous series—about things that appear at the level of the collective and don’t appear at the level of the individuals. Meaning, each of these nine details can also appear among Haredim, but the whole defines it sharply or unequivocally or almost unequivocally. That’s one possibility. Meaning, to try to collect. By the way, in medicine—or even more in psychiatry, but also in physical medicine—they use these kinds of things, and there they do it in an even more sophisticated way, or the opposite, or less sophisticated. What? The Rabbi gave the example: “sleeps in a cemetery and tears his garment.” Ah, okay, yes, exactly, that’s what the Talmudic text does, but modern psychiatrists do the same thing. When you want to characterize some psychiatric symptom that is complicated, then you need to satisfy three out of five characteristics. It doesn’t matter which three. And then the definition is that you suffer from I-don’t-know-what, paranoid paranoid schizoid, I know, all their names. Or I don’t know, seven out of ten, whatever, there’s some standard of the psychiatrists’ association, usually the American one—they decide everything, after all—there’s some standard of how many out of how many you need to satisfy. That thing arouses deep suspicion. Is there really such a concept, or is it just a definition for the sake of I-don’t-know-what, discourse, or I don’t know exactly what. The claim is that if you’re supposed to treat this thing in some way, it’s supposed to reflect a concept that really exists, otherwise it’s just… But. On the other hand, I didn’t understand—if the concept exists, then what is its definition? That concept is meant to provide legal certification for thousands of therapists and enable treatment. Explanations in a psycho-postmodern style. No, there’s also a legal issue here. That professional comes to court. No, I understand, you’re explaining the need for the thing. There has to be a definition. But I’m asking about the justification, not the need. Practical. In the legal world there’s something called justification of need and justification of value, justification—I don’t know, there’s justification of something, there are all sorts of these. Necessity defense, necessity defense. A defense that you had to, say self-defense is sort of necessity. Justification means that you were right to do that thing. There’s a difference. No, so there you go—what Ido said here is a necessity defense. He basically explained why an association of psychiatrists has to, needs to, offer a definition; otherwise what kind of association are you? I mean, what status do you have? How can you license one person to practice and another not to practice? I’m asking what the value-justification is—or what’s the other one called? I don’t remember. The justification, yes—not the necessity defense, but what is the justification? Does it really reflect something real? That’s the interesting philosophical question. I understand why they need it, but what do I care that they need it? We talked a bit about homosexuality too once, I think—that people constantly cite the fact that the American Psychiatric Association already removed homosexuality from the DSM in the 1970s. That always makes me laugh anew. Who appointed them? In what capacity did they remove it from the DSM? According to what did they determine that? What, were there some new scientific findings they discovered? It’s obvious this is a social, value-based, ideological process. They decided it’s legitimate. Fine, that’s their right, but as psychiatrists they have no added value on this issue compared to a layperson. As psychiatrists they can say what the root of this symptom is. Not whether it’s legitimate, but whether it’s not a mental illness. You can’t determine that it isn’t a mental illness. There is no professional way to determine whether something is a mental illness or not. If some bearded psychiatrist forcibly hospitalizes a homosexual, you’re going back to necessity. Exactly, you’re going back to necessity. I’m asking about the justification, the grounding. But independently of the legal issue, the DSM is a definition of, say, mental illnesses. Obviously—and how do you define what illness is? How do you define what an illness is? A deviation from the norm? Is being tall an illness? I’m worried. There is a definition of illness. Fine, but do you believe there is a definition? No, I don’t believe. What do you mean you don’t believe? No. I claim that the definition of illness is an ideological definition, not a professional one. I claim that as long as people believed homosexuality was morally or ideologically wrong, then it was defined as an illness. To this day that’s how it works. Those who say it’s an illness are those who basically claim that this thing is not okay. And those who say it’s not an illness say that it’s okay. But they don’t say it’s okay because it’s not an illness; they say it’s not an illness because they think it’s okay. It works the other way around. Nobody knows what the root of homosexuality is. I spoke to people who know a bit about these things; they told me there is no clear agreement today about its root, where it comes from, certainly not regarding treatments, if treatment is possible at all, though a bit of a consensus is forming—I think that too is somewhat ideological—but there is no agreement on it. So how is that different from kleptomania? Because it’s obvious to us that theft is a bad thing. Everybody is clear about that—for the time being no one has challenged that yet. So kleptomania is still inside the DSM. But homosexuality isn’t. Why not? Because in the 1970s they discovered the gene responsible for homosexuality? They discovered nothing. Rather, in the 1970s an ideological view crystallized saying that homosexuality is legitimate on the moral level. It has nothing to do with professional questions. Now in that sense that’s fine—society can define it that way, I have no problem with that. This isn’t criticism. If I borrow a book and forget to return it, I’m not considered some truly sick thief, a kleptomaniac, right? Or is that a definition of mental illness? It’s not considered mental illness. I don’t know. I don’t know, but what difference does it make? What difference does it make? That’s the example you gave regarding the issue. No, but what difference does it make? Then give me the root. What’s the root? Well, look, I can say why depression is an illness. Symptoms, but there’s no doubt that there are things or negative traits that are different from usual, and because of them a person does not become mentally ill. No, no doubt—you decided. Why is there no doubt? What is the definition of illness? I’m asking—this is exactly why I’m bringing this example here. What is the definition of the concept illness? Give me a professional definition. You’re a professional? Please tell me according to what criterion you determine it. According to what criterion did you write the DSM? Today Ido will tell me: what’s the problem? According to the DSM I determine it. But I’m asking: how was the DSM written? How did they decide what would be written there? That is an ideological determination. It has nothing to do with the professional world. In the professional world you can say what gets included and what doesn’t, how to treat it, what causes it. Those are substantive questions. Those are questions for which the mandate is a professional mandate, to answer them. Because it’s a simple question—you can put it to a test. What? So maybe treatment is part of the illness? But I’m saying—if I don’t want treatment, then I’m not ill. The assumption that by means of treatment I know… Then no problem, being tall is also an illness. By treatment you can cut off the legs in Sodom. You’ll say that medication is a definition too. No, medication has a definition. That’s exactly what I’m saying. Medication is something that changes your condition from what you don’t like to what you do like. That’s all—it’s medication. There is no definition of the concept medication either, in the same sense I’m talking about here. Certainly. There is a definition, and yes, it is scientific. I’m not denying the scientific nature of the field. I partly deny it in psychiatry, but I’m saying on the principled level there are scientific components there. Not very many, but there are some. But those components are not the definition of what illness is and what is not. Rather, it’s the question of what the source of the illness is, how to treat it—that’s the scientific part. That is of course a question of knowledge; you can test it, you can do an experiment, it stands up to empirical testing. But the definition—explain to me according to what criterion you determine what is an illness and what is not an illness. What, if it has an organic root then it’s an illness? I’ve heard many people say the opposite: because homosexuality has an organic root, therefore it is not an illness. Because it’s natural, that’s how the person is, what do you want? So if they discover an organic root for kleptomania, will it remain an illness or not? Certainly yes. Why? Because we don’t like kleptomania; theft is bad. Do you agree that there is a distinction between mental illnesses and other illnesses? Or is there not? Or even illness itself isn’t… Between mental phenomena and phenomena… Illnesses can’t really be defined at all. Is there a difference between mental phenomena and heart disease? Yes, that too is not illness. What? That too is not illness. You can’t define illness even in the physical realm. That’s it—it’s all because you don’t want to die. Whoever doesn’t want to die doesn’t want heart disease. You value life and decide that you want to live. So anything that interferes with your living is defined by you as an illness. But if there is someone who wants to die, then from his perspective he is not ill—heart disease is fine, he wants to die. It’s just that usually we want to live, so here we skip the subjective stage because we all agree on it. But that doesn’t mean there isn’t—that everything here is professional. Before the doctor can define whether you are ill or not, you need to state to him what you want. He can’t define you as ill before you tell him what you want. If you tell him, look doctor, I want to live, I want to feel good, I don’t want it to hurt—fine, now he goes into action. Because now he is the professional; he can determine what hurts, what doesn’t hurt, how to treat what hurts or how to treat what threatens to kill me. It would be hard for me to define pneumonia. My lungs are not in their normal state, and as a result I have a fever. Say if I go… That is a purely professional question. That’s exactly the point. But to define that pneumonia is an illness—that is the question. Exactly. What you’re talking about is a professional difficulty. No, there’s difficulty in medically defining pneumonia. But I’m saying it’s a professional difficulty because he’s asking himself what exactly this concept is that if you take antibiotics, they’ll treat it. You see? That’s a totally professional question. And that’s hard to define; it’s a medical problem. We still don’t know enough to define it. I’m not talking about that type of problem. I’m talking about the question: you diagnosed it—this is what we call pneumonia. Now I ask: should this be included in the list of illnesses? I don’t know—if I want to have pneumonia, then it’s not an illness, then I’m okay with it. Just like homosexuality was an illness until the 1970s; after the 1970s I’m okay with it, it’s fine, I don’t have a problem with it, so it ceased to be an illness. And rightly so, by the way—that’s not my criticism right now. My criticism is directed at the other side, at those who try to turn it into a professional claim. Put it on the table that it’s an ideological claim, and then that’s fine; I accept it. It’s legitimate that you think differently from me or don’t think differently from me, maybe I think that too. I came across several articles claiming that mild overweight actually increases life expectancy. Okay. According to that, taking the people who are currently considered… I think they were relying on you, not you on them. Mild overweight. I got it, I got it. No, it’s mild. Don’t insult Shmuel—it’s mild. By the way, that claim stems from an error, and it’s actually a good example, because what happens is that many people at the final stage of illness lose weight, and therefore in the statistical definition those with a bit of extra weight come out healthier because the end-stage people entered the statistics. But that’s a sign, not a cause. Yes. But then it’s no big wisdom—it’s like they survive illness better because they have those energy reserves. Ah no, that’s another claim already. But for our purposes, that would mean taking all the people who are considered normal weight today and turning them into patients because they suffer from a deficiency of a few kilograms. Yes, and it’s clear that all these definitions—also the definition of blood pressure below the norm, what is the norm, survive surgeries better—okay, so now what happens is that this positively affects life expectancy. So who is sick and who is healthy? And that’s the question: what is normal blood pressure? And the answer is that if you want to live… To live, then there is a definition of what illness is. Let’s check what will bring you maximal life expectancy. Fine, that’s a scientific question, and it may be that in certain life circumstances precisely this increases life expectancy, and then that means it is defined but comp… I have no problem with that. So it’s defined but complex. I’m talking about a principled problem. I claim that illness, for example, is not of the same type as art, poetry, left and right, and all the other things. I claim there is no such concept as illness. With left and right I claim there is such a concept. The definition is hard, complex, we’ll discuss it. But regarding illness, my claim is that there is no such thing. It’s an ideological concept, not a professional one. What’s wrong with “my boss”? Anything you want to cure. There’s a range of… Exactly. Whatever you want, that’s the definition. Fine, no problem. No, that’s not a professional definition. Whatever you want to cure, fine. So not a definition. You tell me what you want. Yes, one second. So there is no definition. A universal definition… At one end of such a scale… right… No, but I claim that with right and left that is not the case. I claim that with right and left there is an objective definition. One uniform definition, complex, but one. Not relative. No. That’s exactly what I want to argue. Again, on the principled level. I’m trying to sharpen what we’re talking about, do you understand? I claim there is a difference. There are complexities that are technical complexities. There may be complexities that are essential complexities, but even behind them sits some concept that has meaning. I claim that illness is a third type, a third category. There is no such thing. There I am postmodern. There is no such concept as illness. Illness is a question—ask the person whether he is ill or not, not the doctor. Yes, it’s a narrative. And again, narrative not in the dismissive sense. I don’t dismiss a person who wants to live—I also want to live. It’s just that he should define what his goals are, and the doctor will help him. By the way, in that sense it’s exactly like psychiatry or like psychology. There too, basically the psychologist is supposed to… this is the whole dilemma of psychologists who treat homosexuality. I have a student, a disciple of mine, who finished—or rather, he came to consult with me a little on these issues. Rabbi Sherlo published some ethical paper for therapists and so on, a very nice paper. In any case there’s a not-so-simple dilemma there, because the basic assumption is that the psychologist is supposed to help a person live with what he is. He’s not supposed to cure him in the old paternalistic sense. The new psychologist is a psychologist who is supposed to… and therefore treating homosexuality is basically a dirty word among psychologists. Because it means you’re paternalistic—you’re telling him it’s not okay and you want to change it. The new approach says: if you’re homosexual that’s perfectly fine, only if it bothers you then come, I’ll help you live with it. Not that I’ll cure the homosexuality. I’m not discussing right now whether it can be cured; I’m asking what it is that you’re looking for. They won’t conduct research on how to cure homosexuality because there’s no need. The ideology says there’s no need. Rather, what is needed is to enable you to live in peace with who you are. So this is exactly—you see—that it’s simply the provision of services. You tell me what you want or who you are, and I’ll try to help you live in peace with what you are. I can’t define for you whether you are ill or not. You need to come—yes doctor, I’m sick, like the old comedy sketch, yes… You need to come to the doctor and tell him whether you are ill or not, not the doctor. The doctor can now say, ah, you feel bad—fine, that’s my professional skill, I’ll try to tell you why you feel bad, independently… They’ll also give him medication—what is medicine for one may be a drug for another. Right, depends what you want. Correct. There are things like, say, you have such-and-such a cancer; they define it, and the treatment… No problem. But if I want to die, then I’m not ill. The cancer is my way of dying—what’s the problem? I don’t want… if you give me that then I’ll keep living, and that is exactly what I don’t want. No, I have cancer whether I want to live or not; you have an illness… No, no. You have a definition of cancer, not of illness. Whether I want to live or not, clearly I have cancer. That’s a scientific fact. But the question whether that cancer is an illness—that already does depend on whether I feel bad about it or good about it. Now most of us feel bad about it, of course. So therefore we skip—again, there are many things that although they are subjective, we all agree on them, and therefore it seems to us that they are objective. We skip the stage of “tell me what you want” because we all want the same thing. The question is whether it’s good or not. Is he sick or healthy? That’s a definition of a state. No, being tall is also a definition of a state. Why isn’t being tall an illness? It too is a deviation from the norm, and it’s a definition of a state, because I don’t have a problem with being tall. That’s all. Is there anyone who has a problem with being tall or goes to a psychologist or goes to Sodom where they cut off his legs, I don’t know what… and they treat his illness because he defined it as an illness, it bothers him. A child who gets up in the morning and tells his father… Is every deviation from the norm an illness? Is every physiological condition that differs from the normal an illness? Of course not. There are forms of otherness that are simply ordinary otherness. So what if you’re different? Suppose your skin is darker than other people’s. Is that an illness? If there is abnormality and an organic basis, I assume. So what? Would someone define that as an illness? If you feel bad about it then it’s an illness, then you’ll treat it, fine, I don’t know. But you understand, this issue is paradoxical, but… What do you mean? Because a child who gets up in the morning and says to his father that he doesn’t feel good and he’s sick and doesn’t want to go to school—he should be sent because he is healthy. Ah. Why? Because that’s what he wants. He wants to feel bad because he doesn’t want to go to school. Fine, so he doesn’t want to go to school, why send him? Exactly because he is healthy; only a sick child… isn’t sent to school. He is not healthy, he doesn’t want to go to school, so what? Yes, but he doesn’t feel good. A healthy child gets sent. A healthy child who doesn’t want to go to school, so what? If he wants to go to school, don’t send him, because he’s mentally unhealthy, so he should stay in bed. Like the… What kind of paradox is that? Then he’s altogether sick. It’s like criminality in Jewish law, where they have to warn the offender and he has to say “yes, and on that condition I am doing it.” So a person like that has proved that he is completely insane, so of course he should be exempt from all punishment. I mean, he is delivering himself to death by his own hands—what is he, crazy? If he’s crazy, he’s exempt. But apparently that answer itself is an insane answer. Okay, so there’s the responsum of Rabbi Moshe Feinstein; that’s an interesting responsum. We also talked about that once, in the year of responsa. Anyway, so I’m saying this is a good example, the example of illnesses. Or another question, for instance. I’m just bringing examples now so we can get an impression of the field, or of the richness of the field, because I think it hasn’t gotten enough attention, this field. I hardly know of treatments of the whole issue of definitions and what they are. It could sustain a whole year at least. What? Easily. I think of writing a book about it sometime, by the way. It’ll keep me busy for about a year maybe. No, really, because it’s a field that’s wide open, and in many places there’s confusion around it, and in my opinion it’s very important to clarify these things and the different types and understand—not to mix everything together. The postmodernists really love to mix everything together. There’s nothing, everything is nothing, everything is hallucinations, everything is this. They bring examples that maybe in some cases are good, but who said all the examples are the same? There are complexities of this kind, complexities of that kind, essential, technical… things need to be defined. It’s not… many times it’s the laziness of the humanities, the postmodern laziness. It’s that laziness that says, ah, it’s complicated, so apparently there’s no such thing, and that’s it. And then they bring a few examples to show you that it’s complicated or to show that there’s no such thing, and that’s it. But that’s not enough. Do some more orderly work. After all, we are talking here about something; you can’t say we’re talking about nothing. Try to give some kind of outlines of what poetry is or what art is. You can’t tell me “whatever is displayed in a museum”; that’s just throwing up your hands, it’s a joke. I’m not paying you as a lecturer in art in order for you to tell me that. By the way, the whole move is brilliant. Gideon Ofrat has a very impressive analytic ability. Meaning, the move is brilliant, how he examines each definition—it’s a smart move, not… he’s a smart man. It’s just that in the end the conclusion is like this: okay, so I surrendered. Basically he turned the question mark into an exclamation point, yes? What is art? What is art! Meaning, art is this, it’s whatever you ask “what is art?” about. So that surrender is what I’m trying to deal with in this series. I think we don’t have to surrender. And complexity should be handled carefully, but it should be handled. They’ll tell you that you also surrendered in the case of illness. They’ll say, why? I don’t agree. No, because it leads—for example, the Holy One, blessed be He, promised us, “All the illness that I placed upon Egypt I will not place upon you.” Thank you very much—who needs it? I actually do want illness; I’ll show that it… No problem, no problem, the Holy One, blessed be He, will give you what you want—that’s the illness. Illness is what you don’t want. The Holy One, blessed be He, imposed on the Egyptians things they didn’t want, and therefore He imposed illnesses on them. Illness is something you don’t want, and therefore the Holy One, blessed be He, informs us. Obviously. But if you want to shorten your life, then you have no problem with it, right? I’m saying again: there is a difference between objective and intersubjective. Intersubjective means, say, the world of colors—we talked earlier about colors, yes, whether there are colors or not. So let’s all be optimistic and say that we all see red here, and let’s say we all see the same color—what I call red, you also call red. We have no way to verify that, but let’s assume it’s true, okay? I have no way to define the concept red, and the concept red also doesn’t exist in reality; it exists only in my consciousness. But it exists in all of our consciousnesses. So is that objective or subjective? So I… that’s the notion of intersubjective. It’s not objective, because in the world itself there is no red, there is wavelength. But it is intersubjective—it exists for all subjects. In that sense there is an objective dimension here. So I’m saying: since all human beings want to live—almost all of them want to live, except those who are sick and don’t want to live—so I’m saying, most human beings want… here people simply skip the question to the person, tell me what you want. Do you want to live? Whoever comes to the doctor obviously wants to live; otherwise why did he come? And the doctor is supposed to help him toward what he wants. So we have some feeling that there is no question in the background at all, because it’s obvious, it’s objective. But that’s not true. There is a question in the background—we’ve simply already answered it. The moment we came to the doctor, we answered the question. But still, in the background there is always a question. Now there are places where that’s more obvious. In the case of homosexuality it’s much more obvious. There it’s clear that this is an ideological question and not a scientific one. In the context of influenza or cancer, by contrast, it’s different, of course, because there it’s hard to notice that there is something subjective here, since we all want to live. But that’s only because we all happen to want to live. Still, the desire to live is in the background of the definition of cancer as an illness. You can’t ignore that. It’s easy to ignore, but it’s not correct to ignore it. It’s what the horse wants, but when I see that a horse at such-and-such an age can’t carry such-and-such a weight like most horses of its age and weight, then I go to the veterinarian, and the veterinarian doesn’t ask the horse what it wants. Rather he does blood tests, I don’t know what veterinarians do, and so forth. Why? Because the veterinarian is treating you, not the horse. You want the horse in order to use it, right? You need this horse—regarding some people… You need the horse, you need it. No, really, I’m serious, this isn’t a joke. The fisherman loves fish—again, from the old comedy sketch, yes? You go to the veterinarian not for the horse, you go to the veterinarian because you need the horse. You want a horse that will work for you. So of course, your interest is that the horse live, not that it not suffer. You don’t go to the veterinarian so that the horse won’t suffer; you go so that you’ll have a horse to work with. So fine, there you’ve clearly defined what you want. The veterinarian isn’t treating the horse; he’s treating you. No, I mean it seriously, really. The one who defined the horse as sick here is you, not the horse. You can’t ask the horse, so that’s also a problem. It’s like a mechanical fault in a car, that too… No, a car isn’t a living being. The car can’t make it uphill, the horse can’t make it uphill, therefore you treat it. The fisherman loves fish and therefore he eats them, yes? It’s exactly the same thing. He loves fish very much, yes. As my grandfather used to say, he loved animals very much—in a pot. Okay, so these concepts are concepts that I say, you could accuse me that I too am surrendering in the field of illness. But let’s say this is to my credit: in other fields I do not surrender. Why did I choose to surrender specifically here? Because here I really think this way; this isn’t surrender. You know, just because you’re paranoid doesn’t mean they aren’t after you sometimes, right? As is well known. So I too once heard that attributed to Kissinger—I don’t know who the original source is, it’s an interesting question who the source of that saying is; I once saw it in Kissinger’s name. But I’m saying, same thing here: the fact that you’re chasing the postmodernists doesn’t mean they’re never right. Meaning, the fact that they’re wrong in many places doesn’t mean… you know, even a stopped clock tells the right time twice a day. It’s the only one that shows—yes, exactly. Well not the only one; a slow clock also shows it, just not twice a day, maybe once and a half times a day or something. You overtake it, you know. A clock that runs fast at a constant rate—say always a minute ahead of time—it never shows the correct time, do you understand? But a clock whose rate is different will always show the correct time, the only question is how often. So I’m saying, in these contexts I completely accept their claims, but this isn’t postmodernism because it’s true, it really is there. There really is no such thing as illness. Postmodernism, in my view, is taking something that really does exist and saying that it doesn’t. That’s what postmodernism is. They claim that really there is nothing there either, but here it’s at least a question you can try to grapple with. Come, I’ll offer you a definition and tell me whether you agree or disagree. Fine? So here one can already engage. On the contrary, I’m also willing to engage regarding illness. If someone offers me an objective definition of illness, I’ll accept it. I don’t know such a definition. I’ve asked people—psychologists, doctors, among those I happened to speak to a bit about this issue. Most of them don’t understand what I want. But those who understood what I wanted agreed with me. Yes, exactly. You have to be careful—if it’s the district psychiatrist, then you’re not allowed to ask him that question. He has the authority to hospitalize by force. But those who understood what I wanted agreed with me. Those people have a basic inability to understand things that challenge their profession a bit; that’s a problem. Instinct. Yes, there’s something there that perhaps all of us have a little of. Okay, so those are the questions of definition. Now, what does it mean when we take this act of definition—what exactly are we doing here? Here too I want to give various characterizations of the act of defining. Now I’ve left illness. To define a definition. Yes, exactly—to define the concept of definition, or describe the concept of definition, okay? So here really, when we see a chair—let’s take Ido’s example—we see a chair and want to define chair. We are not defining an object; you can’t define an object. An object is simply here because it’s here. We define a concept. Always. A definition refers to concepts, not to objects. Now when this object is a chair, that means this object is a concrete expression of the concept chair. There is an abstract concept called chair—assuming optimistically that there is such an abstract concept. Something like a form, no? What? The set of all chairs? A set or an idea, yes, I’ll get to those concepts in a moment. And no, the set of all chairs—that’s the mathematicians, and that’s the mathematicians’ fallacy. Mathematicians define number—say after Russell, once set theory was defined in an orderly way—then they define the number three, for example, as the collection of all sets that have three elements. That’s an absurd definition philosophically, because the concept of number is not a collection of sets—what kind of nonsense is that? The collection of those sets is a collection of things that express or instantiate the concept of the number three. But what is the number three? The number three is not a collection of sets. Only mathematicians can give definitions like that, because these are definitions that pass an entirely precise test and you can build on them. Fine, I’m not accusing them. It’s simply not really a philosophical definition of the concept number. So I’m saying, when I define a concept, I never define an object; I define a concept. Why do we always think we are defining objects? Because an object is always classified for us through concepts—what you called projection earlier. Yes, we basically project it onto the world of concepts. We have concepts: red, tall, kind-hearted, I don’t know exactly what. Now I see a person who is red, tall, and kind-hearted, so I say: okay, that’s probably a fat Native American, or something like that. Red, tall… well, fat people are always kind-hearted, as everyone knows. So never mind. I take a collection of concepts and I say: this object is a concrete expression or realization of those concepts. Now if I’m lucky—or if I know how to define well, and we’ll get to that in a moment, and then it won’t be luck but more a matter of ability—then I can find a concept such that an object instantiates one concept, not a collection of concepts. A chair, say: if I define the concept chair, then this chair instantiates the concept chair. The object chair instantiates the concept chair. If I haven’t defined the concept chair, then I say it instantiates the concept of having four legs, and also the concept of having a backrest, and of being used for sitting, and of being brown, and of being several things—then it too instantiates a collection of concepts. The definition of a simple concept is a simple concept; the definition of a complex concept is to try to take the collection of concepts instantiated in one object, and it turns out that this is probably generic, meaning there are many objects in which this special set of concepts is instantiated, and then I create a new concept by means of a definition. So now we discover something else: a definition always, of course, uses words and concepts. It not only defines concepts; it also uses concepts. And here we have a problem. Because then what does it mean? Exactly. Then it means, the question is how can you use concepts before you have defined them? What will you do—define also the concepts you use. Fine, and in those definitions which concepts will you use? Turtles. Turtles all the way down. In the end you need to work with a set of concepts that are not definable. Another thing mathematicians don’t admit. There are Jewish laws the Sadducees admit to, and there are definitions mathematicians don’t admit to. No, axioms are something else; I’m talking about definitions, not axioms. Mathematicians try desperately to define all their concepts. At least some of them, those who don’t have enough philosophical awareness, have some sense that mathematics defines all its concepts all the way down, but that can’t be, because there is no such thing as defining concepts all the way down. As a mathematician you need to understand this, because to define concepts is always to use other concepts, so that infinite definition is infinite? Exactly. Or circular. Or circular. And therefore Quine really wanted to argue that we do not define linearly but circularly. There is a network of concepts, and all those concepts have very complex relations among themselves, and it is circular. Meaning, you can move along paths in that network; you start from this concept, use its five nearest neighbors, a nearest-neighbor definition of nearest neighbor, yes? You use the concepts close to it, but those too you define by means of it. In the end an understanding is formed in us, because that mutual interaction, that back-and-forth, creates in us an understanding of all the concepts together. It isn’t built linearly: I know these concepts, and by means of them I define exactly this concept, and then by means of it I define the next concept. That would be creating something from nothing, right. Right. And his claim is that this is what we do, and there is much justice in that. Practically, it’s true. You can like it or not like it, but practically it’s true. When I define a concept for you using other concepts, it depends on focus. When I put the spotlight on this concept, then all the other concepts serve me in defining it. When I put focus on one of those other concepts, then I’ll have to define it, and it may be that I use this one to define it. But in the end it creates some kind of understanding. It’s a valuable process even though it’s problematic on the logical level. But it’s a valuable process because that’s how one understands things. You put focus. In that sense I think he correctly describes how we work. Whether we like it or not, again. And I think our understanding works that way… today we even know this physiologically. Our brain is built as a neural network. Okay? A neural network perhaps also reflects—I think the way it works also reflects—an understanding that really is not point-by-point understanding, not an understanding of concept by concept, but an understanding of a fabric of concepts. When you understand well how they are connected to each other, then each one of them also comes out more understandable to you. Now in order to do that you need to move along a linear path on the network. You choose a path, you go from this site through the bond… yes, it’s a network. Fine, not always a linear path. Sometimes a circular path around a point. It doesn’t matter, but to focus on something and put a spotlight on it. After that you’ll come from somewhere else. In the end you want to understand the network. But in order to understand the network you move on this path and then on that path, and sometimes they intersect and cross and so on. In the end you understand it. So one must also be careful not to expect too much from definitions. Meaning, not to expect something logical, neat, and linear that starts from some set of concepts, yes, mathematics, and builds all the other concepts on top of them. We’ll go back on our tracks and so on, but in the end it will come out sharper and clearer. And in the end the goal of a definition is an intellectual goal, not a logical goal. I want to understand better what I’m talking about, so it will be clearer, sharper, so I know when it is and when it isn’t. If the way to do that is circular, then fine. By the way, there are, you know, in electronic circuits, because they are non-linear circuits, then in mathematics in order to find the current and voltage in every part of the circuit, many times you have to assume a premise and check consistency. And not calculate by starting with assumptions and doing a bottom-up calculation or from one side to the other, but rather you assume a premise and then check yourself. And if it doesn’t work, then you adjust it a little and… and that is exactly the point. Once you’ve reached a solution and the solution is consistent, meaning it comes out fitting, the whole network fits together, then that’s the right solution. I understand. Like doing iterations in programming. Yes, exactly, sometimes you do iterations. In the end—now with mathematicians it’s still orderly, because a mathematician first proves there is a unique solution. So once you have proved that it’s consistent, then it’s the solution, and they proved there is a unique solution for that kind of problem, so that’s the solution. But physicists don’t care. If it’s consistent, then that’s the solution. Once someone from the Technion came to give us a course on something that there wasn’t anyone at Bar-Ilan to teach. Do you remember? Were you there then? Boris Shapiro from the Technion came to talk to us about diagrams. He gave a course on diagrams. So at some point—physicists do this at every step in diagrams—you sum an infinite series. Say there’s a sum and then an integral over some function. Never mind, for those who don’t… well, the integral diverges or the sum diverges, never mind. So you swap the order. You pull the integral outside, do the sum, the sum is wonderful, converges, then you do the integral and it too converges, everything is wonderful. And I, having studied mathematics with mathematicians—at Tel Aviv University in engineering you study with mathematicians. Not as mathematicians but the lecturer was a mathematician, so it’s half. So I said to him, “Wait, but did you prove it converges absolutely? You can’t interchange summation and integration if it doesn’t converge absolutely.” It has to converge in absolute value in order to do that. He didn’t understand what I wanted at all. If there’s an answer, that’s obviously the right answer, no? I can show you series—for example one plus one minus one plus one minus one and so on—I can show you that it converges to zero or to one or to two or to ten, whatever you order, whatever you want, also minus two and a third or minus pi squared. It doesn’t matter. Tell me what you want and I’ll arrange this series so that it comes out minus pi squared. And there, there’s an answer. The nice point about… I’m drifting a bit today, but never mind, this is circular work. I’m defining the definition in a non-linear way, okay? What he wanted—he made a very interesting point, to his credit. He said, “Look, in physics one thing happens, another thing doesn’t happen. Now if you found something that you can calculate from that thing, then apparently that’s what physics does.” Now the mathematicians can come afterward and prove that it really was justified and that’s the right solution, fine. But I’m a physicist; I want to know whether this describes reality correctly. So I say: I found a solution. Infinity is certainly not the correct solution, because in reality it works, there is something here that is not infinite. So I say: infinity is not the right solution; so I switched and found a finite solution, and apparently that’s the right one. That’s an empirical proof. And by the way he’s right. He’s right because in reality indeed you see nothing infinite is happening here, everything is finite, that’s fine. He’s only wrong because I could have shown him other finite solutions. That’s what I wanted to say. In control systems, stability criteria, root locus, it’s all the same. They don’t have a mathematical proof, but often people really ask, “So did you run a simulation or something?” And another thing is the behavior of pressures, the response of controls when you’re near the speed of sound; according to the original equations it diverges to infinity. By the way, people think… There can’t be such a thing, and certainly airplanes—and many airplanes—crashed until they found the laws of waves. Although I’m sure they may have crashed, but it wouldn’t have reached infinity even if they hadn’t crashed. Yes, it would have stopped at a million. Therefore it really isn’t exact. In physics nothing reaches a million, but that is the justification of these approximations: what goes to infinity in theory reaches a million in physics. And a million also crashes. Meaning, you understand, so that’s the justification. Why are there no phase transitions in reality? Because in phase transitions people always assume infinitely many particles. There is no system with infinitely many particles. But there are phase transitions in reality—they’re soft, not sharp, not pointed. From liquid to solid or between different thermodynamic states. In mathematical theory there are infinitely many particles and everything is sharp; it gets cut with a broken derivative. The function looks like this. In life it looks like this. Fine? Yes, physics always rounds off the corners of infinities and discontinuities and so on. Yes, and if you look, say, in modern kettles without an exposed heating element, you hear those sounds inside because of the collapse of the bubbles. Now if you ignore these things, you get corrosion problems. Fine, okay. You’re saying the mathematical models are usable even though they’re not exact. I completely agree. Okay, the definition of the concept of definition is attributed to Aristotle. Let’s start a little more systematically. He says: when we define something, it always goes with genus and species. Meaning, when you want to define a human being, you say it is a speaking living being. The living being is the genus, and the human being is one of the species within the genus. Yes, genus is something broader than species. The genus is divided into species. Okay? So when you want to define something, you need to explain to what genus it belongs and how it differs from the other species within that genus. That is the concept of definition according to Aristotle. Okay? Now I don’t know whether all definitions meet the Aristotelian test of definition, but that is generally how people relate to the basic concept of definition. When we speak about complex definitions, we’ll have to ask ourselves whether that is what they are. The concept of poetry and right and left and all kinds of things like that, or art. What do we see here? What did Aristotle actually do here? When I see, say, a person and I say “this is a speaking living being,” then understand that what I’ve actually done here is some kind of abstraction on several planes. First, a human being is also a creature with two legs. You could define him that way too: two legs, two arms, and a nose. But I decide that being alive and speaking is more essential, right? than having two legs, even though having two legs is also true. But it is more distinctive, more meaningful. By the way, also in the forbidden labors of the Sabbath—maybe that’s another example worth dealing with, I hadn’t thought of it. We’ll also deal with the forbidden labors of the Sabbath. There are very fascinating discussions there about the concept of definition. How do you define what a primary category of labor is? How do you classify the labors? And there the Talmudic text at the beginning of tractate Bava Kamma says: “Whatever was significant in the Tabernacle is called a primary category; whatever was not significant in the Tabernacle is called a derivative.” And whether “significant” or without “significant,” those are variant readings in Tosafot there and so on. Now what does significance mean there? When I taught that topic, it came out to me that significance has two meanings in that context: importance and distinctiveness. Two different things. Meaning, if the labor is significant—it effects a significant change in the state. It was like this before and now it changed in an essential way, not that I just moved it from here to there. That’s not an essential change. It is a change, but if it’s an essential change then I define it as labor. If it’s not, I don’t define it as labor. It’s not significant labor. But there’s another point—distinctiveness, not significance. Distinctiveness means: how is it different from other labors? Now there are labors that are very distinctive, so I define them as a primary category. Other labors are very significant, but I won’t define them as a separate primary category because they resemble other significant labors. They are not distinctive enough to count as a separate primary category. Do you understand that what lies behind this is exactly genus and species? Right? When you want to define the concept of labor, the labor of selecting, and ask yourself whether selecting is a primary category of labor, you need to check two things: first, does selecting create a significant enough change to be worth defining as labor? Second, does it distinguish a category unto itself against the other significant changes, against the other primary categories of labor? Okay? Two examinations I need to make, and that is exactly genus and species. Just to understand what is significant in it, what genus it belongs to. He is alive, the human being—that’s the genus. He also belongs to the group of objects that are between one and a half meters or between one point two and two point five. That too. But nobody will define that as an essential property. Why not? Because we decided it isn’t essential. Fine? There is some kind of choice here of what is essential in my eyes and what is not. And after that I also need to understand: okay, but there are also other living creatures, animals, other living beings, and so on. So you need to define—there are several species in this genus of living being. So you need to explain what distinguishes this species from the other species in the same genus. Then you’ve defined the definition. Fine? Significance and distinctiveness. And then you’ve defined the thing. A definition needs to contain the meanings of the concept and its distinctiveness. Okay? That’s basically what Aristotle said. Now we need to understand what that means. It basically means that when we look at—we never really look at a concept; we look at an object. If I want to define what a donkey is, I don’t look at the idea of donkeyness; I look at donkeys. Okay? Now I say to myself: okay, but a donkey has many characteristics. And each characteristic is an abstraction. This donkey is brown and has four legs and maybe is a good or bad work animal. There are more concrete characteristics—brown, so I can see it. We talked earlier about brown; maybe that’s a good example. I can see it, never mind. It has a certain color, it has four legs, that’s something I can see. But there are finer characteristics; there are characteristics that are abstractions, not something I simply see. Kind-heartedness or things like that—I sense them indirectly. It’s not something I can observe directly in a simple way. But still, that too is an abstraction I need to make. And after I make these abstractions, actually over many many objects, I’m working in two directions. I do the abstraction, I go from the objects to the concepts. Because concepts as such are hard for me to know; I see them through the objects. I see that there is such a thing as the color brown—how do I see that? I never saw the color brown as such. I see objects that are brown. Fine? Or objects that have four legs, and then I understand that there is such a property as having four legs. Okay? So that’s abstraction from the objects to the characteristics. But afterward there’s another step that says I return from the characteristics to the objects. And that’s an interesting step. Why? Because it’s not a trivial step. It’s not trivial because think, for example, of a democratic state. I look at a state and I need to make abstractions in order to decide whether it’s a democratic state or not. For that I need to define the concept of democracy. The concept of democracy consists of all kinds of characteristics: a government that changes every few years, civil rights, citizens elect, separation of powers, never mind, all the definitions we want to include in democracy. All of these are of course abstract concepts. So I make an abstraction. Afterward I need to decide which of the abstract concepts are essential to the concept democratic state. Every democratic state is also a state of more than a million inhabitants. In fact, I suppose that’s the case—or whatever, lower the number if you want. It doesn’t matter. But I can also say that this is not essential to the democracy of that state, right? So I don’t include it. Even though that too is a characteristic there, it’s not an essential characteristic, so it won’t enter the definition. So I need to decide which characteristics are essential to the definition, but more than that, I also need to decide which collection of characteristics creates a concept. I wrote about this in my book. There is a brilliant story by Borges called “Tlön, Uqbar, Orbis Tertius,” or maybe in a different order, but those are the three words—that’s the story’s name. And there he tells about some planet called Tlön. Of course it’s all wild fictional inventions, in Borges’s usual way. He was a genius, Borges, the only writer about whom I can wholeheartedly say that he was simply a genius with a diploma—not merely a talented writer, but literally a genius. I don’t know another writer you can say that about so clearly—maybe I don’t know enough, but among those I know. So that story is one of the amazing examples of his genius. Really, I recommend reading it. What’s the name of the story? “Tlön, Uqbar, Orbis Tertius.” It’s in the collection Fictions translated by Yoram Bronowski, of blessed memory. So one of the first stories, I think, in that collection is called “Tlön, Uqbar, Orbis Tertius.” I highly recommend it. What kind of story is it? It’s a fiction, not a story. A sort of fiction, not much happens there; it’s more that he describes something in a totally crazy way. So he says: on that planet, it’s a planet of idealists. I mean philosophical idealists. Philosophical idealists are people who don’t believe in the existence of entities. They claim there is no objective world; everything is only the result of concepts in our definitions. They do not recognize an objective world—sometimes they call them solipsists, yes? people who don’t recognize an objective world. At their head stands Berkeley, Bishop Berkeley, yes, who was like that, an idealist, an empiricist idealist, an amazing combination. Anyway, he then begins to describe the two parts of the planet—he goes completely wild there—never mind, the two parts of the planet, and they found some writings describing what goes on in that planet, and there is some scheme there to take over Earth by that planet, which of course from the point of view of the people of that planet Earth doesn’t exist, just as their planet doesn’t exist either. It’s all just plots for them to have a movie in their heads about taking over, and so forth, from their perspective. After all, there isn’t really any world, no universe. Anyway, he says that in their dictionary—and this is the most brilliant thing in the story—in their dictionary there are no nouns. There are only verbs. Because there is no moon—the moon does not exist—there is only moon-feeling, moon-consciousness. So in their language, when they want to say “the moon rose above the flowing river,” they say “it mooned above the ongoing flowing.” Is there consciousness? There is consciousness? No, don’t start arguing now with idealists; I don’t agree with them either. They say there is nothing at all, there are just movies running in my head. Movies running in my head, that’s all. What do you mean “in my head”? I see movies. There is no head, I see movies; I describe movies that I see. What does it mean to see? No, that’s the movie, the movie in consciousness. No, no problem—they have nothing, nothing at all. There is only the movies I’m talking about, and there there is no sunrise but “sunrising.” When do people experience sunrising? Exactly. There is no sunrise really. But you understand, the linguistic implementation is brilliant. I mean when he says there are no nouns in their language, only verbs. Now he says more than that: in the southern part of the planet Tlön, there are—some dictionary was found of the language of the southern part, the dialect of the southern part—and there there are objects. Not everything is incomprehensible; there are objects that you can compose, and now this opens beautifully—it really opens a wonderful door to wildness. It’s a wonderful Purim exercise, by the way. Maybe I’ll do something with it for Purim. So he says, for example, there is an object—in the southern part there are objects. One of the objects is: the cloud flying in the sky with the bird’s cry in space. That is one object. What kind of object is that? What’s the problem? I connect several characteristics and create from them a complex concept. Cloudiness with the bird’s cry in space. What I’m really saying is: why define the concept democratic state through this collection of characteristics? Government change, the citizen’s right to vote, civil rights, separation of powers, whatever, gather a few characteristics, it doesn’t matter, and that’s it. Why not define a new concept: the collection of all objects that are brown, are of size three meters and up, are at eight hundred feet in the air and above, and are nice. No problem. Let’s call the collection of all these characteristics, I don’t know, chizbatrons. Fine? And that’s it, I want to define that concept. Fine, so what? Democracy will be called some other combination. Ah, so now the question is really: is the concept democracy a useful fiction? And here we return to questions similar to those we discussed in the previous series. Is it a fiction—as you assume, and I disagree with you—that this is a useful fiction? We gather a collection of characteristics that often cluster together and let’s give them one name so it will be convenient to deal with them. Or alternatively, the alternative proposal is that we are actually claiming there is such a concept called democracy and these are its characteristics—that it is an essential concept. There is such a concept. So call it “the cloud flying in the sky,” and call all that democracy. Exactly! No, “the cloud flying in the sky” is not such a concept, that’s just a collection of characteristics. You can collect them, do whatever you like. That’s illness. The concept illness is a collection of things that don’t really have a true definition, but for the convenience of conversation it’s useful to use this concept, so it’s convenient for me to use it. Without it, it’s hard to talk. Okay, so that’s fine. These are fictive concepts that we define for the sake of conversation. Here I’m looking at the concept of definition, and this is how they see it in southern Tlön, or in the southern sector of Tlön: definition is just an arbitrary construction, a collection of characteristics to which I assign a label. In Kripke’s terms, Kripke argued that this is how concepts are produced. Kripke, by the way, an Orthodox Jew, used the concept of baptism—it’s very interesting—in order to define a concept. When we define a concept that we all understand, how do we do it? We baptize it. It’s an arbitrary process. You say: this baby here is called Moshe. And from now on everyone will call him Moshe. There is nothing essential in this baby that requires him to be called Moshe; you could just as easily call him Shaul, like Kripke, or something else. Doesn’t matter. Fine? But we baptized him, and that’s it. He relates to the definition of concepts as baptism, as an arbitrary act. The concept doesn’t describe something real. There are no ideas; in that sense he’s not Platonic. There is no Platonic idea of horseness. Rather, horseness is a collection of characteristics. It’s convenient for us to talk about it, because many animals have that collection of characteristics—the horses, as we call them—so it’s convenient for us to talk about horseness. We say horseness, but there is no real concept of horseness; there are objects, horses, but there is no concept of horseness. And similarly there is no concept of a democratic state—that is not a real concept, it’s a useful fiction. Fine? That’s basically the conventionalist claim, what you expressed earlier. This is conventionalism. We agree among ourselves, and in that way we coin concepts. There is the essentialist approach, which says no: if the concept of a democratic state didn’t exist, it would have had to be invented, because there is such an idea, it just wasn’t actualized until I don’t know when—until two hundred, three hundred, five hundred years ago, whenever you decide democracy was born. But until then it wasn’t actualized; it was there somewhere in the world of ideas, and at some stage it was also actualized. Of course before it was actualized perhaps we couldn’t know it or recognize it, fine; maybe it required good intuition to understand that there was something here to actualize. But it captures something real. The concept democracy is not just a combination; it does not collect this set of concepts arbitrarily. There is some essential connection between changing government, civil rights, separation of powers. It’s not by chance that we gathered this set of characteristics. Why not say: the collection of all states located in the center of a continent that have more than two million inhabitants and above which there are pink clouds? Fine, let’s call that hippocracy. Fine, that’s it. You can define that too. Definitions can tolerate anything. But those are definitions that are fictive definitions, useful or not useful—here it probably isn’t useful, so we won’t use it, we won’t do that. If it’s useful, we will. There are those who understand that all definitions are like this, and they are Aristotelians, not Platonists—the opposite of the Platonists. Platonists believe there are ideas, there is meaning to the things we define, there are such things. Definition tries to hit something, to strike something. It’s not something I create; it’s something I uncover. Whereas Aristotle, when he related to definition, for him it was our construction. It was not uncovering something real. Okay? So in that sense, for Aristotle abstraction is abstraction as a mental process. And for Plato abstraction is a cognitive process, in which I try to understand what stands before me, to recognize what stands before me—not that I am doing internal work within myself and making abstractions, creating concepts inside myself. It’s not an act of thought; it’s an act of cognition. Okay? So these are two modes of approach, and this will accompany us later too, because this too is related to postmodernism. Because postmodernism usually also says there are no essences. Which basically means that we define concepts according to what is convenient for us; these are practical definitions. They have practical value, but they do not capture anything essential. Someone else can define differently, and that’s perfectly fine, exactly as much as my definitions. There, there’s nothing to argue about regarding definitions. I claim there is something to argue about regarding definitions. People always say there is nothing to argue about regarding definitions. Not true—there is something to argue about regarding definitions. There is someone who defines correctly and someone who defines incorrectly. And mathematicians will be shocked when they hear this, because for them definition is a construction. But that’s not right. A definition ought to hit something real. And that takes me back to the point I opened with: that someone who is good at definitions, and offers a definition for a certain phenomenon—we all understand that he…