Negative Attributes, Lecture 4

[Rabbi Michael Abraham] Let’s go back once more to the summary of the whole line of thought we’ve developed up to now, because it’s important for what follows. I’ll say it maybe in telegraphic form. We talked about negative attributes, we talked about several concepts of negation. There’s oppositional negation, privative negation, and in the end the conclusion was, it seems to me, that what is closest to the doctrine of negative attributes is abstracting negation, negation by abstraction. And I began this with a bit of discussion about the relation between Torah and poetry, and I tried through that to illustrate these concepts. Today I thought that actually the concept of poetry expresses this on two levels. First of all, I tried to show how this comes to expression in conceptual, halakhic / of Jewish law, Talmudic study, this matter of abstracting negation. When we try to define a concept and we offer various definitions and reject them one after another, until in the end we’re left in a state where all the definitions are wrong. None of them captures the concept properly, and still the process had meaning. The fact that we rejected all the possible ways of defining the concept somehow carved into us some intuitive understanding of that concept. Somehow after this whole process something remained in us, some understanding of that concept that very often we can’t put into an explicit definition, but this negative path built some positive understanding. I said that in this sense Torah is a bit similar to poetry. I’m returning to that because I want to say one more thing about poetry that illustrates it. Today I simply thought about the fact that also in poetry, really—I spoke about how meaning doesn’t really pass through the literal meaning of the words, but rather the words create an atmosphere or some kind of something that is somehow supposed to generate in us the meaning the poem is meant to convey. It’s not a literal translation of the words. “The white lantern is lit in the street”—when that’s written in a poem it’s not the same thing as when it’s written in prose. In prose it describes a situation. In poetry it’s supposed to describe some kind of situation that when you enter into it, you experience something that isn’t connected at all to the literal meaning of the words. And in this sense there’s a similarity between Torah and poetry, and both of them actually serve as an illustration of a negative approach, of abstracting negation. We arrive at meaning through abstraction from positive meanings. We strip away the positive meanings until in the end we’re left with something we can’t define, but that is apparently the thing we’re trying to grasp. What I was thinking about is that I didn’t really carry out the whole move of—because we did this really at the end of one of the lessons—of how to define what poetry is. I gave the bottom line and mentioned that as for positive definitions of the concept of poetry, you can probably reject all of them. I told you that when I looked in the encyclopedia there was no entry for poetry. Somehow the idlers there in the humanities apparently aren’t doing their job and there’s probably no good definition you can write an encyclopedia entry on. But it’s clear that in a process like this—like What Is Art, I mentioned Gideon Ofrat and his book, where he tries to offer various definitions and rejects them all—in the end he remains with the conclusion that art is something displayed in a museum. That’s the end of the book. But of course that’s a conclusion of despair, it’s a mistake. Because he thinks that once we’ve rejected all the definitions, that means there’s probably no content to the concept. Basically there’s no content, because clearly no definition stands, so presumably it’s just a conventional matter. Whatever we agree to display in a museum is what’s called art. But that’s not right. It’s precisely against that that I think Maimonides goes out in the doctrine of negative attributes. He’s basically saying that even if you’ve rejected all the possibilities of defining something, that doesn’t mean you’re left with nothing. It means you’re left with something that doesn’t fit into an explicit definition. In the end, after you’ve rejected all the definitions, the whole path one goes through with Gideon Ofrat is an illuminating path, by the way, a beautiful book, magnificent analyticity. Brilliant, I mean a beautiful analysis of the concept, negating each of the definitions through counterexamples, distinctions, and so on—you learn a tremendous amount from it about art. And in the end you’re left with the claim that art is what is found in a museum. He himself doesn’t understand the meaning of the path he took. Right, exactly. So why did you write the whole book? The point is that the whole book itself is very instructive, if not for the last line. Because suddenly—what?

[Speaker C] So that you’ll know it has no meaning, only from yourself.

[Rabbi Michael Abraham] Yes. That’s what he thinks, but I think that really—

[Speaker C] The point is that when you get to a museum you’ll know what it isn’t.

[Rabbi Michael Abraham] So this path in the end carves into us, as I said earlier, some sort of understanding that remains inside us after we’ve peeled away all the definitions and rejected them. Something remains there afterward. We understand much better what art is. True, we also know—we’re already smart enough to know—that it doesn’t fit into some simple definition that can be verbally formulated here. In that sense—but that doesn’t mean we were left with no understanding at all, that the whole path was unnecessary. That’s a mistake. Now, the exact same thing—I mentioned that once I did this on the internet, a little stunt, after I saw that there was no entry for poetry in the encyclopedia, so I gave a series of lessons there on the methodology of the humanities and how to define poetry. And I followed a certain path that suddenly today I remembered. In the end I arrived at the conclusion that—what?

[Speaker D] Which encyclopedia?

[Rabbi Michael Abraham] You said encyclopedia—which encyclopedia? What is this, an escort?

[Speaker D] Ah yes, the Hebrew Encyclopedia.

[Rabbi Michael Abraham] The meaning of that path was exactly a negative path. It was an attempt—in the end, what definition did we reach, that I reached? I told you: the definition is that poetry is something whose meaning does not pass through the literal meaning of the words or the sentences. Fine, that’s a definition by way of negation, right? Now if I say that to someone who has never encountered a poem, it seems to me it won’t tell him almost anything. Okay, fine, he’s never encountered it, he doesn’t know what it is. In other words, he knows only prose. Fine. Now tell him: poetry is a text whose meaning does not pass at all through the literal meaning of the words and the sentences. You haven’t told him anything. Nonsense. What do you mean—but it has meaning. What? I didn’t understand. Yes, it has meaning, and it’s not the literal meaning of the words and the sentences.

[Speaker B] And not in addition to the words either.

[Speaker E] Huh? It’s not only literal meaning.

[Rabbi Michael Abraham] No, not literal meaning at all. The claim of this—that’s already a question, it already touches on the whole move that I didn’t make. The move I didn’t make—I can, in… I’ll say it in one sentence, because it seems to me interesting. What’s the problem? Why don’t people define the concept of poetry? Because it’s a concept that appears in many shades. That is, there’s a certain poetic element also in plays, also in—I don’t know—in all sorts of things, in various kinds of prose, literary writing—it’s also not prose in the coldest sense of the word. There’s something poetic in it. There’s something in it that doesn’t just describe things, it also conveys something beyond the meaning of the words—literary writing. As opposed to an encyclopedia, where maybe an encyclopedia is really the purest form of prose. Now when I look for the opposite pole, the extreme opposite pole, maybe it’s a utopia, there is no such thing, but that’s what’s called poetry. I’ll define it by way of negation. It’s something that has no meaning whatsoever connected to the literal meaning of the words. None at all. That’s what is called poetry. Now every concept—one second—every instance of poetry that we do know, then you’re right. Meaning there is the meaning of the words there, and something else wraps around them. But precisely for that reason, it’s not a pure appearance of the concept of poetry. And therefore people don’t succeed in defining it. In other words, I’m trying to suggest that once we’re dealing with many forms of appearance of a concept, forms that don’t let us define it, because every definition we’ll reject—each time we’ll have some other example showing it’s wrong—the wisdom here is to understand that all these concepts are not a pure appearance of the concept. That is, to try to look for a pole opposite, say, prose—yes, of the radish, yes, the encyclopedia. That’s prose that is just dry as can be. In other words, what the words say—that’s the meaning. Now I’m saying: what is the opposite pole? It’s a utopia, there isn’t really such a thing, but theoretically, what is the opposite pole? The opposite pole is a collection of words all of whose meaning is entirely unrelated to their literal meaning. That’s the opposite pole, the theoretical entity. Now I ask myself where I see such a phenomenon. Now in all the phenomena we know, we see a dosage of such a thing. We don’t see it in its purity. Okay. Fine. So we’ve defined here an idea just for theoretical purposes. So I say: that’s the definition of poetry, that’s the definition of pure poetry. And now I claim that all the intermediate concepts—and there I gave quite a broad breakdown of plays and literature and this kind of poetry and that kind of poetry and songs and poets’ poems and all these things—each one of them is simply a matter of where it falls on the scale between prose and poetry, the question is where you are located. That is, is it 0.9 prose and 0.1 poetry, 0.8 prose and 0.2 poetry, or do you get really close to poetry? Once you get really close to poetry, you’re already there. And then we arrive at these abstract poems in which you don’t understand at all what he wants from you. Which in a certain sense, ironically, is the most poetic poetry. Meaning that’s really poetry. But of course poetry always—form always needs matter. Form doesn’t appear without matter. And therefore poetry can never be completely detached from the literal meaning of the words, fine. That’s necessary so that this abstract idea can appear concretely in the world. But if one wants—and therefore with all these phenomena of concepts that appear in a very shaded way, and therefore are hard to define—it seems to me that as a method it’s always worthwhile to look for the definition this way. To try to refine an abstract concept even if it is not identical with any of the concrete phenomena standing before our eyes, but to try to understand from them what the poetic feature in them is, and then to define in refined form that Platonic pole, that idea called poetry. Then I say: fine, and now in all these phenomena that Platonic concept appears in different dosages. And therefore I think this can be done with many vague concepts that people struggle to understand—among them a concept like art, a concept like poetry, all kinds of concepts in this family. Now why?

[Speaker B] What? So what is art?

[Rabbi Michael Abraham] I quoted a definition there too of what it is, but for that I need—let’s leave that for now. Maybe we’ll talk about it one of the next times, we’ll see. In any case, why am I elaborating on this? Because this way of defining poetry—now I’m not talking about what poetry is, but about the method, how I worked in order to reach that definition—that is really a negative method. Abstracting negation. Right? Essentially I did the same process Gideon Ofrat did regarding art, supposedly. Of course in brief here and I didn’t spell it out, but never mind, that’s the principle. The principle is to try and offer some definitions that are all partial, reject them because they don’t really fit, then move to an even more sophisticated definition, reject that too, and in the end be left with no definition at all, because no definition captures the concept in its purity. But then I understand it. I understand it after I’m left without a definition. That means the whole set of definitions was placed here only as targets at the shooting range so I could fire at them and reject them, knock them down. Only that way can I eventually arrive at understanding the thing. Now if someone doesn’t explain it to me negatively but positively, I don’t know how he’d do it. How do you define poetry positively by saying that it is poetry? Exactly—that’s ars poetica. That is, the way poets define poetry, what’s called ars poetica, that’s exactly how they do it, right? Poetry is rhythm-wave and humming, you built yourself a palace with bare hands without gloves—

[Speaker F] Of logic, yes, exactly.

[Rabbi Michael Abraham] All kinds of things of that sort that say nothing. Why? Because they’re trying to define positively the thing itself, when in truth you can only arrive at understanding it negatively. Now these definitions can add something. Why? Because we do know this concept, we’ve encountered it. But if you try to say this to someone who has never seen a poem—what is it? It won’t say—it’s just nonsense, but what will it tell him?

[Speaker G] You can say, like poetry says something to you—not in a sharp-cutting way—like poetry says something to you.

[Rabbi Michael Abraham] No, poetry says something to you because the world of meanings it conveys to you is a world you do know, one that speaks to you.

[Speaker G] But you won’t be able—

[Rabbi Michael Abraham] If you haven’t encountered a poem, these definitions won’t tell you anything. Anything. You’ll simply think the person is talking nonsense. By the way, I often feel that way toward the Kooknik discourse of Har Hamor, all sorts of things of that kind that often seem to me like a collection of words that say nothing. They’re just playing with words there, and all kinds of—I don’t know—it sounds terribly deep and spiritual and all that, and says nothing. And somewhere, sometimes I rebuke myself and say, wait a second, for those people who are inside it, it does mean something to them. Now they probably can’t empty it into vessels that would convey it to an ordinary mortal like me, who tries to define it, understand it, set it against negation—who’s all closed up inside himself like that—but that doesn’t mean, it isn’t necessarily true that it says nothing. I don’t know, I don’t know how to judge it. But I assume that if people inside enjoy it so much and lick their lips over all these things, then apparently it does mean something to them. I don’t know. Maybe. But here too, if they tried, say, to convey it, to translate it to someone on the outside, they would have to use a negative path. That is, they’d have to say: look, you think an idea is such-and-such? Let me show you that it isn’t. And it’s not this either, and not this either, and not this either, and then you’re left with some something that maybe comes close to understanding what it is. I think I mentioned Suzuki, right? Some Japanese scholar whose whole business is translating Zen to a Western ear or Western mind. He brought Tennyson’s poem and the Zen poem—didn’t I bring this? I think I mentioned it. There he compares a poem by Tennyson with a Zen poem from I don’t know what century, maybe the thirteenth, something like that. In Tennyson it’s a flower between the cracks of the wall: I shall pluck you from your place and I don’t know what, understand the inwardness of your being, all sorts of things like that. And the Zen poem says: I saw a flower between the cracks of the wall. That is, Eastern passivity versus Western conquest, that domineeringness, the attempt—so he tries somehow to illustrate the difference between the two. Now clearly all his explanations can only work by way of negation. It’s like the Kookniks. That is, when you address a rigorous mode of thought, one used to arguments, orderly definitions, and you try to suggest something that simply isn’t its way of thinking, that is, it doesn’t work like that—then how will you explain to it that there is something here at all? You’ll try to show it, to take it in a sophistic way, like Socrates, right? To take it along its own path and show it that its own path fails in certain places. You’ll try to show it: here, let’s try to define this, now define it for me. So you’ll offer a definition. He’ll show you that this too ought to fit the definition and it doesn’t. Ah, true indeed, so I think again, define it—then I offer another definition. He shows you that this one doesn’t fit either. And in the end I can take someone with a very rigid logical mind and show him that there’s something beyond this whole business. That is, this doesn’t exhaust everything. Now if you manage to do it cleverly, then maybe you’ll also give him some positive notion of what you mean, but you’ll never succeed in formulating it positively. The formulations will always be negative. The understanding that arises from them is a positive understanding. And I think that exactly this process, of defining concepts such as art, poetry, or other abstract concepts, and of course the Holy One, blessed be He, as perhaps the most abstract concept, must necessarily be done by the negative path. But this is negation in the abstracting sense, as I said—that’s what we’ve been discussing the last few times—not negation in the logical sense, neither privative negation nor oppositional negation in the logical sense, because otherwise it’s simply nonsense. That is, it says nothing. One more remark—these are just points that came to me today in the context of negative attributes. I think I also mentioned in one of the earlier times Hilbert’s hotel, right? With the paradoxes of infinity. Hilbert, David Hilbert, was a very prominent mathematician at the end of the nineteenth century and beginning of the twentieth, I think. Around the turn of the century there was a conference where he presented the open problems of mathematics. So he did quite a bit with infinity, and he tried to show the meaning of different levels of infinities. The classification of Georg Cantor—for those who know—there are countable infinities, there is the continuum, there is an infinite hierarchy of larger and larger levels of infinities. Yes. And the terms are aleph-null; he uses the letter aleph. So he tries to illustrate this through all sorts of paradoxes that he calls Hilbert’s hotel. Think of a hotel with infinitely many rooms, okay? And all the rooms are full. Now a person comes and says to the hotel owner, I want to stay here. No problem. He says: every occupant of room n will move to room n+1. So everyone is settled. Now room one has been vacated, so he puts him in room one. Now another one arrives. No problem, you can put him in too.

[Speaker C] It’s the whole paradox of infinity.

[Rabbi Michael Abraham] Because you say infinity—the paradoxes of infinity—that’s what he’s talking about.

[Speaker C] When you bring in one more, why is that simpler than just telling the first one to move after the last room?

[Rabbi Michael Abraham] What? After the last? No, there isn’t one. You have to define it. It’s not mathematically defined. You have to speak about a defined n. You can’t talk about after the last—that’s words. Tell me what the algorithm is. In other words, every n moves to n+1 and room one is vacated. No—you can never talk about the infinity itself, you have to talk about the ones here.

[Speaker C] Move room by room to n+1 until there’s no more—

[Rabbi Michael Abraham] No, no—you’ll never get there. That’s exactly the point. By the way, these processes too are very delicate in mathematical definitions. Whoever wants to be more exacting—these descriptions aren’t precise. Because you have to—one second—this process of moving everyone one room over is itself not defined, it takes infinite time. The room has to become vacant immediately when the next person enters. Not even one second later, because otherwise it never comes out at all. There are several subtleties here one could discuss. I don’t want to get into that right now.

[Speaker B] I’d already go in with someone else.

[Rabbi Michael Abraham] In any case, so yes, exactly. What about the cleaners? There are probably infinitely many cleaners too.

[Speaker C] No, but they have to clean so many rooms. What’s the problem?

[Rabbi Michael Abraham] There are infinitely many cleaners. Half-infinity, and each one cleans two rooms, so no problem. It’s well defined.

[Speaker C] That too is something you’re not allowed to say.

[Rabbi Michael Abraham] Yes, because—

[Speaker B] There are infinitely many—

[Rabbi Michael Abraham] People in the hotel.

[Speaker C] Where did the extra one come from?

[Rabbi Michael Abraham] What’s the problem? There’s one more.

[Speaker C] There are infinitely many people in the hotel—

[Rabbi Michael Abraham] And besides that there’s one more.

[Speaker C] And there are also rooms without—why? Because if infinity stretches, it stretches. Obviously it stretches. If you add two to infinity it stays infinity. If you add three and take them out, so what’s the problem? He opens rooms for the next people.

[Rabbi Michael Abraham] Right, but you need to define a mathematically well-defined algorithm with all sorts of subtleties that defines how you do it. Because not every way works. And he says, at the next stage now infinitely many people arrive. No problem. You do this thing infinitely many times. Now buses arrive with infinitely many people. Now he says: infinitely many buses, each with infinitely many people. No problem, that too can be done. Why? You do a transfer like this. First of all, you move 1 to room 2, 2 to room 4, 4 to room 8. n moves to 2n. To room eight. All the odd-numbered rooms remain vacant. No, n moves to 2n. Yes. So all the odd-numbered rooms remain vacant. Good. Now there’s a theorem that there are infinitely many prime numbers. That’s a theorem the Greeks already proved. There are infinitely many prime numbers, right? So now take the prime numbers 3, 5, 7, 11, and so on. 3 to the power of n, where n equals 1, 2, 3—that is, 3, 9, 27, 81. There are infinitely many such numbers, right? 3 to the power of n, and n can take any value. Put the passengers of the first bus in the rooms numbered by powers of 3. The passengers of the second bus in powers of 5. None of them equals the others, because they’re prime. That’s why they need to be prime. Okay? And they’re all odd. Right, because the odd rooms are free. What do we gain from this? First of all, we gain lots of money.

[Speaker B] But no, beyond that, for the purpose of publishing papers.

[Rabbi Michael Abraham] Publishing papers is also important. Infinite money. Right—the question whether the hotel is profitable isn’t so simple. The fact that it earns infinite money doesn’t yet mean much; it also has infinite expenses. In any case, that’s not the punch line. The punch line is the question whether there is a certain number of people that cannot be accommodated in the hotel. Could some quantity of people arrive that cannot be put into this hotel in any way? There is no algorithm that will succeed in getting them all into the hotel. So the answer is certainly yes.

[Speaker B] The real numbers, for example.

[Rabbi Michael Abraham] Right, but he did… there are nicer illustrations of this. Gadi Alexandrowicz has a very nice math blog. So he says, for example, let’s take ID numbers with infinitely many digits. People with ID numbers that have infinitely many digits. Okay? Once all the ID numbers are occupied—let’s say that’s an infinity of people—he won’t be able to get into the hotel. You can prove it by contradiction. How? Let’s put them all into the hotel. Assume they all do get into the hotel, and I’ll show you that I still find one who didn’t get in. He’ll be there. Right? So in that way I’ve actually refuted the assumption that everyone is in the hotel. How? Suppose everyone is inside the hotel. Now I go room by room. In the first room I say to the person: what’s your ID number? He tells me, and I change his first digit. Meaning, say his first digit is two, I write down three. I go to the second room, I say to him: what’s the second digit of your ID number? I don’t need more than that. The second digit is five, I write down four. Okay? Each time I do something different. When I finish, I’ll have in my hand a list of infinitely many numbers—in other words, an ID number—such that the person whose ID it is is not in any of the rooms, because it differs in the nth digit from the ID number of the person in room n. Right? Meaning, for every person in every room there’s an ID number different from the one I constructed like this.

[Speaker C] But the process never ends.

[Rabbi Michael Abraham] Right, it never ends. But you still won’t arrive at the ID.

[Speaker C] No, I can.

[Rabbi Michael Abraham] The process of writing down the ID numbers. Come on, I’m not being mathematically rigorous here, but you can define it mathematically too, say with real numbers. Okay? That’s the original definition. And then what it basically means is that there are certain quantities of people that won’t fit into a hotel with infinitely many rooms. In other words, there is an infinity bigger than this infinity, which is called countable. Countable means you can number the rooms: one, two, three, four—there’s an order to the rooms. So you can number the rooms, and since you can, it’s a countable infinity. An infinity that is not countable cannot be counted. What does it mean to count? To assign a number to an object. That’s what counting is. To find a correspondence between the sequence of numbers and the objects. Okay? So that’s how Hilbert’s hotel is used. Now, the first part of this argument is often used to show what kinds of paradoxes we can reach if we assume an actual infinity rather than a potential one. Meaning, what are we really assuming? That there is a hotel here with infinitely many rooms. That means that’s the number of rooms in the hotel. No—actual. Exactly. There’s a hotel here. Meaning, this hotel has infinitely many rooms. That means there are infinitely many rooms before us. The number infinity, usually in mathematics—this is one of the criticisms of George Cantor’s classification—is that he too looks at infinity as something actual and not potential. But usually in mathematics, in calculus, everywhere else, infinity is defined in a potential way, not an actual way.

[Speaker H] Meaning, it’s striving toward…

[Rabbi Michael Abraham] It’s striving toward… or greater than every real number we know. So I didn’t say it positively—notice how I said it—in a negative definition. Right? When I define infinity, I’m not saying what it is, I’m saying what it is not. It is not any of the real numbers I know, and it’s also greater than all the real numbers—or integers, doesn’t matter—that I know. Okay?

[Speaker C] So there’s infinity plus one. What? Infinity plus one is bigger than infinity.

[Rabbi Michael Abraham] No. Why is it bigger than it? You have to define what bigger means.

[Speaker C] There’s no such thing as plus one.

[Rabbi Michael Abraham] No, you need to define what bigger means. Define it. And what plus means. And one more. You need to define what plus is and what bigger is. Infinity plus one? If you define what plus is and what bigger is, then you’ll see it’s not bigger. A sign that there is something bigger than infinity. No—who said there is something bigger? It, infinity plus one.

[Speaker B] No, who said infinity plus one is bigger than infinity?

[Rabbi Michael Abraham] The question is how you define the concept of bigger. No. The question is how you define the concept of bigger. You can define the concept—how does Cantor define the concept of bigger? By the fact that you can’t find a one-to-one correspondence between the two sets. In other words, here there is a one-to-one correspondence. The elements of one set correspond to the elements of the other set, but in the second set there will be elements that don’t correspond to this set—that means this one is bigger than that one. Now, infinity plus one and infinity—there is a one-to-one correspondence between the two sets. For every element, in either direction.

[Speaker C] Infinity plus one is not bigger than infinity?

[Rabbi Michael Abraham] No. Not by the definition. There is a one-to-one correspondence between this set and that set. I can show you—say, the even numbers and the integers. It’s easier to show it there. Which is bigger? Apparently the integers, right? Because the evens are only half. No, I’ll show you there’s one-on-one in both directions. There’s a one-to-one correspondence. One corresponds to two. Two corresponds to four. Three corresponds to six. Four corresponds to eight. You won’t find any integer that doesn’t have a match among the evens, and vice versa.

[Speaker C] Wait, but here you stopped the correspondence, I’ve got some left over…

[Rabbi Michael Abraham] No, no, you didn’t stop anywhere. You didn’t stop. The correspondence is infinite.

[Speaker C] So I don’t have any left over…

[Rabbi Michael Abraham] No, you didn’t stop anywhere. The correspondence is defined from n to 2n. That’s the correspondence for every n. Now you won’t find an element among the integers that doesn’t have something corresponding to it among the evens, and vice versa. You won’t find one. That means it’s the same number. And the rationals are also the same number. Rational numbers are quotients of integers. Okay? Logic gives contradictions if it doesn’t say that. Meaning, logic would be contradictory. You can’t say otherwise. Otherwise you get contradictions. As numbers, you’re right—the numbers, you’re right—but once you get to infinity, infinities are not numbers. That’s exactly the point. And why? Because we treat infinity only as a concept, an abstraction. There is no such thing actually. Exactly. And it’s only a concept of a limit; you can talk about something bigger—no, no, no, that’s not what you understood—not that there’s no such thing, but that you can’t define it the way you define numbers. That’s the point. And you also can’t treat it the way you treat numbers, because otherwise you get contradictions. To say there is no such thing—that’s the same mistake as Gideon Ofrat, who says that since you didn’t manage to define what art is, there is no definition. No, that’s not true. Maybe for this…

[Speaker C] There is a definition.

[Rabbi Michael Abraham] Well, that is to say…

[Speaker B] You can’t tell people…

[Rabbi Michael Abraham] But there are definitions of infinity. I said, a definition by negation. Yes, but you’re not defining what infinity is; you’re saying it’s something greater than every number you know.

[Speaker C] Once I asked a mechanical engineer here—not here—the dean of the mechanical engineering faculty at Tel Aviv University what a machine is, and nobody knew how to say. Nobody, including the dean, sat there for fifteen minutes, half an hour, and didn’t know how to say.

[Rabbi Michael Abraham] To this day I still don’t…

[Speaker C] Know what it is.

[Rabbi Michael Abraham] I’ll give you a definition afterward.

[Speaker C] Machine, not infinity.

[Rabbi Michael Abraham] Machine, machine. So that will be a positive definition, not a negative one.

[Speaker B] Deus ex machina. So I assume that ninety-nine percent of people don’t have a definition either way.

[Rabbi Michael Abraham] Okay, in any case, I brought all this in order to show that abstract concepts are things we also handle in our lives by way of negation. When we try to define the concept of infinity, the route we take is a route of negation, not a route of affirmation, and therefore one shouldn’t be so surprised that when we deal with divinity too, Maimonides tells us that it must be dealt with in terms of negative attributes. That doesn’t mean it says nothing. All the paradoxes I mentioned at the beginning—not in this lesson, in the first lesson where I talked about this—if so, what’s the difference between defining by double negation and defining positively? It’s not double negation, because this is not logical negation; it’s abstracting negation. Abstracting negation is exactly of this type. Just saying that infinity is not any of the numbers—well, a bird is also not any of the numbers. So clearly that’s not enough to define infinity. Infinity is of the same kind, in some sense, as the numbers, but it is not any one of them. So I did say something positive here. To say that a bird is not any of the numbers is nonsense, because it’s irrelevant; it’s not even on the same plane, not in the same semantic field—bird and numbers. Infinity does belong to the same semantic field, and nevertheless I say it is not any of the numbers. So you understand that at the foundation of this negation there sits some positive statement: that they are of the same kind, but not this kind. Right? Like the Aristotelian definition, by the way—an Aristotelian definition is always genus and species. When I want to define what a human being is, I say: a speaking animal. What does that mean? First of all, the genus is animal; within that genus there are many species, and I’m talking about the speaking species, meaning one that differs from the other species that do not speak. Whenever I deal with opposites—we also talked about concepts of opposites—whenever I deal with opposites, I always assume some underlying similarity between the two sides, and only then can I say that this is the opposite of that. But if there is no connection between the two sides, I would never say one is the opposite of the other. Opposite means there is a connection between them. The Maharal talks about this too. Meaning, a bird is not the opposite of a number, but infinity is in some sense—not sure if opposite—but it is not a number. Not in the sense that it is of the same kind but not.

[Speaker B] Zero too. What?

[Rabbi Michael Abraham] Zero too, in many respects, right. And therefore when we speak about negation, very often at the foundation, without even saying it, we are actually saying something positive. We are not saying it—we are implicitly assuming something positive. When I say that infinity is not any one of them, or greater than all the other numbers, or it is not any of the numbers known to us, in that I have said that it still belongs to this field of numbers in some way. It’s just not any of the members I know. So whenever I say “not,” behind that sits some kind of “yes” that I did not say.

[Speaker B] There is some comparison there that…

[Rabbi Michael Abraham] I didn’t say because I don’t know how to say it. Not that you didn’t say it—you can’t say it. I can’t say it, right. If I say infinity is like the numbers, I’ll be mistaken; that’s not true. It’s not like the numbers. But on the other hand it’s also not true to say it’s not like the numbers in the way a bird is not like the numbers. A bird is simply not anything—it’s not the same sort of thing. Infinity is in some sense of the same sort, otherwise why put it there at all, why mix it in there. Therefore when I negate, I’m always… behind it I’m actually also saying something positive. But very often the only way to say that positive thing is precisely in the form of negations. It’s not a number, and it’s greater than all of them, and that’s all—but of course all of this is within the field of things that somehow are similar to numbers. So I can explain to someone what infinity is. If I just say to him, it’s not numbers—in the sense of logical negation, not abstracting negation—then when I said to him it’s not a number, it could just as well be a bird. In logical negation. And when it’s not a number, then you haven’t said anything. Meaning, you’ve left many other possibilities open. When I say infinity is not a number, it’s not in the same sense that a bird is not a number. It’s not that kind of “not”; rather, it is not one, but it is of the same kind in some way. So I did say something about infinity. And therefore I think all these examples nicely illustrate what at least it seems to me Maimonides means when he speaks about the doctrine of negative attributes. When he speaks about abstracting negation and not logical negation. Okay?

[Speaker I] Okay. It really does remind me a bit of the story about what a song is, for someone who’s never heard a song.

[Rabbi Michael Abraham] With respect to the Holy One, blessed be He, that’s a big question. Because if we really had no way at all of grasping what divinity is, then it seems to me that the negative way of describing Him would tell us nothing. And I don’t think that’s the case. I think we do have the ability to grasp Him; we don’t have the ability to define Him, to put Him into a category. But we do understand, we do grasp, what divinity is. Otherwise, what do we believe in? Meaning, do you see? I just don’t know how to put it into words, into an explicit definition, in the positive sense. But clearly I have some grasp of the thing, because otherwise a definition by way of negation would tell me nothing. Exactly like defining a song by negation for someone who has never seen a song, never encountered a song—that won’t tell him anything. It just says nothing. And therefore I say that in a certain sense there is a positive grasp here of divinity. When we try to translate it into definitions, the definitions will always be by way of negation. That negation paves the way toward the abstract thing that will remain, but it is positive. It is not negative. It is a grasp of what divinity is. The way to define it, to make it cognitive, is always by way of negation. We talked about Mary, Mary’s room, right? With the colors. She was in the room—the physicist who was in a black-and-white room—and she knew all of optics backwards and forwards. The question is whether she knows what the color red is, and the answer is of course not. Right? She does not know what red is. She knows the electromagnetic theory that describes the wave that generates the sensation of red in my eyes. But until you’ve seen the color red, it won’t tell you anything. For example, I said, she won’t understand why that color annoys bulls. She can do all the calculations of wavelengths and scattering of light and all kinds of… it won’t help her at all. To understand why it annoys a bull, you need to experience the color red once, and then you can try to understand. Even though we’re not bulls, we can understand why it annoys bulls. It’s such a striking, piercing color. Maybe because it reminds them of blood. What? Maybe because it reminds them of blood. But for that—for that—I need the immediate grasp of the color red. Right, so how does she… oh, yes? So how does she…

[Speaker B] So why did the…

[Rabbi Michael Abraham] Oh, yes? Well, if so, that’s very interesting. Fine. But how do you know? How do you know she’s color-blind?

[Speaker C] They asked him. No, he didn’t invent it. It was—there were ways to check such things. It’s not a problem. You can check in the brain. It’s not a problem. If you want to try to annoy him, use a color…

[Rabbi Michael Abraham] No, it could be in the eye, it could be in the brain. It doesn’t matter. It could be both.

[Speaker C] Both. But for example fish—the same intensity of light and only the shade is different, and it can’t distinguish. Aha.

[Rabbi Michael Abraham] Yes. Fine, never mind. In any case, so maybe that example isn’t good. Why do we get annoyed? Hm? Exactly. So why can the color red annoy us? Let’s leave the bulls alone, “let our lips substitute for bulls.”

[Speaker H] Why did they make the audience color red?

[Rabbi Michael Abraham] Exactly. Why did they make the audience color red—so that it would identify with the bull getting annoyed? Meaning, now we can understand that, and Mary won’t understand it. Now when she tries to define—now Mary has seen the color red. She left the room, and now she finally sees what red is. Now she’ll try to explain to her colleagues closed up in the room what it is. She doesn’t have the slightest chance of succeeding. She cannot do it. Meaning, there are things that until you encounter them, you simply don’t… there’s no way to put them into verbal definitions. It’s not something you can do at all. Language doesn’t allow it. I don’t know whether it’s only a limitation of language, or of thought, or of…

[Speaker F] It’s interesting whether it’s only a limitation of language. Maybe she could do the same process that she… come to them and say, think of something you know, but someone who didn’t know it—the same process to lead them through? Then they would get an understanding…

[Rabbi Michael Abraham] Exactly, that’s again a negative route.

[Speaker F] No, a positive route.

[Rabbi Michael Abraham] No, why? Negative.

[Speaker F] No, because you testify to the same thing, but…

[Rabbi Michael Abraham] It’s like explaining a fourth dimension. You say to a person, look, think for a moment how two-dimensional creatures think about our world—yes, Flatland, the book Flatland. That’s how you can try to imagine what happens in the fourth dimension relative to you when you live in a three-dimensional picture. So that’s a negative explanation. So all these are examples trying to show the meaning of the negation Maimonides is talking about.

[Speaker J] But here you have some grasp of something you have no real relation to. What? You have some grasp of something that isn’t part of…

[Rabbi Michael Abraham] No, because with the concept of dimension I apparently do have a relation. I understand what a dimension is; the fact is I understand the difference between two and three dimensions. But a person who lacks the power of abstraction—you really won’t be able to explain even two dimensions to him, not just four. He knows three dimensions; the concept of dimension itself is not yet present in his thought at all, in his conceptual world, so truly you won’t be able to explain even two dimensions to him, not only four. But once he succeeds in making that abstraction, then he already has some touch of what four dimensions are. I think I once told about… there was an article in Nature once about the Pirahã tribe in Brazil. It’s a tribe that counts using a one-two-many system. Meaning, they have one, two, and many. Those are the numbers they have. They get through math easily in first grade and that’s the end of the story—there are lots of advantages to it.

[Speaker I] One, two, many, infinity.

[Rabbi Michael Abraham] Yes, and their grades too, by the way, are one, two, or many on the report card. So they weren’t able, for example, to count or distinguish, say, between five objects and seven objects. They couldn’t. Now with very large numbers they do see, they do understand, but say when they’re close together, you need this precise conceptual world in order to make the distinctions. So of course they eventually succeeded in explaining it to them, because they have the preparation—the conceptual preparation to absorb these things is there for them too—but it simply hadn’t developed in them. Exactly, yes, but it still hadn’t developed in them. Okay? So that’s why I say: anything that you can come to some understanding of in a negative way means that the thing you understand is something you already have some touch of beforehand. An intuitive touch that you don’t know how to define to yourself, you don’t know how to fully attain it, but you do have some touch of the thing. Otherwise it’s just empty word-chatter and it doesn’t help at all. Okay, let’s return to Maimonides; the introductions always take me to the end of the lesson, I don’t know—the topic really is pathological. We were basically in the second paragraph; let’s read it quickly. “And after this introduction, it says that the blessed Name, since there is already a proof that He is a necessary existent, there is no composition in Him, as has been demonstrated concerning Him, and we apprehend only His existence alone, not His essence. If so, it is false that He should have a positive attribute.” Maimonides, I think, basically means to say—maybe I’ll keep reading—“because He has no essence apart from His existence, and an attribute points to one of these. The explanation: He has no essence apart from His existence, and an attribute points to one of them, all the more so that His essence should be composite and the attribute point to two parts, all the more so that He should have accidents and the attribute also point to them. And if so, He has no positive attribute in any respect.” There cannot be a positive attribute for the Holy One, blessed be He. Why? Because all we can say about Him is that He exists. We cannot describe Him; we can describe His actions or say that He exists, but we cannot describe Him. So if that’s so, what would the attributes apply to? To the fact that He exists—that’s not an attribute, we already talked about that, that He exists. So if every other attribute, some other attribute—what would the positive attribute attach to? The Holy One, blessed be He, is utterly simple in the highest possible sense—that is Maimonides’ assumption—there is no composition in Him, yes, that’s what he writes here, and therefore there is in Him only what we called the substance and not the form, or only the being and not the “what is the thing that exists,” or some particular character or descriptions of Him, His features. So since that’s so, what will the attribute attach to? There’s nothing for the attribute to attach to. “All the more so…” that’s what he says here. “And if so, He has no positive attribute in any respect. However, negative attributes are what must be employed in order to direct the intellect toward what one ought to believe about Him, may He be exalted.” Meaning, negative attributes can describe Him, because no multiplicity results from them in any respect. And multiplicity here, I think, means composition… no, no, I think it means composition.

[Speaker B] Isn’t that from Schwartz?

[Rabbi Michael Abraham] What? No, not from Schwartz, I don’t have Schwartz’s text. “And they direct the intellect to the utmost that a human being can apprehend of Him, may He be exalted.” Yes, so it’s only meant to direct the intellect toward what can be apprehended of Him. Now what does it mean to direct the intellect toward what can be apprehended of Him? That’s what I said: this negation is not logical negation. When I say that the Holy One, blessed be He, is merciful. Okay? So what? On a simple reading, Maimonides seems to mean to say that it is not true that He is cruel. Right, but “not cruel” is merciful. What is there here beyond that? So why is there a difference between a positive attribute and a negative one? It has to do with the way Maimonides formulates it…

[Speaker B] There in the abstraction… without abstraction. No, no—without abstraction. Not cruel and not merciful…

[Rabbi Michael Abraham] Is someone who has no feelings. Okay, fine, right. Not cruel not in the sense of minus one, not in the sense of privative negation, the negation of the opposite.

[Speaker I] They certainly don’t mean that. What? And they certainly don’t mean that. When I say He is merciful, they certainly don’t mean to say He has no feelings.

[Rabbi Michael Abraham] No, come on—with that, I already ruled that out in the introduction when I said that if we speak of privative negation—not opposite negation—meaning turning “cruel” into “without feelings,” not into “merciful,” then if that were the intention, it would mean that I could say He is cruel just as much as I could say He is merciful. Because in both cases the privative negation would lead me to “without feelings.” So what preference is there in defining the Holy One, blessed be He, as merciful rather than defining Him as cruel? That Maimonides certainly does not mean. Therefore it is clear that this is not privative negation. That’s how I explained why I think it can’t be that when Maimonides speaks of opposite negation—that certainly can’t be, because then it would just be double negation leading me to the same place; it’s simply the same thing. But privative negation also can’t be, for a very similar reason. Because the privative negation of cruel and of merciful is the same thing. So if my intention is privative negation, then I can just as well say He is cruel and say He is merciful. And also say He is vegetarian. The privative negation is the same thing too—it’s just zero. He’s just nothing. That’s it. So what difference does it make what I say about Him? But this message does mean to say something. The fact is that I choose attributes like merciful and not the attribute cruel. Why? Because the negation here is not logical negation of opposition and not privative negation; it is abstracting negation. Like infinity, which is not a number. Not like a bird, which is not a number. Right? Infinity, which is not a number, is abstracting negation. I take the concept of number, refine it further, and I say: this is not the concept in the way of the numbers we know, but it still has this dimension of number in it. I refine it. That is what is called abstracting negation. And that is what Maimonides means when he says that the negating attribute directs the intellect toward the thing we are trying to understand. What does that mean? This refining, abstracting negation ultimately creates the understanding. After we negate all the partial, unrefined definitions, we are left in the end with something positive. Only that positive thing cannot be described verbally. Thought cannot turn it into some positive definition. But an understanding does remain with us after we have peeled away all the definitions, negated all the definitions—that remains, and that is what he calls directing the intellect. By the way, this expression recurs here; there’s something from Dehān here, he translates it here, I don’t know what it is in Arabic. So this expression recurs a lot in these chapters of negation of attributes, and I think it points exactly to what I said in the introductions, where I said I think Maimonides is speaking of abstracting negation and not ordinary negation. Abstracting negation is exactly the point. When we negate all the possible definitions of delivering a bill of divorce—that example I gave of yeshiva-style conceptual analysis—then after I negate all the possibilities of defining delivery of a bill of divorce, in the end I’m left with a good understanding of what valid and invalid delivery of a bill of divorce is. Even though I can’t give the definition. I don’t know how to formulate what the definition is. No formulation passes the test of all the examples. So that is what is called directing the intellect. Meaning, all these examples are just meant to give me a sense of direction, where I’m headed, but in the end I’m left not with definitions—I peeled all the definitions away—I’m left in the end with where the definitions were pointing me. And that is something I do not know how to formulate in words.

[Speaker F] It works on intuition. It works on intuition.

[Rabbi Michael Abraham] It trains the intuition, right, right—focuses it, maybe, yes, right. “And an example of this is that it has become clear to us by demonstration that there is the necessary existence of one thing other than these substances perceived by the senses and those whose totality the intellect knows.” Right? Suddenly we understood, we reached the conclusion, say, that there is an object, some substance, different from all the substances perceived by the senses or understood by the intellect. It is different from all of them. And we said of it that it exists. What can we say about this thing? If it is totally different from all the substances we know and/or understand, that means we cannot say any attribute of it, right? Because if we say of it some attribute—that it is red—then it isn’t totally different.

[Speaker B] Why the assumption that it has nothing in common? Why the assumption that…

[Rabbi Michael Abraham] So, we talked about that last time. In the second line it says, “and there is in it of commonality and deficiency,” what Maimonides writes. Maimonides assumes that there is nothing at all in common between the Holy One, blessed be He, and any other object.

[Speaker B] Is that like a foundational assumption?

[Rabbi Michael Abraham] He even claims that he proved it. We won’t get into where exactly he got it from. So we reached the conclusion that such an object exists; it differs from everything we know or understand with the intellect—so what can we say about it? No attribute except to say that it exists. Right? It simply exists. We talked about the cosmological proof there—what does it mean? I reached the conclusion that there is someone who created the world, or something that created the world, but I can’t say anything about it. So have I said anything by that? Yes. Often the atheists’ criticism of that proof is: basically you didn’t say anything. What does it mean, “created the world”? You said nothing.

[Speaker F] You said two things: it exists and it created the world.

[Rabbi Michael Abraham] You said—no, so the claim is that there exists an object about which I can’t say anything in the sense of describing it, but there exists something that is not the world. In that sense I said that to say of something that it is not something else is also not a description. And the proof of that is the ontological proof, right?

[Speaker C] In talking about positive things, you said it exists and you said it created the world—you did manage to say a little.

[Rabbi Michael Abraham] No, of course, but the question is: who is the one who created the world? Did I say… I can always say there is something that created the world. That says nothing. What did I say about it? I also said of it that it created the world. That says nothing. Tell me who the subject of the sentence is. The predicate I understand, but who is the subject? And that subject is some “there is” that exists. That I can say of it, okay? The question is whether that says something.

[Speaker B] He existed, at the very least.

[Rabbi Michael Abraham] He existed, yes, never mind.

[Speaker E] No, it does say something. Why does it say something? Because you have an alternative—the alternative of thinking that the world came into being by itself.

[Rabbi Michael Abraham] And therefore I said it has meaning. Of course, that’s what I’m saying. That the atheists are mistaken in this criticism. I think it does say something. It says that there exists some object that is not the kind of thing we know or understand, period. Why is such a statement meaningless? It is not meaningless at all; it definitely has content, it has meaning. And true, I don’t know how to describe anything about this object. So what? And I can still say that it exists. That is a completely legitimate statement.

[Speaker I] No, but that’s a claim saying there’s no, let’s call it, functional statement here. Meaning, you say it is something and it is there, and okay, that’s all.

[Rabbi Michael Abraham] That’s what I’m saying. What’s the problem?

[Speaker F] And that’s actually…

[Speaker I] Very far-reaching, because it brings me very close to observing Torah and commandments.

[Speaker F] We talked about this; without that statement I’m much farther from observance of Torah and commandments. No, it says a lot, it’s very practical…

[Speaker I] If you stop here at this stage.

[Speaker F] Yes,

[Rabbi Michael Abraham] Right, but that’s a different discussion; we won’t get into it now. It’s also connected to the stage of knowledge. No, but this description gives it very great importance…

[Speaker I] To talk about it, and not for nothing. That was basically Aristotle’s form too. You could say Aristotle also said there is some kind of form. It didn’t advance him toward anything in terms of…

[Rabbi Michael Abraham] No, it didn’t advance him in the religious sense, fine, that’s another discussion. But first of all, it is something with content. It is not a contentless statement. In that sense, that is what I need here.

[Speaker B] But Aristotle argued that the world is eternal; that’s not the conclusion.

[Speaker C] No, yes,

[Rabbi Michael Abraham] But that’s what he says. God in the sense of an existing being—so not to say anything about Him in the religious sense. Yes, that’s deism, not theism, as it’s called. The point is, then we said of this—we said of this that it exists, “because its nonexistence is false.” Now again, on a simple reading one might think that means—well, that’s nonsense. If its nonexistence is false, then it exists. What’s the difference between saying this and saying that? Double negation. But that’s not right. Because “its nonexistence is false” means a falsehood that abstracts. It is not falsehood in the sense of logical opposition. The falsehood is negation, yes? This is not negation that is logical negation, but abstracting negation. I abstract the concept of existence. We talked about this—for example, in what sense does light exist? There are people who think light doesn’t exist. After all, it has no mass, it takes up no place in space, so it doesn’t exist. There’s no such thing as light. But that’s not true—light exists. Even though it has no mass and does not occupy space. So in what sense does it exist? This is the concept of existence when we abstract it from the properties we usually know in existing entities—that they have mass, that they occupy space. The concept “exists” still retains meaning. I don’t know how to define it positively. If I say this phone exists, then I know—it has mass and it’s here, I can say positive things about it. Once I’ve abstracted all the positive things away, all I can say is that it exists. But what does “exists” mean? I can’t say anything positive about it, but I do understand what it means. How do I understand it? By abstracting from the concept “the phone exists” or “the book exists.” I abstract and try to understand what the concept of existence itself is, without placing it in entities with mass that occupy space. And that too can be said about the Holy One, blessed be He. And that is what Maimonides means by “because its nonexistence is false.” “Its nonexistence is false” does not mean the logical negation of nonexistence; it means the abstracting negation of nonexistence. You abstract the concept—the abstracting negation of existence. You abstract existence, and I am left with something that is also a negation of nonexistence, but it is not the concept of existence as I usually know it. Okay? It is some more abstract concept.

[Speaker F] He thinks about the concept of existence as if existence is a property. What? Existence is a property according to… right, right.

[Rabbi Michael Abraham] In several places, by the way, you can see this in Maimonides; here I don’t agree with him. But “and afterward we apprehended that this existent is not like the existence of the elements, for example, which are lifeless bodies,” and we talked about minerals, yes, the inanimate. It’s not like that, it’s not inanimate. “And we said that He is living. And by our saying that He is living, the meaning is that He, may He be blessed, is not dead.” What does “not dead” mean? Again. “Not”—this is not negation in the ordinary sense. “Not dead” means living. What does “not dead” mean? No, this is abstraction, not logical negation. I abstract the concept of life. It is not life in the biological sense, not life in the sense that He has a circulatory system made of carbon molecules or something like that, but it is still something that is not dead. So that is abstraction; it is not logical negation. Yes. “And afterward we apprehended that this existent is also not like the existence of the heavens, which are a living body. And we said that He is not a body, and we said that He is not a body. And afterward we apprehended that this existent is not like the existence of the intellect, which is not a body and not dead, but is caused.” The intellect is already very close—not the brain, of course. Intellect—intellect is a mental function, yes? The brain is an organ. So the intellect is already something that comes very close to the reality of the Holy One, blessed be He. It too is abstract, has no mass, does not occupy space, as “the soul fills the whole body,” the Talmud in Berakhot, “so the Holy One, blessed be He, fills the whole world,” yes. So it does not take up space. But there is still a difference, because the intellect is caused and the Holy One, blessed be He, is not. “Caused” means produced by something—meaning it is not, what’s called, self-caused. “And we said that He, may He be exalted, is eternal, meaning that there is no cause of His existence.” “Eternal” here again does not mean that He exists for an infinite amount of time, but that there is no prior cause that brought Him into existence. He is self-caused, as it is called. And afterward we apprehended—I think, I’m not exactly sure, one could quibble a bit here about what he means—the question is whether he is speaking of causal priority or temporal priority. It could be that he means to say that I abstract the concepts of temporal priority and translate them into causal concepts. A cause can precede the effect in a sense—not in the temporal sense, in the causal sense. For example, if we say that the world is eternal, okay? But it still draws its power, or acts by the power, of the Holy One, blessed be He. But say it is eternal—there is still room to say that the Holy One, blessed be He, precedes the world. He precedes it not in the temporal sense, because the world is eternal. He precedes it in the causal sense. It’s not that He was before; that’s not—it’s not—we are usually accustomed to the idea that one component of the relation between cause and effect is temporal priority. And here we abstract that element, and still I can say of Him that He is prior, once I make that abstraction.

[Speaker I] From Maimonides’ perspective it seems that what didn’t really trouble him about the eternity of the world was the eternity itself; only the issue of miracles troubled him.

[Rabbi Michael Abraham] Yes, when he deals with Aristotle’s eternity. Here, for me, eternity is only an example.

[Speaker I] Yes, maybe that also somewhat supports what you’re saying—that the eternity itself doesn’t really trouble him…

[Rabbi Michael Abraham] In itself, and still he can see the Holy One, blessed be He, as the cause of the world even though the world is eternal. Yes. “And afterward we apprehended that this existent—its existence, which is itself, is not sufficient for it merely to exist alone, but many existences flow from it.” Meaning, realities derive from it; additional realities flow out of it. And in that sense His existence differs from the existence of other things.

[Speaker K] Is all this a summary of the previous chapters?

[Rabbi Michael Abraham] No, no, no.

[Speaker K] What does “and afterward we apprehended” mean?

[Rabbi Michael Abraham] We’re now attaining, understanding. He’s not drawing a conclusion, right. He’s trying to show how one attains the Holy One, blessed be He, by way of negation. So he says, he’s going step by step. We keep stripping things away; notice that the process is a process of abstraction. We say that He is living; “living” is still that kind of concept. After that, “existent” is a more abstract concept. “Primordial” is already something more like intellect, so to speak—existent like intellect, not really existent like ordinary bodies. We are going through a process of abstraction, and he is basically demonstrating for us here in practice how one carries out the process of abstraction of negative attributes. That’s why I keep coming back and saying that it seems to me very clearly that when Maimonides speaks about negative attributes, he is speaking about abstraction and not about negation in the sense of a logical operation. “And it is not like the pouring forth of heat from fire, nor like the emanation of light from the sun; rather, the overflow continuously extends to them permanence, existence, and ordered governance.” As we will explain. What he means is that the outflow of light from fire—or heat from fire and light from the sun—that is an automatic outflow. It’s simply a mechanical process. There is no sun that does not emit light; it’s not in its hands, it doesn’t think, decide, and produce light. It’s simply a product of its very existence. In contrast, reality as influenced by the Holy One, blessed be He—how it is created from the Holy One, blessed be He—that relation is not an automatic relation, but rather a relation in the sense that “He continuously extends to them permanence, existence, and ordered governance.” There is here a process of planning and producing, like that between an artisan and something he creates, not like that between the sun and light or between fire and heat. Although there is a relation of cause and effect here, it is cause and effect in some non-mechanical, non-deterministic sense. Actually, maybe I don’t know if it’s not deterministic, but one that has a dimension of planning influence, of some kind of conscious control, I would even say. That relates to what he said above, that He is living, apprehending, and living, right? That’s what he says—he says it later, I don’t remember. “And because of these matters we have said of Him that He is able, wise, and willing.” What, again? We’ve gone back to positive attributes. Now Maimonides explains, according to his approach, what these attributes mean. On the face of it they seem positive, but now he translates them. “And the intention in these attributes is that He is not weary”—yes, from the language of weariness—“nor ignorant, nor confused or neglectful. And the meaning of our saying ‘not weary’ is that His existence contains sufficient power to bring other things into existence besides Himself.” Right? He can do what He wills; He does not have exhaustion of power in that sense. Right? “And the meaning of our saying ‘not ignorant’ is that He apprehends”—that is, is living—“for everything that apprehends is living.” Now here again, this is not life in the carbon-based sense, but life in the sense that He is not just inanimate and passive. The inanimate is passive; it apprehends nothing, it’s simply there. The Holy One, blessed be He, is not inanimate. In that sense one can say that He is living, or that He indeed apprehends, meaning He is living—but not living in the biological sense. “And the meaning of our saying ‘not confused and not neglectful’ is that all these beings proceed according to order and governance; they are not abandoned and do not come about by chance, but rather because everything that governs them is by one who wills, with intention and desire.” Right? In contrast to light and fire. “And afterward we apprehended that this existent has no other like it, and we said that He is one.” Again, here too you see where this comes from. I argued that saying He is one is not an attribute. In the introduction where I spoke about what attributes are in the philosophical sense, regardless of the Holy One, blessed be He, I said that to say something exists is not an attribute; to say that something is not someone else is not an attribute; and to say that it is one and not two is also not an attribute. That is a statement about the essence and not about the form. So on these matters Maimonides, in my view, did not quite hit the mark. “It has thus become clear to you that every attribute by which we describe Him is either an attribute of action, or its meaning is the negation of its absence, if the intention in it is the apprehension of His essence and not His action. And you should not make these negations either, nor permit them regarding Him, may He be exalted, except in the ways you already know.” That is to say, positive attributes cannot apply to Him except with respect to His actions. You can speak about His existence. But if you want to speak about the Holy One, blessed be He, to describe Him only with negative attributes—and even there he says, “except in the ways you already know.” What does that mean? What kind of negation are we talking about? This is not negation in the ordinary sense. “For sometimes one negates of a thing that which is not of the sort that should be found in it, as when it is said of a wall, ‘it does not see.’” All right? Here I don’t know whether he means to say this is what one should not do with regard to the Holy One, blessed be He, or whether this is an example of what one should do with regard to the Holy One, blessed be He. Yes, I’m not exactly sure. I think he means to say this is what one should do with regard to the Holy One, blessed be He. When one says that the wall does not see, that’s a somewhat subtle point, because when I say of a person that he does not see, it’s not in the sense that infinity is not a number. When I say that a wall does not see, I am saying that seeing is not a relevant parameter for walls at all. It’s not that this is some defective wall that can’t manage to see. Right? No. Walls are not… maybe in a more extreme way it’s like the sentence “a good trait is triangular” or “red.” Right? It’s not relevant. A good trait is not described in terms of triangular, red, or tall. All right? Therefore it is neither a false sentence nor a true sentence; it is simply irrelevant. So there are certain negations that say that these attributes are not relevant to Him, not that they are not true of Him. But if he really means that, then it is not completely precise, or at least the way I understand it—I don’t mean that kind of thing anyway. If he means this as a positive example and not a negative one, I’m not entirely sure here. Because when we negate with regard to the Holy One, blessed be He, true, it is an abstracting negation, but it is an abstracting negation that still leaves some sort of positive dimension in it—like infinity is not a number—not like a bird is not a number. If I make the negations like “a bird is not a number,” then I could also say of the bird that it is also not a wall. So what—what is better about saying it is not a number rather than saying it is not a wall? What difference does it make? Or “not merciful” like “not cruel,” right, what we talked about earlier. Therefore it is clear that what is meant here is an abstracting negation that has some subtler shade to it than mere negation of relevance. That is, to say that this is not relevant with regard to the Holy One, blessed be He—that is too strong. If we say that all these things are simply irrelevant to Him, then we really haven’t said anything. If we say that this means something, then we have to speak about abstracting negation, but not about negation of relevance. And therefore, the fact that a wall does not see—I don’t know if that is such a good example. Why?

[Speaker B] In his reading, he says exactly what you’re saying.

[Rabbi Michael Abraham] As opposed to that a wall does not see? I don’t know.

[Speaker B] He says, sometimes—

[Rabbi Michael Abraham] Maybe, I don’t know, it’s not clear to me, could be. In any case, where were we? “And you, the person who studies this discourse of mine, know that this sphere is a body in motion. We already know its dimensions and its cubits, and we know the measure of its parts and most of their motions, yet our intellect grows utterly weary of apprehending its essence.” All right? By the way, this is an interesting point. Here it seems to me this is really Mary’s room. What does it mean, “our intellect grows utterly weary of apprehending its essence”? We know the theory of the sphere—the strange theory of Maimonides, never mind, but that is his theory of the sphere. I can say that it is substance and that it has form and that it moves, but that’s all; that’s the equation of the sphere. But what is the material of the sphere? Can I have some immediate experience of it, like the color red? That is what he means when he says that I have no knowledge of its essence, no apprehension of its essence, even though we know necessarily that it has matter and form, except that it is not this matter that is in us. Therefore we carry out here some kind of abstraction, right? “And because of this we cannot describe it except by non-affirming names, not by an affirming positive description.” It seems to me that is what he means here. When I describe the color red, I can describe this or that property, but not its essence. What is the color red? What is the color red? I have no way to convey it to someone else, to define it for someone else. “When we say that the heavens are neither light nor heavy, nor affected”—“affected” meaning influenced, because they receive influence—“and therefore do not receive action, and are not possessed of taste nor possessed of smell,” and the like of these negations—how does he know all this? I don’t know—“all this is due to our ignorance of that matter. And what, then, will be the state of our thoughts when they strive to apprehend that which is free of matter, absolutely simple in the utmost simplicity, necessarily existent, having no cause?” He is now summarizing a bit the abstract concept to which we arrived after the long process of abstraction he described here. “And no notion additional to His essence apprehends Him”—right, He has only essence, no form, no properties, and no notion additional to Himself—“the perfect one, whose perfection consists in the negation of deficiencies from Him, as we explained, so that we apprehend nothing other than His existence alone.” Only His existence we apprehend, and that, by the way, in the positive sense, not the negative one: “that there is an existent unlike any of the existents He brought into existence, and sharing no aspect with them in any way whatsoever, and in whom there is no multiplicity and no weariness in bringing into existence what is other than Himself.” This is really a concise summary of everything that came out for us after all the abstractions. So the summary is by way of negation, but suddenly we see that in the end we did learn something about Him. That is what he wants to teach here, after all. That after we negated all the possibilities, negated all the definitions proposed along the way, look how many things still remained in our hands; we nevertheless learned something. “That He, may He be exalted, governs all beings”—and again, just to guide the intellect, right? Not a real likeness, but to guide the intellect—“that He, may He be exalted, governs all beings,” meaning that He sustains them and preserves their order as it should be. “And this matter has now been explained more broadly than this. Blessed is He such that, when minds direct themselves toward His essence, their apprehension turns into incapacity of apprehension and knowledge; and when they consider the necessity of His actions from His will, their knowledge turns into ignorance.” As if, if you think you know something positive about Him, that is only ignorance. “And when tongues strive to magnify Him by attributes, all excessive speech turns into weariness and deficiency.” The more positive things you add, the more mistaken you become. And therefore the way to apprehend Him is only by way of the abstraction that he has described until now. Okay, let’s stop there for the time being.