Negative Degrees, Lecture 2

Table of Contents

• The pre-Maimonidean framework according to Sefer Ha-Ikkarim: essence and actions
• Idea, ideal object, and essential versus accidental properties: the paradox of the “third man”
• Definition by extension versus definition by content, and the confusion among three levels
• Halakhic applications: love of the convert, hatred, and a bound slave as a model of an ideal object
• Essence versus properties and description: why it is impossible to describe the Holy One, blessed be He
• Attributes of action, “Just as He is compassionate, so you too be compassionate,” and Rabbi Chaim Vital’s question
• The basic problems in the theory of negative attributes: symmetry, double negation, and the sage versus the fool
• Annihilating negation and opposing negation, and three-valued logic
• The theory of negative attributes as an analytic learning process: giving a bill of divorce, the ladder that gets thrown away, and the understanding that remains
• Kant, properties as experiences, and abstraction toward physical phenomena
• Dynamics versus statics, and the two pictures of quantum theory as an illustration of abstraction through negation
• Art, poetry, Zen and the Art of Motorcycle Maintenance, and the negation of definitions that is not despair
• Sefer Ha-Ikkarim chapter 30: the difference between negations and the sage’s advantage

Summary

General Overview

The text presents a framework for understanding divine attributes through a distinction between statements about the essence of the Holy One, blessed be He, and descriptions in the sense of properties, and it tries to justify the move from the pre-Maimonidean layer of avoiding attributes to the Maimonidean layer of negative attributes. Throughout, it builds the claim that philosophical and analytic failures stem from mistakenly identifying an entity with the collection of its properties, and on that basis it proposes reading the theory of negative attributes as an “analytic” process of negating definitions that yields abstract understanding rather than despair. At the end, it brings a passage from Sefer Ha-Ikkarim that formulates a distinction between types of negation, from which the advantage of the sage over the fool is derived in knowledge of the different modes of negation and the levels of apprehension.

The pre-Maimonidean framework according to Sefer Ha-Ikkarim: essence and actions

The philosophers who preceded Maimonides hold that it is impossible to describe anything with respect to the Holy One, blessed be He, and that only two kinds of statements may be made: statements about His essence and statements about His actions. Sefer Ha-Ikkarim presents the statement that He exists and that He is one as belonging to His essence, while statements like “He created the world” are about His actions and are not descriptions of Him. The text emphasizes that statements about His essence are not “descriptions” in the sense of attributing characteristics, and places this within the distinction between referring by way of a name and referring by way of a description, where a description relates to characteristics and a name points to the bearer of those characteristics.

Idea, ideal object, and essential versus accidental properties: the paradox of the “third man”

The text brings the “third man” argument in Plato’s dialogue Parmenides against Plato: if the idea of humanity is included in the group of all things that instantiate the properties of humanity, an infinite loop of ideas is created. It argues that the failure comes from a category mistake in inserting the idea into the set of human beings, because the idea is the properties themselves and not another “human” endowed with them. A distinction is proposed between “the idea” and “the ideal object,” where the ideal object is an entity that possesses only the essential properties and not accidental ones, while the idea is the form detached from the bearer of the form.

The text links these confusions to Leibniz’s principle of the identity of indiscernibles, and argues that missing the difference between the bearer of the properties and the collection of the properties gives rise to paradoxes. In shifting the paradox from the idea to the ideal object, it argues that the loop stops, because the idea remains the same collection of properties and the recurring ideal object is the same object. It also argues that modern mathematical definitions suffer from a similar failure—for example, in Frege, who defines “three” as the collection of all sets that have three elements. The text argues that number is an abstract or ideal object and not a collection of sets, even if the mathematical definition is needed for consistency.

Definition by extension versus definition by content, and the confusion among three levels

The text draws a distinction between definition “by extension” and definition by means of characteristics, and argues that a definition by extension does not define the concept itself but serves as raw material or a “link” to the abstract concept. It claims that the use of extensions mixes together three distinct things: the idea, the ideal object, and the collection of concrete objects that partake of the idea. The text argues that such distinctions resolve philosophical paradoxes and also clarify points in halakhic definitions.

Halakhic applications: love of the convert, hatred, and a bound slave as a model of an ideal object

The text cites Rabbi Yitzchak Hutner’s interpretation of the commandment to love the convert, according to which this is not love of converts in general but love of a person because of his conversion. Therefore, one who loves a convert without knowing that he is a convert does not fulfill the commandment. It argues that this avoids a full overlap between love of a fellow Jew and love of the convert, and makes room for a distinction between love directed toward a particular person and love directed toward an abstract idea, where “love of the idea” is presented as missing the point. The text proposes describing this as a requirement to love “the ideal convert,” meaning that component in the person that is defined by conversion, in a way that also allows one to hate that same person because of another component in him, without logical contradiction.

Another example is presented from the Talmudic topic that “a moving courtyard does not acquire,” and from the Talmud’s case of a slave who is bound and asleep. The text argues that the halakhic statement is not dealing with a concrete slave who happens to be bound, but with an “ideal slave” from whom the property of mobility has been neutralized. It is only because concrete slaves are not like that that tying him up is needed to illustrate the law. From here it argues that halakhic language is sometimes directed toward ideal objects that abstract away irrelevant properties.

Essence versus properties and description: why it is impossible to describe the Holy One, blessed be He

The text returns to the Holy One, blessed be He, and formulates that statements like “existent,” “one,” and “not two” are statements about His essence and not descriptions of characteristics, and therefore they are possible even without sensory interaction. It argues that descriptions in the ordinary sense require sensory interaction and perception within ordinary categories, and since direct interaction with the Holy One, blessed be He, is impossible, and He is not something “visible” within those categories, positive descriptions like “red” or “kind-hearted” are not merely unknowable but logically irrelevant. The text distinguishes between the epistemic difficulty of “how do you know” and the nonsense of attributing a property that simply does not belong to the concept of divinity, similar to saying “virtue is triangular.”

Attributes of action, “Just as He is compassionate, so you too be compassionate,” and Rabbi Chaim Vital’s question

The text presents the interpretation of attributes of action as a way to understand “compassionate and gracious” as a mode of action and not as a psychological trait, and sets this against Rabbi Chaim Vital’s question that the Torah seemingly does not command the cultivation of character traits. It argues that the Torah commands “to walk in His ways” and “Just as He is compassionate, so you too be compassionate” on the plane of action, but from that it does not follow that there is an obligation to be compassionate in one’s inner psychological nature, because the Holy One, blessed be He, has no psyche in the human sense and no psychological “traits.” From here it argues that someone who acts compassionately, even if his nature is cruel, fulfills the commandment in the formal sense of the obligation to act.

The basic problems in the theory of negative attributes: symmetry, double negation, and the sage versus the fool

The text describes how Maimonides seeks to say that the verses “The Lord, the Lord, God, compassionate and gracious…” refer to the Holy One, blessed be He, Himself and not only to His actions, and therefore he adopts the language of negative attributes. But a simple formulation of “He is compassionate” as “it is not true that He is not compassionate” seems to add nothing. Three problems are presented: the lack of an explanation for breaking the symmetry between “compassionate” and “cruel” if both concepts are equally inapplicable to Him; the absence of any real difference between a negative attribute and a positive one if double negation returns us to the original content; and the difficulty of explaining how the sage has an advantage over the fool in knowledge of divinity if supposedly there is no conceptual content that can be grasped.

Annihilating negation and opposing negation, and three-valued logic

The text proposes distinguishing between the annihilating negation of “zero” and the opposing negation of “minus one,” using the example of light and darkness as against heat and cold. It argues that in multi-valued logic, double negation does not necessarily return to the same place, but even so this does not solve the problem of breaking the symmetry between compassion and cruelty with respect to the Holy One, blessed be He. The distinction is presented as a partial tool that clarifies how “it is not true that He is not compassionate” may differ from “compassionate” in simple logic, but by itself does not provide a basis for why the Torah specifically chose attributes of compassion.

The theory of negative attributes as an analytic learning process: giving a bill of divorce, the ladder that gets thrown away, and the understanding that remains

The text proposes a different meaning for negative attributes based on a model of an analytic learning process, using the example of the Ketzot’s attempt to define “giving a bill of divorce” either as a transfer of ownership or as physical giving, and the negation of each definition through cases such as a bill of divorce involving prohibited benefit or giving by way of a courtyard. It argues that the process does not produce a short, satisfactory definition, and sometimes the definition swells until it looks like little more than a collection of cases. But despite that, an intuitive understanding of the concept is formed through the negation of the rejected definitions. The text argues that this is exactly the meaning of “negation” in Maimonides: the definitions are a ladder you climb and then throw away, and the negation is not an emptying-out but an abstraction that leaves behind an apprehension that cannot be formulated in a simple positive way.

The text states that if one had climbed the “ladder of cruelty,” one would not have arrived at the same destination, and therefore the process of negation has directionality and not every negation is equivalent to every other one. It argues that the negation here is not logical oppositional negation but abstracting negation that enables a transition from the properties to the bearer of the properties, somewhat like the claim that love encounters a person through his properties but does not identify with them.

Kant, properties as experiences, and abstraction toward physical phenomena

The text rejects a reading of Kant as a claim about “limitations” that prevent access to the thing as it is in itself, and argues that color and sound are not properties “out there” but cognitive products of interaction, whereas outside there is wavelength or an acoustic wave. It argues that to “grasp” always means to grasp in terms of the cognitive system, and this is not an incapacity as opposed to the very way cognition works. At the same time, it argues that there is value in abstracting from experience toward a more objective description, like describing sound as air movement and pressure waves, even if every such description still depends on the way we think.

Dynamics versus statics, and the two pictures of quantum theory as an illustration of abstraction through negation

The text uses the distinction between dynamics and statics to show how we arrive at a concept we have no direct ability to imagine: at first, dynamics is grasped as a sequence of static states, and after abstraction one understands “pure dynamics” that contains nothing of statics. It argues that in a certain sense, “in a world where a body has velocity, it has no position at all,” even though the concept is built through positions, and this is also illustrated through mention of uncertainty principles and two complementary points of view. From here it argues that negative attributes work in that way: the initial framework of perception is negated, but a real apprehension remains that cannot be directly translated into the language of that initial descriptive framework.

Art, poetry, Zen and the Art of Motorcycle Maintenance, and the negation of definitions that is not despair

The text brings Gideon Ofrat’s book, which proposes and rejects definitions of art again and again until it arrives at “art is what is found in a museum,” and argues that the final line is mistaken because it identifies the definition with the thing itself and falls into a Leibniz-like error. It argues that Ofrat himself must be holding an intuitive concept of art in order to choose examples that refute definitions, and therefore the negative process really does refine understanding even without a formal definition. It also brings Pirsig’s book Zen and the Art of Motorcycle Maintenance as a pursuit of a definition of “quality,” and the text interprets the conclusion not as the cancellation of the concept but as the claim that there is such a concept as quality even though it is not fully susceptible to analytic definition, and that the only way to approach it is through negating mistaken definitions.

The text compares this to written poetry that is not set to music, and argues that the words are a medium that conveys a message not reducible to their literal meaning, so that abstraction from the words enables a grasp of the content that prose cannot capture in the same way. From here it argues that the mechanism of abstracting negation is a general tool for grasping concepts that go beyond ordinary systems of definition.

Sefer Ha-Ikkarim chapter 30: the difference between negations and the sage’s advantage

At the end, a passage from Sefer Ha-Ikkarim chapter 30 is quoted, stating that there is a difference between negating one opposite and negating the other opposite, and that in this lies the advantage of the sages in knowing the modes of negation. Sefer Ha-Ikkarim distinguishes between negating attributes that for us are deficiencies—such as “dead, not-eternal, lacking power, ignorant, illiterate, evil”—which are negated of Him by “absolute negation,” such that their opposite, which is perfection, is found in Him; and negating attributes whose meaning for us is perfection—such as “living, able, wise, wealthy, good”—where the intention is not to attribute to Him the opposite, which would be deficiency, but to say that the perfection is not found in Him “in the manner that it is found in us,” but rather “in a more honorable and elevated manner,” between which and our concept of perfection there is no proportion. Sefer Ha-Ikkarim states that it is impossible to describe Him even with negative attributes unless one first understands the positive attributes as they exist among us, along with the aspect of perfection and the aspect of deficiency in them, and only then “turns oneself to negate them of Him” in the proper way. From this follows the variation in levels among the sages, “according to the variation in the apprehension they attain of the attributes of perfection ascribed to Him, in what manner they may be ascribed to Him.”

Last time I basically opened with some kind of introduction to the topic of the divine attributes. Positive attributes and negative attributes, but with the negative attributes we only got there at the end. Today I want to continue. I thought—I mean, I was a bit torn about how to do this. Usually when you start with the reading, with part of the Guide for the Perplexed, then somehow you drown inside the reading and, I mean, in the end you never get to the overall picture. So I decided to try reversing the order: first present the picture and only afterward read. So last time I began with a kind of introduction that Rabbi Yosef Albo, the author of Sefer Ha-Ikkarim, gives—he is later than Maimonides of course—where he says that the philosophers before Maimonides thought that you cannot describe anything at all with regard to the Holy One, blessed be He. You must not say anything at all about the Holy One, blessed be He, except for two things, two kinds of things. One kind is statements about His essence: that He exists, that He is one, all kinds of statements like that. And I spoke a bit about the question of what the difference is between statements about His essence and statements that describe Him, meaning statements about His characteristics, as with any other object. And the second kind of statements is about His actions—what He does. But you cannot give any description of the Holy One, blessed be He, that would be relevant to the Holy One, blessed be He. The Holy One, blessed be He, is awesome, good—those are the problem they deal with—but that is what the philosophers claim, and I’ll get to that in a moment. That is what the philosophers claim: that basically you cannot describe the Holy One, blessed be He, in any way. What you can do is either say things about His essence—I spoke last time about why that is not a description; statements about His essence are not descriptions—or say things about His actions, meaning what He does. Which is fine; let’s say He created the world—that is not a statement about Him.

And as I continue, let me just remind us of the framework here. I made a distinction there between two ways of pointing to something, of referring to something, in Bertrand Russell’s article—I think I may have mentioned it earlier, I think—between pointing to a thing through a name and pointing to it through a description. I can describe a thing, and I can call it by a name. And the difference between these two forms of reference is that a description refers to the properties of the thing, whereas a name is the way I refer to the bearer of the properties, to the thing itself.

Here maybe a little amusing anecdote. I just now saw that an ocean of ink has been spilled over some problem in Platonic philosophy, and you look at it and say: what do they even want? Parmenides, in Plato’s dialogue called Parmenides—what? In Plato’s writings? No, wasn’t it before Plato? Parmenides himself was earlier, but the Platonic dialogue called Parmenides deals with the argument between him and Parmenides. And the claim is that Plato thought that the form of things is an existing idea, a kind of being. It’s horseness. It’s not—as Aristotle saw it—some generalization common to all horses. So by looking at all the horses, you can distill some collection of features that it is convenient for us to attach some title to; that is called horseness, okay? Plato claimed that horseness is some thing that exists, a kind of being. It exists in the world of ideas in some different sense. And then Parmenides raises against him the claim called the Third Man. What is that claim? Well, in one formulation, it goes like this. Suppose you look at a collection of human beings and from them you extract the idea of humanity, human-ness. Now, the idea of humanity of course instantiates all the properties instantiated by human beings, the essential properties that human beings have. Therefore, in the group of objects described by those properties, not only the human beings are included, but also the idea of humanity—the idea too is described by that whole set of properties. Okay, but if so, the definition of the set is itself part of the set. The definition of the set is part of the set. This is that paradox, right? In many ways parallel to more modern paradoxes. And the claim is that now there is a new list of objects, and to the new list there should correspond another idea, because it’s a different list. Every list is supposed to correspond to some idea. Now that idea too, of course, instantiates all those properties, so it too… in short, there are infinitely many human beings or infinitely many ideas corresponding to the same set of properties.

And that is because the idea of the human being instantiates the properties of a human being? That seems wrong to me. And that is its definition. Why? What do you mean? The idea of the human being is the idea of a creature, say, that has two legs and two arms. It’s not that the idea itself has two legs and two arms. The idea is something abstract. No, it’s not that materially it has two arms and two legs; it has the idea of being possessed of two arms and two legs. Different things. Okay, that is one possible answer to this issue, and it seems to me maybe in a more… I would formulate it more simply. There is a difference between looking at the idea and looking at an ideal object. The idea of humanity, or of human-ness, is not the same thing as speaking about the pure human being. Right? Say, a human being who has only the property of human-ness and no other property, or the collection of properties we call human-ness and no other property. Every human being has more properties: he is this height, this weight, kindhearted, cruel. Everyone has specific properties of his own that are not part of the set of properties that defines what a human being is, such that without one of them he would no longer be human. Those are accidental properties—we spoke about essential and accidental properties.

Now the definition of a human being is the collection of the essential properties, the properties without which he is no longer a human being. Into the idea enter only those properties, not the accidental properties. But there is another Platonic object, and that is the ideal object, not the idea. The ideal object means a kind of… a human being who has only the essential properties, no accidental properties. He doesn’t have the properties that are not necessary in order to count as a human being. Now I don’t know whether there is such a person in our world; probably there isn’t. There is no human being in our world who doesn’t have all kinds of additional properties that are not… everyone has some kind of weight, right? The weight is not… No, not the weight. The mere fact of being possessed of weight. No, that’s what I’m saying. A human being has to be possessed of weight, not the property of being possessed of weight. Yes, that’s what is somewhat connected, I think, to what you said earlier. And therefore one must distinguish here—and I think they don’t distinguish there—between the idea and the ideal object.

What’s the difference between them? The idea is the form of the human being, detached from the substance that bears the form, bears the properties. We spoke about Leibniz’s principle of the identity of indiscernibles, where he too basically missed this point. And the ideal human being is: there first of all is a human being before the properties. There is an owner of these properties. There is someone endowed with these properties, and he is a human being in every respect. I mean, “in every respect” is perhaps a bit of a phrase, but there is such an object, and this is an entity, a kind of entity. And it has the properties of being human; humanity characterizes it. Humanity by itself, detached, is a form. Fine? But the ideal human being is not a form; the ideal human being is an object whose form contains only the essential components, without components that are not necessary for defining the human being. Fine?

Now one could formulate this Third Man paradox only about that and not about the idea. Because to put the idea into the set is a category mistake. That is, the idea is not another kind of human being. More than that—as Arik said earlier—I also really don’t think that the idea is endowed with the properties with which a human being is endowed. The idea is those properties themselves. It isn’t endowed with those properties; it is the properties. So is the idea of greatness itself great? That is what Parmenides asks there.

But if the ideal human being doesn’t really exist, then it isn’t there. What? He isn’t a tangible human being. No, I can say he exists. And that is the most significant thing that every human being is—he exists. In the same sense as a Platonic idea, I can also say that he has Platonic existence. In another world, the ideal world. There is the world of ideas and the ideal world, okay? So he exists there. Never mind. If I am willing to accept the existence of ideas, why shouldn’t I accept the existence of ideal human beings? They are probably not human beings of the kind we know. Right? But it seems to me this definition sounds self-contradictory by definition. If the moment I say that there is here something that instantiates the property of being possessed of weight—and not just… not the property itself, but it instantiates the property—then it has to have some particular weight. No, no. I don’t think so. I mean, okay, that’s an interesting question; it needs more thought. I don’t think so. You are right in our world; I don’t think you are right logically. That’s not a logical difficulty; it’s a physical difficulty. And if you are speaking about some other Platonic world, then I think one can live without that too. But okay, that’s entering into Platonic philosophy.

Now what I want to say is that once you convert this into the ideal human being, not the idea itself, then the loop stops, of course. Because what am I saying? Who enters the set of human beings? Who gets added? After all, you created the idea; the idea is not a human being in the set. You can say the ideal human being is perhaps a kind of human being; he is an object endowed with those essential properties. Okay, so he enters the set of human beings. So now we have the set of human beings plus the ideal human being. Now I ask: what is the idea corresponding to this set? It is the very same idea. It is simply the same collection of properties. Now produce the ideal human being corresponding to that idea—it will again be the same ideal human being, and therefore he is already in the set; it does not expand further. That is, it stays the same. But once one understands the difference—and I’m bringing this up here simply because we were dealing with it now in Talmudic logic; we’ve just been dealing a bit with Platonic issues—once one understands the difference between an idea and the ideal human being, the paradox solves itself. That is, one can’t even formulate it. It’s not at all clear what they wanted. And you wouldn’t believe how much ink has been spilled over this paradox. I mean, there are tens, hundreds of articles published to this day by logicians and philosophers, and various Plato scholars make a living off it. I don’t know, it sounds a bit problematic to me.

What? Where is the parallel in the Talmud? Ah, there are all sorts of Platonic implications, Platonic ways of looking, in the Talmud. For example, when I say that one must love the convert, once we spoke about Rabbi Yitzchak Hutner, “the conversion within him.” That’s it. So once we spoke about Rabbi Yitzchak Hutner, who brings there that a certain sage asked him: why do we need the commandment to love the convert? There is the commandment to love the Jewish people. After all, you are supposed to love all of the Jewish people, and the convert is a Jew. And Maimonides in the Shorashim says that if there is a commandment that adds no new content, it is not counted separately, and yet Maimonides does count this one. So Rabbi Yitzchak Hutner said that there is the commandment of loving the convert or loving a Jew. Suppose you have a neighbor who is a convert and you don’t know he is a convert—we spoke about this—and he is a nice person and you love him, then you have not fulfilled the commandment to love the convert, even though you loved a person who is a convert. But you did not fulfill the commandment to love the convert. Why? Because the commandment to love the convert is not to love converts; it is to love him because of the conversion. And if you don’t know he is a convert, then you didn’t love him because of the conversion; you loved someone who is a convert. But that is not the commandment of loving the convert.

Now once it is defined that way, then of course there is no overlap between the commandments; they are completely different commandments. Therefore, for example, on the other hand, when you love him because he is a convert, you have not fulfilled the commandment of loving the Jewish people; you fulfilled the commandment of loving the convert. Even though he is a convert… and also, does that count as fulfilling the obligation? Or despite his being a convert. “Despite his being a convert” is just an addition to the commandment to love the Jewish people. No, his being a convert doesn’t mean he isn’t included in the commandment to love the Jewish people. Despite his being a convert, the commandment to love the Jewish people also applies to him. But if that were all, then this would be just a detail within the commandment to love the Jewish people; it would not be counted separately.

The same thing with the commandment of hate: “Let sins cease, not sinners”—what they say there, that one does not hate the person but the problematic things in him. Now this—what? That doesn’t fit with the second half of the verse, “and the wicked shall be no more.” Ah, fine. “Let sins cease, not sinners” is the homiletic reading, not according to the plain sense of the verse. “And the wicked shall be no more” means that they are no longer wicked, according to that interpretation. In general, one can say that someone who has repented is as though newly born, and therefore “the wicked shall be no more”; no problem, the gates of interpretive creativity have not been locked. In any case, once one defines it this way, people have some tendency to think that what is needed is to love the conversion, not the convert. And it is very easy to arrive at that definition, and then this basically means that this love is not directed to human beings at all; it is directed to ideas. My grandfather once said about the Satmar Rebbe that he loved the Jewish people very much; it was just the individual Jews that he had some problems with.

So when we speak about the commandment of love, we are not speaking about love for an idea. Love is directed at human beings. But on the other hand, the halakhic definition is to love the convert because he is a convert. So what does that mean? It seems to me that as a logical definition—again, this is still a logical construction—instead of saying “to love the idea,” it is more correct to say “to love the ideal convert.” For example, if that convert is wicked. That can happen, right? Then I need to hate him because of his wickedness and love him because of his conversion. The very same person. I have to direct at that same person two contradictory emotions. And there is no principled problem with that. Again, psychologically it may be hard to do, but there is no logical problem here. That is, it is well-defined and there is no contradiction here. You can hate him for that and love him for that. Fine, the commandment to love the Jewish people too—you have to love him because of his Jewishness. Right, obviously. Tosafot. No, that’s why I say: but it is very easy from there to get to a situation where you don’t actually love human beings who are Jewish, but rather Jewishness in general. Many misanthropes are lovers of Israel. They used to say about the socialists—not today, God forbid—that they loved humanity and did not love people. Exactly, it’s the same principle.

Now obviously, to define the commandment of love as something not directed at a person—there is some kind of missing the point here. Love for an idea is nonsense. What is love for an idea? There is no such thing. Maybe there is such a thing, but that is not what is meant when people say “love the convert.” So what is meant? After all, the concrete convert has many aspects, some of which may even deserve hatred. So as a logical construction you can say: there is a commandment to love the ideal convert. Now, within every concrete convert of course there is an aspect of the ideal convert, plus other aspects. I love that aspect. But not “aspect” in the sense of that idea, because then the love is directed at the idea and not the person. But the love has to be directed at the person; otherwise it is just… that is not what we mean. So it seems to me that here one can see a kind of Platonic approach saying: I love the ideal convert. You have to love the ideal convert. That is what you are supposed to love. Okay. That does not exempt you from the concrete converts, fine? But it is not identical with the concrete convert. It is perhaps a certain component within him. Fine? Incidentally, that is not just his form; it includes something of his substance as well.

Now what happens in this Parmenidean paradox of the Third Man? It is the same failure as Leibniz’s identity of indiscernibles and many other things. Incidentally, in mathematics too, the way numbers and sets are defined in modern mathematics seems to me to fall into the same failure. The same philosophical failure. Again, for the sake of mathematical consistency there is probably no choice and one has to define them that way. But it is not correct to think that by that you have captured the concept of number. Say Frege defines the number three as the collection of all sets that contain three elements. What kind of nonsense is that? A number is a collection of sets? A number is an abstract creature, and a collection of sets is another kind of… something completely different. That is also circular; completely circular. No, no, it isn’t circular, because it is circular only in the way you phrased it. Maybe I didn’t formulate it carefully enough. Gather the collection of all things that have three elements, where you know what those are. The collection of all those things is the number three. Do you see? Treat it as a constructive definition. That is, I build the definition; I am not placing two propositions here and identifying them. Okay? But it is still not correct. Because the number three is a kind of object, or idea, or ideal object; it is not a collection of sets. It is the form common to all the sets in that collection. Exactly the idea we are talking about. But that is not the number. If I want to say—I can say that is the number three, I can say that it is some kind of ideal set such that all that characterizes it is that it has three elements. Those elements have no smell and no taste and no other property except that they are three. That is, they have no form. They can only be counted as three elements. That set I would be willing to define as the number three. Maybe. That ideal set. But not the collection of sets.

Now mathematically, in order for a definition to be consistent and not lead to contradictions, and also to allow things to be derived from it, there is apparently no choice—I am not expert enough in the area—but apparently there is no choice except to define it this way. But clearly that does not really capture the philosophical concept of number. That is not a number. Okay? And therefore many times when we use extensional definitions—for example, a democratic state is a list of states. A definition by extension. Simply the collection of states that instantiate the property of being democratic states. Fine? That is one way, a certain mode, of defining the concept of democracy. Another way is to give the features of the concept democratic in itself. Fine? Now the extensional definition is a problematic definition; it does not define the concept. It gives us an understanding of what is meant by the concept. It is some kind of link to the concept; it is not a definition. For example—exactly, that is an example. No, it’s all examples. No, it’s more serious than that. Otherwise you would suffer from other problems. If these were only examples, then there might be some inaccuracy here. No, the issue is not inaccuracy; there is no inaccuracy here. It is raw material, basically. Raw material. Yes, exactly. It gives you some kind of link to the abstract concept. In truth this connects very much to something maybe we’ll see later. In all these places we confuse the idea, the ideal object, and the collection of objects that partake of that idea. Okay? And those three things cause no small amount of confusion in Platonic and Neoplatonic philosophies, with various paradoxes and so on.

And in halakhic definitions too you can see that when you make these distinctions, many things fall into place. I spoke a bit about this when we talked about ukimtot, because there too I basically said that when you say that a slave acquires by virtue of the law of courtyard, that if someone places a bill of divorce in the hand of a slave then he can divorce the woman, they say to him: but that is a walking courtyard, and a walking courtyard cannot acquire. So the Talmud establishes there that we are dealing with a bound slave. We are talking about a sleeping slave, and the Talmud adds that he is also bound. Right? So what does that mean? I asked: couldn’t Rava simply tell us that he means a bound and sleeping slave? Why do I need to reach that through some analysis and through questions and answers? Doesn’t Rava know how to tell me that he is speaking of a bound and sleeping slave? Because he is not speaking about a bound and sleeping slave. He is speaking about an ideal slave, a slave from whom the property of mobility has been neutralized. He is not mobile. Neither fixedness nor mobility applies to him. That axis is not relevant; erase that axis. Now there is no such slave; every slave is either stationary or mobile, a concrete slave cannot be like that. So I construct some ideal slave—he acquires. Now with concrete slaves, in order to see this, you need to tie them up. Because otherwise they really will not acquire. It is only because of the limitations involved in the fact that we are dealing with concrete entities, but the halakhic determination deals with a Platonic entity, an ideal entity. Fine? And therefore it seems to me that in many halakhic contexts one can see this form of looking at things.

And how can one love an ideal convert? Exactly the same way. How can you love—no, I’m saying that in every real convert there sits some component, a certain component: the ideal convert, plus all kinds of other components. So that component within him I love, not his property. You don’t know how to define who that is? No, I know how to define him; what is the problem? A person who comes to cleave to the Divine Presence, who loves the Holy One, blessed be He, wants to cleave to the Jewish people and the Divine Presence, and that’s it. Apart from that he has no properties; he is transparent apart from that. That is the only thing I know about him. So this object I can define very well, and that is the one I need to love. Now who is this object? There is no such thing. That is, a real convert… because of the other things, you also love that thing. What? No, only that thing. Because he has all kinds of other things, you try to love that thing. No, no, the opposite. Someone who does it out of the other things has not fulfilled the obligation. No, you—it is formal love, meaning you fulfill the obligation. It is not a matter of loving; we… this is lulav by force of joy, meaning you are not rejoicing, you wave the lulav by force of the law of joy. These are two entirely different things.

Anyway, the claim underlying this whole collection of examples is that the misunderstanding and the failures and the paradoxes created there all arise because people do not understand that behind the object there is something beyond the totality of its properties. There is something else—itself. That is, the bearer of the properties is the object. It of course has properties, but the bearer of the properties is the object. Among the properties, some are necessary properties, without which it would not be called a human being, a convert, or a slave, or whatever. And there are accidental properties. The property of mobility or immobility is completely unimportant to the definition of a slave. That is, it does not really define the concept slave. It is simply that a slave is usually a human being, and a human being is either stationary or mobile, fine—but the form of a slave does not include whether he walks or does not walk; it is irrelevant. Therefore we try to neutralize irrelevant properties when we speak in this language, because we want to reach the ideal object. But the ideal object is… of course this is a construction; I do not need to commit myself to the thesis that it really exists, the Platonic thesis, right? It is only a logical construction. That is, I am trying to define here a kind of human being so that the love will be directed at a human being and not at a property. Fine? That is the…

Okay. So if I return to the Holy One, blessed be He—or before that—once I distinguish between the thing itself and its properties, then I can now define two kinds of statements as a result. When I say something about the thing, that is usually a statement about its properties, its form, except for statements of the type “A exists,” which is a statement about its essence, because otherwise we enter into… not a problem, but that’s the failure in the ontological proof—I mentioned it, the proof for the existence of God. And the claim that A is one, that this is not two objects but one object—that too is a claim about its essence. And the claim that A is not B—that too is a claim about its essence. Not B not in the sense that it is unlike B, but that it is not B, that it is another entity; not that it is an entity different in its characteristics, but that it is other. Fine? All these are statements about its essence.

All these things can also be said about the Holy One, blessed be He, according to Maimonides. That is, because these are not descriptions of Him; these are not attributes; this does not belong to the doctrine of attributes. These are statements about His essence. About His essence I can speak. And why can I speak of that? Because statements about essence do not require sensory contact. When I want to describe this lectern, I say it is brown, it is made of wood, it is tall, it is short, it has two legs, and so on. All that requires some interaction—to smell it, to see it, to hear it. Without that I cannot say what the properties of the thing are. Okay? Now with the Holy One, blessed be He, there is no way to create direct interaction, certainly not sensory. And therefore, the descriptions in the ordinary sense we cannot give concerning Him, because descriptions are the result of interaction.

And therefore—again, not because we haven’t done it. I have never seen the prime minister of Australia either, but in principle he is accessible to me. That is, when I see him I will see something like any other person: a person with two legs, two arms, kindhearted or not kindhearted—in all the ordinary categories I know and know how to grasp and understand. When I… even if I were to see the Holy One, blessed be He, it’s not only that I can’t see Him; He is not an object of sight. It’s not that He is in Australia. Rather, He does not enter into the ordinary categories that can be seen. “And under His feet was the likeness of a pavement of sapphire stone”—right? Fine, these are all the wonderful midrashim of Maimonides in the Guide. So the Holy One, blessed be He, cannot be described because of the inability to produce interaction. But the inability to produce interaction prevents only descriptions. To say that He exists—for that I do not need interaction, at least not in the sensory sense. I do not need interaction. You can ask me: then how do you know if not through the sensory faculty? Fine, good question, never mind. But it does not require direct sensory interaction in order to claim that He exists. At most you can ask me: fine, if you did not see, then how do you know? Fine, good question, I am not dismissing that question, but it is not the same as when I claim that He is red. There they won’t ask me how I know He is red—He is not red. That is, He is not describable in that way. To say that He exists has no logical problem at all. At most one can ask me how I know that. Fine, that is already another question: how one reaches that, and we dealt with that in one of the earlier classes when we discussed all the proofs.

Why is it a logical problem to say He is red? Because He is not red. No—what logical problem? Redness is not something that describes Him. It’s like saying “virtue is triangular.” What is that? Is that sentence true or false? Neither true nor false—it’s nonsense. A false sentence also says something; it says something false. But this is nonsense. Such a sentence says something—it says, astonishingly, that virtue is something with a shape. No, and therefore it’s false. But that is the definition of virtue; it’s a problem in the definition. Exactly. Virtue—but virtue is not like that. Exactly. The definition of virtue is that it is not like that; otherwise I don’t understand what virtue is. Hidden assumptions, yes.

In any case, the problem with saying He exists and the problem with saying He is red or kindhearted are two different kinds of problems. To say He is red or kindhearted is not because I can’t know that since I have no interaction with Him; rather, there cannot be interaction with Him because He is not red. Not that He is not red because I have no interaction; I have no interaction because He is not red. Fine? It’s the reverse. In contrast, with saying that He exists, there is no principled problem; He exists. It may be that I can never know that, because I have no way of verifying whether He exists or not. The concept of the Holy One, blessed be He, does not contradict the statement, the ability to say about Him, that He exists. So that is perfectly fine; there is no logical problem with that at all.

Regarding the statement—these assumptions that you put aside, maybe justifiably—that He has no redness, and therefore there is a logical contradiction here, is that too something agreed upon? You ask how I know? Doesn’t matter, tradition. He told me at Sinai that it’s so. That really is a question, but I am talking about the concept of divinity that stands before Maimonides when he writes these chapters, or before the medieval and later authorities who talk about this. Since He has no body, that is why He is not red. So statements about the Holy One, blessed be He, cannot be descriptions. But that does not mean one cannot say anything about Him. Statements about His essence are possible to say. To say that He exists, to say that He is one, to say that He is not this lectern, He is not someone else—all these statements there is no problem saying, because they are not descriptive statements; they are statements that speak about the essence and not the form, not the characteristics.

The statements of the second kind are much simpler of course. These are attributes of action. That is, what He did or how He acts, not statements about Him. And here comes the question of “Just as He is compassionate, so you be compassionate,” which the Sages say—“compassionate and gracious, slow to anger and abundant in kindness,” and so on—that the Sages say: “Just as He is compassionate, so you be compassionate.” So according to this approach, this should really be interpreted as some statement that He acts in a compassionate way. As opposed to—we spoke about this, right?—Rabbi Chaim Vital? Rabbi Chaim Vital’s question why the Torah does not command character refinement. I said there that I never understood that question, because it does. “And to cleave to Him,” “to walk in His ways,” “just as He is compassionate, so you be compassionate”—of course it does command it. Only what? It commands walking in His ways: as He acts, so you should act. But what he asks is: what is the source obligating me to correct my character traits in the inner psychological sense, not in the sense of how I act? That the Torah indeed does not command, because that also cannot be derived from “cleaving to His attributes,” because in cleaving to His attributes—He has no attributes in the sense of what He is. He has attributes in the sense of how He acts. So if I want to cleave to that, then I too should act that way. But how do I know that I also have to be compassionate? That cannot come from cleaving to His attributes, and that is basically his question.

Someone said—I think Maimonides may actually hold—that “just as He is called compassionate,” it should really mean: let your aim be to be called compassionate. “Just as He is compassionate, so you be called compassionate,” so that that is what people call you. That is the first part of the sentence: “Just as He is compassionate, so you…” No, we understand: it is an attribute of action. What I understand from that is what I am obligated to do. I am obligated to behave in such and such a way. How do you understand it? They tell you to do what He does. If you do not understand what He does, how do you know what you are supposed to do? How do they tell you that? They don’t tell you that. They tell you, “The Lord, the Lord, God, compassionate and gracious, slow to anger and abundant in kindness and truth”—that is said about Him. I don’t understand that, but what they tell you is that you too should be compassionate and gracious, slow to anger and abundant in kindness. And if you don’t understand what compassionate and gracious means, then how can you know what you are supposed to do? So that is what the Sages tell you. What am I supposed to do from this set of words written there? So you understand that set of words; otherwise you also could not know what about yourself. That set of words describes the Holy One, blessed be He—after all, it appears in Scripture. “The Lord, the Lord, God, compassionate and gracious, slow to anger and abundant in kindness and truth”—that describes the Holy One, blessed be He. So if you do not understand what that means, then you also do not know regarding yourself. If you understand what it means, that is what Scripture says about Him. Scripture cries out and says it.

Rather, some commentators say that the intent here is only attributes of action. That is one way of understanding it. He acts compassionately, and you too should act compassionately. It is not a claim about the psychological traits of the Holy One, blessed be He; there is no such thing. Just as He is not red, He also has no soul, so He cannot have a compassionate soul. Am I allowed to be cruel by nature, as long as I act compassionately? Exactly. You have completely fulfilled your obligation. For Rabbi Chaim you would even get a medal. I mean, you are a Brisker, a wonderful Platonic compassionate person.

In any case, this option really leaves us in the pre-Maimonidean phase. In the phase that says: we say nothing at all about the Holy One, blessed be He, only about His essence or about the modes of His action, and that’s all. But Maimonides, as I said in the Three Principles—I read that passage last time—moves one step further, and he wants to claim not that. He wants to claim that “The Lord, the Lord, compassionate and gracious,” in some sense refers to the Holy One, blessed be He, Himself, not only to His mode of action. These are not merely attributes of action. But on the other hand, Maimonides agrees that one cannot describe the Holy One, blessed be He, Himself. Therefore he came up with this matter of—he didn’t invent it, of course it already existed before him a bit; I think these things are already in Aristotle in one form or another—and the claim is that one has to speak in the language of negative attributes. We come to negate various things from the Holy One, blessed be He, and not affirm them.

But put crudely, when I say that He is compassionate, I basically mean to say that it is not correct that He is not compassionate, something like that. But of course in that formulation I have said nothing. And does that add anything? Because “it is not correct that He is not compassionate” is two sides of the same coin. Either ask what it adds, or ask whether it adds the same thing as saying He is compassionate. That is, “it is not correct that He is not compassionate” means compassionate. What is the difference? It’s a double negation. So what? Why should that matter? To say He is compassionate means it is not correct that He is not compassionate, just as when I say about another person that he is compassionate, then it is not correct that he is not compassionate. How is the statement about the Holy One, blessed be He, different from a statement about another person? Alternatively, if you do not mean that, and instead you mean to negate the whole concept of compassion from Him, then what have you said? In the same sense, you could also say He is cruel, because I negate from Him non-cruelty; nothing applies to Him, right? If one cannot say anything about Him at all, then just as I cannot say He is compassionate, I also cannot say He is cruel, and I cannot say that He is not cruel or that He is not compassionate. “It is not true that He is not red,” so He is red? It will be the same thing here. No, exactly.

So I say: we could formulate it like this. Look, there are three difficulties—two, I think, or maybe all three, I said last time—three basic difficulties with this simple formulation that I just gave. The first difficulty is: what is the difference between the statement that the Holy One, blessed be He, is compassionate and the statement that the Holy One, blessed be He, is cruel? Why can’t I say that too, to the same degree? Nothing applies to Him at all. Just as compassion does not apply to Him, cruelty does not apply to Him either, nor non-compassion or non-cruelty. Where does the symmetry break here? After all, the Torah chooses to describe the Holy One, blessed be He, with a certain collection of attributes, so presumably that means something. But if this is meant only to say—just a second—that the Holy One, blessed be He, is excluded from compassion exactly as He is excluded from the property of color, then it is like saying that saying He is red and saying He is black are the same thing: saying that it is not true that He is not red or not true that He is not black. Fine, I could equally well have said He is black; red adds nothing here. So in that sense too I don’t understand why “compassionate” enters the list of descriptions there and “cruel” does not. I could say that just as well. Neither of them says anything, basically. You want to tell me that the Holy One, blessed be He, cannot be described at all in this conceptual system—that is what you want to say. You want to tell me—just a second—that He is neither compassionate nor cruel in the same degree. Where does the symmetry between compassion and cruelty break? What have you really said here? You can say He is not on this scale; no statement can be attributed to Him at all. But then we have returned to the phase before Maimonides, the previous phase, where nothing is said about the Holy One, blessed be He, and He is not described at all. But Maimonides wanted to go one step further, as the author of Sefer Ha-Ikkarim says. He wanted to say something about the Holy One, blessed be He, and then the question is: what are you saying? You have said nothing. And if you did say something, then how is that different from a positive attribute? Then you said He is compassionate. Why are you telling me stories? “It is not correct that He is not compassionate” means He is compassionate. What is the difference?

Now whichever way you go: if you mean to negate Him, like “virtue is triangular,” meaning to say that the concepts of compassion and cruelty do not apply to Him because He does not have a soul like human beings, then you could equally well have said He is cruel just as you said He is compassionate. That is no closer to His nature than that, and no farther. It has no connection to Him at all; He is not in this conceptual system. Is that what you want to say? But if you really want to say negation in the sense not that He is outside the conceptual system but that He is not not-compassionate, then you have said that He is compassionate—or you have said nothing. Whichever way, there is something deeply problematic in the logic of this doctrine of negative attributes.

That is the first difficulty: what is the difference between saying He is compassionate and saying He is cruel? Where does that symmetry break if I do not accept that “compassionate” really says something about Him and only negates? He is negated from it; I negate everything, because nothing applies to Him anyway. So where does the symmetry break? Second: what exactly is the difference between saying “it is not true that He is not compassionate” and saying that He is compassionate? In other words, why is a negative attribute not the same thing as a positive attribute? It is exactly the same thing. Then of course the previous problem is solved, but these are two sides of the same coin, a sort of whichever-way-you-turn attack with two heads. Decide: if it says something, then explain to me what—or how it differs from a positive attribute. If it says nothing, then what have you told me by saying “compassionate” rather than “cruel”?

And the third difficulty—which is really just another way of sharpening these things—is: what is the difference between the fool and the wise man? We saw this, yes. Why is the wise man considered to know the Holy One, blessed be He, more than the fool? Neither knows anything. So in what sense can you be wiser in the knowledge of God than any fool? What comes out of your learning about divinity? Because it supposedly makes sense once I negate something here. If I really negated something, then I learned that the Holy One, blessed be He, is not this. Fine, He is not anything. But the fool doesn’t know even that. What, he doesn’t know that the Holy One, blessed be He, is not anything? No, he doesn’t know. So let’s tell him: He is not anything. Now he knows. If he believes me, then he knows. He’ll believe you—why wouldn’t he believe you? Explain to him: the Holy One, blessed be He, is not anything. It’s easier for a fool to believe. Yes. Fine. In any case, the fool will even buy it, but without any meaning to it. The wise man understands that it has no meaning. Fine.

Anyway, these are basically the three difficulties. And if I begin precisely from the second—what is the difference between “it is not true that He is not compassionate” and saying that He is compassionate—then here it seems one has to distinguish between two kinds of negation. The negation of one can be minus one and it can be zero. Right? I think we spoke about this once. Zero is annihilating negation—annihilating, meaning to nullify something, cancel it—and the negation of minus one is opposing negation, contrary negation. Okay? So as we spoke about this, the relation between light and darkness is like the relation between one and zero, while the relation between cold and heat is like one and minus one. How do I know? Because if you pour hot water and cold water into each other, what comes out is lukewarm, right? But if you add light to darkness, what comes out is light. Not weak light—light. Which means darkness is zero, not minus one. Okay, that’s a parable.

So there are two kinds of negation: annihilating negation and opposing negation. Fine? Now if you really accept that picture, it turns out that we basically have three values in our logic, not two: one, zero, and minus one. Say: compassionate, cruel, and not compassionate. Fine? When you say He is not compassionate, then you have not said that He is cruel. You said either zero or minus one, right? You still have not really said He is cruel. But what happens when you say “it is not true that He is not compassionate”? It is not clear. That is, if you want to create some asymmetry between… if you want to tell me that double negation does not bring you back to the same place, that means you are not in binary logic. It does bring you back, doesn’t it? Why doesn’t it bring you back? No, it doesn’t bring you back to the same place. When you negate zero, where do you get to? To one? No. You get to minus one. Zero is also an annihilating negation of minus one. It nullifies minus one exactly as it nullifies one. There is no difference. Whenever there is many-valued logic, negation is not symmetric. That is problematic, unless you define it artificially, saying that the negation of zero will always be one. Fine, but that is artificial. In principle negation is not symmetric. That is what I am saying. “It is not true that He is not compassionate”: minus one is not compassionate, and zero is not compassionate. No, your “not” either negates or nullifies; it either opposes or nullifies. That is exactly the point. So “it is not true that He is not compassionate” can be said this way: “not true” in the annihilating sense, that He is “not compassionate” in the opposing sense. Fine? Meaning the two negations do not cancel each other, because one is opposing and the other is annihilating. But that will not solve all three problems. It will solve only one of them, or perhaps two of them, but not the third. Because if I say “it is not true that He is not compassionate,” you still cannot explain to me why I cannot do the same thing with cruelty: “it is not true that He is not cruel.” Not annihilating that He is not the opposing form of cruelty. Because insofar as He is not cruel, He is also not compassionate; that is, He is totally excluded from this conceptual system. So I can say that too. So if that is the meaning I give to the statement “He is compassionate,” then I could just as well give the same meaning to the statement that He is cruel. So why can I not say He is cruel while I can say He is compassionate? That is, three-valued logic may perhaps explain to me why double negation does not return me to the same place, but it cannot explain to me where the symmetry between cruel and compassionate breaks. The symmetry remains. This is spontaneous symmetry breaking. There is no reason why it breaks, actually, yes?

Okay. Now it may be that the way to understand the attributes… with this I lived like that until these classes—that this whole business says nothing. This whole thing about negative attributes is just a pile of logical gibberish. But actually after the classes you gave there on poetry and on dynamics and statics and giving a bill of divorce, suddenly an idea occurred to me that maybe one actually can give these things meaning. And it seems to me now that when one reads Maimonides through these lenses, it may very well be that this is what he means; it even seems likely to me that this is indeed what he means.

And the claim is basically this. What did I see, what did we see, when we talked about giving a bill of divorce? In giving a bill of divorce I brought it as an example of a classic Brisker analytical move, where we try to characterize some halakhic concept, giving a bill of divorce. Then we say: let’s propose a first hypothesis. Giving the bill of divorce is an acquisition, meaning a transfer of ownership of the document from the husband to the wife. Right? That is the move the Ketzot makes. Then the Ketzot says: okay, but a bill of divorce written on objects from which deriving benefit is prohibited is valid. A bill of divorce can be written on such prohibited-benefit objects, but according to at least some of the medieval authorities (Rishonim), there is no ownership over prohibited-benefit objects. One cannot transfer ownership of prohibited-benefit objects. So that means that if so, giving the bill of divorce cannot be defined as transfer of ownership.

Second possibility: maybe it is physical delivery. Simply to perform an act of delivery of the bill of divorce. Not to transfer ownership of this piece of paper, but to perform an act of giving. But that too cannot be, because if he placed the bill of divorce in his courtyard and transferred ownership of his courtyard to her, that too is valid delivery. I did not perform an act of physical delivery with the bill of divorce. I transferred ownership of the field in which the bill of divorce is lying. So that is not the definition either. Then he goes and complicates the definitions even more, and I said that in the end he reaches some definition where the number of parameters in it is more or less equal to the number of cases. That is, every case that doesn’t fit the previous definition adds another qualification to the definition. Then the definition becomes as complex as the number of cases. In other words, we gained nothing. So why did we do the whole process?

And the truth is that many times it seems to me that someone who works delicately with Brisker conceptual analysis has to do it this way. That is, in the end you propose one possibility and a second possibility that is its opposite pole, show practical differences, and when you check it on the ground you see that it is not that sharp. Every approach contains something of this and something of that, and the practical distinctions do not line up so sharply that here he says invalid and there he says valid. It doesn’t go that way. And then you start patching with little patches, adding appendices and differentiae. We spoke about Ptolemaic astronomy with circles—adding another little circle inside the big circle in order to keep everything in a conceptual system of circles. With circles and straightness. If you want to remain straight, you have to add many circles.

In any case, this method of negating definitions—notice what we are really doing. We propose a definition, negate it. Propose a definition, negate it, right? What are we left with in the end? In the end we are left with the collection of all the definitions left burned along the roadsides like at Bab el-Wad. In the end we reached Jerusalem. If our dead lie by the wayside, still in the end we reached Jerusalem. What does that mean? It means that there is created in us some intuitive understanding, which is the residue left after all the waste we produced along the way. If we had not gone through that road, we would not understand what giving a bill of divorce is.

Now I cannot give you an explicit definition of what giving a bill of divorce is, to convey it simply to anyone so that he will know how to decide in every case whether this is a valid bill of divorce or not. But if he goes through the whole process with me, and I show him that this definition does not work because of this, and that definition does not work because of that, and we modify this one this way, and then improve it, but that still does not work because of this—at the end we are left with all the definitions not working, but I understand what giving a bill of divorce is. I understand what giving a bill of divorce is after I have negated all the definitions. That is exactly the doctrine of negative attributes. I think—at least this is one possible meaning of the doctrine of negative attributes when one reads Maimonides through these lenses—it seems to me quite plausible that he is talking about exactly this.

That is, I try to give definitions of the Holy One, blessed be He, but those definitions are always a ladder that in the end I will have to throw away. I use it to climb higher and then throw away the ladder. But that does not mean the ladder has no meaning. If I had climbed a ladder of cruelty and not a ladder of compassion, I would not have reached the Holy One, blessed be He. By the same token one could ask: if no definition works here for giving a bill of divorce, then giving a bill of divorce is anything. So you have said nothing. Then basically everything is giving a bill of divorce. So why say that giving a bill of divorce is specifically this and not…? How can you even disqualify some form of giving as somehow invalid? The word “invalid”—you have no definition. For something without a definition, anything goes. That means giving a bill of divorce may be the long definition of it, meaning the definition that is… yes, but that is not a definition; that is the collection of cases. But when I speak of an additional case, a case not appearing in the Talmud, and I have to decide regarding it whether it falls into the category of valid giving or not, there is no choice: I must perform some act arising from an understanding of what valid giving of a bill of divorce is. So a definition by way of negation. Exactly. And I think this is a negative process. It is not logical negation; it is certainly not contrary negation. There is no doubt that it is not from that family at all. It is from the family of annihilating negation, but I would perhaps call it an abstracting negation. An abstracting negation.

That is, for example, when I speak about love—we spoke about love. If you remember, when we discussed the commandment of love, I said that if we assume that love is directed at the person, not at the set of properties. But obviously the interaction with him is created through the properties. Whom do I encounter? I encounter the person whom I see, or experience, or smell, or hear—through the senses. But through that I understand what stands behind him. Through the form I understand the essence. Okay? Now in order to understand that there is an essence—where did Leibniz and the whole process we did at the beginning go wrong? They were unable to throw away the ladder. They remained with the ladder. But when I understood that I love so-and-so because of properties A, B, and C, then I identify so-and-so with the collection of those three properties. But that is not correct. That collection of three properties is the medium through which I actually encounter something beyond them. So I pass through the properties and negate them—negate not in the sense that they are false, but in the sense of abstraction. That is, I move on to what is beyond them. I move from the properties to the bearer of the properties. Okay?

And in this sense there is a common misunderstanding of the Kantian conception. Kant made the distinction between phenomenon and noumenon—between the thing itself and the thing as it appears to us. Fine? And people think—and many commentators on Kant, in my opinion, are mistaken on this point—they say that Kant is talking about the limits of human cognition. We are too weak; we do not have the ability to grasp the thing as it is in itself. We are bound to our forms of perception, our forms of sensation or cognition. That is a complete mistake. A complete mistake. It has nothing to do with limitation. It is not connected to limitation at all. When I want to know the color of this thing, its color is here. It has no other color. Because color is defined as that picture produced in me when the human eye looks at the thing. The image produced in me is what is called color. There is no real color that I fail to grasp, and then the color produced in me is merely the limitation of my sensory apparatus. No. Color is what is produced in me; there is no color outside. We spoke about a tree falling in the forest that makes no sound. It moves the air but it does not make a sound. Sound is created only when the air strikes the eardrum.

And so the claim is that those who understand Kant as the impossibility of grasping the thing itself think that there are somehow real colors out there, or real properties, and we simply fail to reach them because we are bound by nonsense. There is no real color. Color is defined as a form of our perception because our brain and our cognitive structure are built in a certain way, so we perceive the world in terms of colors. That’s all. Someone else, built differently, would not speak about other colors; he simply would not speak about colors at all. He would not understand what you want when you talk to him about colors. What do you want at all? Like trying to explain color to a blind person.

Does wavelength determine color? What? Does wavelength determine color? No, no. Why? Wavelength that strikes a human retina determines color. A wavelength that strikes another kind of retina could produce a symphony. And if it strikes a screen, a computer screen? Nothing at all. If it strikes a computer screen you won’t see anything. You need your eyes to see the screen. Fine, okay, and if everything is not—say—you do not hear, you have a hearing problem. Okay. So then sound doesn’t exist? Correct, of course. What exists is an acoustic wave. Sound is a cognitive phenomenon, not a phenomenon in the world. But if others hear, then there is sound? No. For the others there is sound. If others hear, then there is sound in them, not in the world. In their cognition there is sound, obviously. Because sound is a cognitive phenomenon and not a physical phenomenon. The physical phenomenon is an acoustic wave, a movement of air. Sound is not movement of air. No, the acoustic wave exists, but sound is the thing produced when the movement of air strikes my eardrum. No, that enables hearing. No, it does not enable hearing; it creates hearing. It enables me to become aware of the existence of an acoustic wave. That yes. The acoustic wave is in the world, and I can become aware of its existence through the fact that it creates in me a sound, but the sound is only in me. Fine.

So when I say—how can I formulate this? To formulate Kant as lack of ability is a total misunderstanding. How can one formulate the Kantian distinction at all in terms of inability? It is simply a complete misunderstanding. You say: you cannot grasp the acoustic wave, so you grasp only the sound. But that is how one grasps the acoustic wave! How does one grasp an acoustic wave? One puts one’s ear there and it creates a sound in you. Because by definition, to grasp the acoustic wave is always to grasp it in terms of something. That is not a limitation. That is the definition of the concept of grasping. Someone else who is built differently, whose ear is connected to the visual center in the brain, would see acoustic waves; he would not hear them, right? No problem. He grasps the same acoustic wave. He is not limited. It’s not that I know how to do something he doesn’t know how to do. We simply do the same thing differently.

In the Platonic sense, if there are such beings as ideas—what?—that are beings, there are ideas that are beings, then perhaps there is someone who can see these beings or sense them in some sense we perhaps do not know. Then he can touch it directly. That is an interesting remark. Because in the Platonic conception I can indeed say that, for example, someone who is essentially blind and does not understand at all what appearance or color or anything like that is—even if he grasps reality, he has other senses, not my senses, and he grasps reality fully, okay? But clearly he does not have the concept of sight, he does not have the idea of sight. Fine? Unless the idea of sight is itself not the true idea but only some reflection of the true idea as I… But that really is a question; it’s an interesting point, I hadn’t thought of it.

In any case, with respect to objects in the world one cannot speak of limitation. Okay, on that we surely agree. Okay, therefore the claim that when I want to understand what an acoustic wave really is, I cannot be captive to the way I perceive it, because the way I perceive it creates in me a sensation. Someone who wants to understand what an acoustic wave is and translates it into terms of sound is speaking nonsense. An acoustic wave is movement of air. It is not sound. Sound is an indication that the air here is moving. Okay? That is sound. But the acoustic wave is not sound. Sound is an indication of its existence. But this does not mean that there is some objective way to grasp the acoustic wave itself. The acoustic wave is a physical phenomenon. Perception of it will always be in terms of something—in terms of appearance, in terms of sound, in terms of something perhaps I do not know at all, no matter.

What? Some kind of interaction whose result exists only in my cognition. Fine? On the other hand, of course, it is not correct to identify—and this is what Kant said—that there is such a thing as the thing in itself. As opposed to what others say: well, maybe there is really nothing out there at all. There are only the things we perceive, and the whole world is nothing but our experiences and not really something out there. That is what Kant did not accept. Kant said: no, there is something there. And our way of encountering it is by knowing it through our means of cognition. This is not a limitation. This is how one knows. That is what “to know” means: to create an interaction that produces in me some image of the thing. That is called knowing it. But of course, on the other hand, I need to be able to carry out this abstraction that takes that cognition I received and turns it into an equation.

Because understand, until people knew how to perform this abstraction, maybe they knew that there were sounds. Clearly. But nobody knew how to translate that into the fact that actually we are speaking about pressure waves in the air, which we can even describe mathematically. And they have such and such properties, and we can use them to build all kinds of things. Why? Because we have the ability to abstract from our perceptions the objective phenomena, what exists in the world itself, and give it some description that is less sensory-dependent, or perhaps not sensory-dependent at all, but an objective description in a certain sense. Again, that too is not fully objective. We spoke about this when I talked about the images of the bill of divorce, of the arrow in flight, about the two pictures of quantum theory—the snapshot and the video camera. It is also clear that if our physics were constructed by minds built differently, the equations would look different. Maybe we would not use equations but something else, I do not know exactly what. It would describe the same physics. That is, even equations are clearly some function of how we think and construct things. That is how it is. But still—just a second—there is here an abstraction detached from our subordination to the sensory image of things.

A different point of view. What? A different mode of looking at the same thing. Yes, but that’s what I’m saying: it’s not a different visual perspective, it’s a different mode of thought. “View” here is metaphorical. We are detached from viewing, but certainly not detached from how we think. And since we think in a snapshot-like way, we are stuck with uncertainty principles. Someone who thinks in a video-camera way will be stuck with uncertainty principles from the other side. Someone who somehow manages—I don’t know—to live in both those consciousnesses in parallel, if such a creature exists, perhaps he will not have uncertainty principles. I don’t know.

Here you are really taking it one step further: that there are things there which, because we have no ability of access to them, they exist and we cannot know that they exist. No, that is certainly true. Certainly true. Does anyone dispute that there are frequencies only a dog hears and I do not? But he says necessarily that the reason we can describe all things, what answers Hume—what answers Hume, in my opinion, is not really an answer, so that will be difficult. His picture is a correct picture, but it does not solve Hume’s problems. He thinks it also solves Hume’s problems; he presented it as a solution to Hume’s problems. The result is a correct picture, but there is no solution to Hume’s problems there.

So the doctrine of negative attributes is really some process in which the negation here is not negation in the logical sense, not even annihilating negation. It is somewhat like annihilating negation; I would call it perhaps clarifying negation. And in this sense there is something standing behind the idea of compassionate that does belong to the Holy One, blessed be He, and behind the idea of cruel there is not. That is, if I now go through the analytical process that I just described with respect to giving a bill of divorce, or the analytical process we did with respect to dynamic processes that I tried to describe through states, and then tried to abstract and understand that I am bound by my static way of looking. But in the world there is a concept of pure dynamics, which I do not know how to grasp except by means of rapid successive snapshots. So this is a kind of abstraction I perform—that is really negative attributes. I characterize dynamics, and in the end I understand what dynamics is. I understand what dynamics is in a completely intellectual way. I cannot imagine dynamics because I must see a change of state in order to see the movement of a body. I cannot see its velocity in itself; I only see that at each moment it is in another place. But in intellectual understanding I understand what a moving body is, and I arrived there through abstraction. These are negative attributes. Exactly negative attributes. I negate the static way of looking, but that does not mean I cannot say that it is dynamic. That is, there is something that remains after the negation. And here I return to what I spoke about regarding poetry, or what I spoke about regarding the definition of art. I think I mentioned there Gideon Ofrat’s book, where he tries to define what art is. He goes through twenty-something chapters in the book, and in each one he proposes a different definition—exactly the same process, like the Kehillot Yaakov. In the end he negates one possibility; he brings some work that does not meet the criterion he proposed, and yet it is clearly art, and therefore he throws away that definition, proposes another, negates that too by all kinds of examples of paintings, symphonies, sculptures, other things. He negates all the definitions, and in the end he is left with the definition that art is what is found in a museum. And that is art.

And I agree with the whole book except for that last line. Because there he falls into the same failure as Leibniz, the principle of the identity of indiscernibles, which says that the definition is the thing. Not true. The definition is an attempt to capture the thing, and after you negate all the definitions you are still left with something. There will be things that enter a museum and are not art. Although I cannot give a formal definition, a conceptual definition, I say: I cannot give a formal definition of the thing, but that does not mean there isn’t one. It only means that the form of the thing—there is an essence there—its form does not fit into my ordinary conceptual system. But then what does that mean? That I should give up? Not know it? That I cannot know it? No. I will go with the categories I have; that is what I have. When I describe dynamics, I go with a static system because that is the perspective I have. But suddenly through the static perspective I can understand: look, this is not static—but let’s make many consecutive photographs at a very high speed. That starts to bring me closer to the idea of what dynamics is, and in the end I negate statics completely. Pure dynamics is something that contains nothing of statics. In a world where a body has velocity, it has no position at all. It has no position. But I arrive at the concept of velocity only by means of positions. I know it is located here and then here and then here, meaning it has velocity. And suddenly after abstraction I find myself without the ladder. That is, a body that has velocity has no position at all. I completely negated it. So does that mean I understood nothing? That the whole road I traveled is worth nothing? Absolutely not.

That is, I proceeded with the tools I have because those are the tools I have. After I negated them all, I was left with something that I do not know how to formulate positively in my tools, but it is not true that I am left with nothing. The same with poetry. We spoke there about the definition of poetry—people try to define what poetry is, and nothing stands the test. Then in the end they basically arrive at the conclusion that poetry is what people think is poetry. “A Jew is whoever thinks he is Jewish,” and all sorts of jazzy definitions like that, definitions that express a kind of despair or intellectual laziness, call it what you like. And that is a kind of despair because the positive, analytic path does not succeed in reaching a definition that captures the thing. Then they say: well, if so, then everything we did is worthless, so it’s just… But on the other hand I very much believe that Gideon Ofrat himself means what I am saying now. I’ll tell you why: otherwise he would not have written the book. Beyond economic considerations, that book did not make money, I can tell you that already today. So why did he write the book and publish it? To teach us that there is no definition of art? That means he thinks he is teaching us something in this matter. That is, he tried to teach us what the definition of art is, except that he is trapped in this conception, and here he is mistaken: he does not read himself correctly. He is trapped in the conception that says: since there is no definition, that means there is no such thing. There he made an error in interpretation when interpreting himself, because he did understand correctly. He does understand what art is. He knows what art is. Otherwise how does he know that one work is art and another is not art? After all, throughout the book he brought examples that negated his definitions. This example shows that definition 13 is wrong. This example shows that definition 9 is wrong. How do you know those examples are art if you still have no definition? You know that even before the definition. Well, that means you have some intuitive concept of what art is; you are only trying to refine it, sharpen it, but always in a negative way. You try to propose a definition and then throw it away.

There is a book—maybe I mentioned it—Zen and the Art of Motorcycle Maintenance by Pirsig, a cult book in its day. That book is a race in pursuit of the attempt to define quality. It’s about a rhetoric lecturer trying to define the concept of quality. And at a certain point in the book he comes to a kind of illuminating insight, and whoever has gone through the whole process with him understands how illuminating this insight is. Anyone who just reads that sentence will say, okay, so what, I understand it, why read the whole book? The insight is that the Greeks messed up our minds. They thought that everything has to have a definition. So he searches for definitions and doesn’t find them; he cannot define the concept of quality. As a teacher he has to give a grade to an essay. He was a rhetoric teacher in an American college, and he has to give grades to students on essays. Now he gives them grades—this one is better, this one worse—but he cannot define for himself what criterion he is using. Then he is in a frantic pursuit of this definition, and in the end he comes to an illumination that says the Greeks messed up our minds by making us think that everything has to have a definition. Do you understand?

But what does that mean? If you arrive at that from the despairing side, from the side that says: okay, it has no definition, so probably it’s just arbitrary, merely subjective—then you have accomplished nothing, and there is no need to read the book. His point is the opposite: there is a concept of quality even though it cannot be defined. And this heroic chase, this pursuit after the attempt to define it in our concepts—which fails—is the only way we have to grasp it. After we have negated all the possibilities for defining it, we understand better what it is—maybe not fully, but better. Like dynamics through static tools. Therefore the attempt—or giving a bill of divorce after negating all the definitions—we are left with some intuition of what valid giving of a bill of divorce is and what invalid giving is. And after we have completed that route, then indeed, as much as we possibly can, we understand what the thing is. And what a good essay is and what a bad essay is, exactly.

Therefore there is definitely value in the attempt to define it, even though you negate all the definitions one after another. And there are incorrect definitions. This does not mean all definitions are equally correct; that is a mistake. This is an abstracting negation.

I’ll read you just one passage, and with this we’ll finish, one passage from Sefer Ha-Ikkarim, which seems to me to say this in the end. This is much later already. It’s chapter 30; the previous passage I read you was chapter 21. “It should be understood that there is a difference between negating one opposite and negating the other opposite. And in this lies the advantage of the wise over one another”—this is the advantage of the wise man over the fool. It says everything I have said now. Therefore the wise man is wiser than the fool; one who has read Gideon Ofrat’s book understands better what art is than one who hasn’t, even though the one who has read the book also remains without a definition—he understands that he has no definition. “And in this lies the advantage of the wise over one another in their knowledge of the modes of negation. How so? Since not all negations are said of Him, blessed be He, in the same manner. For all the attributes which among us are deficiencies, such as dead, ignorant, lacking power,” yes, “foolish, blind, evil, and the like—we negate them from Him by complete negation, meaning that this attribute, which is a deficiency, is not found in Him at all. Rather, the opposite, which is perfection, is found in Him. But when we negate from Him the other opposite, whose meaning among us is perfection, such as living, able, wise, rich, good—the intention is not to say that this is not found in Him and that its opposite, which is a deficiency, is found in Him. For such a negation would not only not be perfection; it would be blasphemy and abuse.” If when you say you negate Him by saying He is wise, you understand it as taking away the property of wisdom from Him—if you understand the negation in the logical sense, opposing negation—then that is blasphemy and abuse. By contrast, if you negate from Him the property of foolishness and wickedness, that can indeed be logical negation. The first negation is denying negation, as I said before. Negating wickedness from Him is logical negation. He is not wicked. Okay?

“Rather, the intention is to say that the perfection which among us is understood as living or able or wise and the like is not found in Him, blessed be He, in the way it is found in us, but is found in Him in a more exalted and more elevated way, such that there is no relation between that perfection as it is among us, or as understood and conceived among us, and that perfection when attributed to Him.” But it does tell us something by way of extension. Again, this is exactly the abstraction, right? This is negation through abstraction. Because he does say that He is wise, only not in the ordinary sense in which we understand wisdom in ourselves. So we are indeed describing in Him something that is in some sense positive. The negation is not to say that we are not saying anything positive about Him. The negation is abstracting negation. We say something abstract about Him, but in the abstract sense it is positive about Him; it is not negative. We say something about Him. Maimonides does indeed add something to what those before him said, those who said that one can say nothing at all about the Holy One, blessed be He.

“And it follows from this that one cannot describe Him, blessed be He, even with negative attributes unless we first understand the positive attributes, in what way the object described by them is described among us.” Right? If we do not understand what statics is, we will not understand what dynamics is, even though we understand dynamics only after negating all the possibilities of describing it statically. Or giving a bill of divorce—after negating all the definitions, in the end we understand what giving a bill of divorce is. “And the aspect of perfection in that attribute and the aspect of deficiency in it, and then we turn ourselves to negate them from Him, for by this one understands the way negation works. For not all negations are said of Him in the same way, as we have said.” When I negate wisdom from Him, that is not the same as when I negate foolishness from Him. Negating foolishness is logical negation. Negating wisdom is abstracting negation. Do you understand?

“And in this lies the difference among the wise and the investigators, the lesser and the greater alike, for the levels differ according to the difference in the apprehension they attain of the attributes of perfection attributed to Him, and in what way He is described by them.” Okay? This basically takes us back to all the previous classes where we talked about what poetry really is: poetry tries to grasp that thing which prose fails to grasp. That is, what ordinary linear definitions fail to understand. Fine, but it is still described in words. We have no other way of expressing it. There may be something in music too, but let’s leave that aspect aside for the moment. Let’s talk about poetry, unmusical poetry, written poetry.

You are basically using words—it is like describing dynamics by means of states. But the message that passes to you is not the verbal content of the words. It is not the literal meaning of the words. The words are the medium which, after you negate it or abstract from it, may leave you with the thing that is really the message the poem wants to convey to you. And therefore I think that this is also the meaning of Maimonides’ negation of attributes. Now we didn’t manage even to begin reading Maimonides at all. Next time we’ll begin straight away with reading Maimonides, and hopefully now we have the tools to understand it. Thank you very much.