Simplicity, Lesson 2

[Rabbi Michael Abraham] Abstraction, abstractions. So last time I spoke a bit and gave a few examples of concepts of abstraction, of virtual space, where today, in our era, it seems to me much more natural to relate to abstraction—to the point that sometimes people may not even feel that what we actually did was an abstraction. This is not really the thing itself. We talked before about children; for me, for example, this phone is a kind of abstraction of the old telephone. Meaning, it sort of does the same job, just in a different way. A child won’t see any connection between those two things. That one is a dinosaur and it’s not even clear what you’re supposed to do with it, and this is a phone. Meaning, if you live inside this world, then you lose the ability even to understand that we’re dealing here with an abstraction. This is just the world. There are people for whom the virtual world is the real one, and the real world is just some strange analogy. Yes, if we exaggerate a little. But when we return to the logical question—what is abstraction, how do you do abstraction—then I said there are two ways to define concepts. You can define them by extension and by intension. An extensional and an intensional definition. A definition by extension is to try to list objects that instantiate those concepts. If I’m talking about a democratic state, I can define it by the features of a democratic state—that’s a definition by content, by intension. And I can define it by extension, simply by listing the democratic countries in the world, and that too is some kind of definition. What do these two definitions actually give me? They give me the ability to decide, about a given country, whether it belongs to the category of democratic states or not. With both of these definitions you can do that. If I go by content, then I try to compare the characteristics of that country to the characteristics of the concept. If I go by extension, then I simply look for that country to see whether it appears on the list or not. So the operation I’m performing is a completely different operation. But in principle there is supposed to be an equivalence between the two operations. Yes, it reminds me of examples that come to translate the operations a person performs in such a way that a machine could perform them too. For example, yes, John Searle’s Chinese room example. He says: suppose you seat a fluent Hebrew speaker in a closed room, and he has no idea what to do with Chinese. He has a huge barrel of Chinese letters. Okay? And he has a booklet, and each time someone asks him a question in Chinese—he has no idea what it means—he has to assemble some answer from the letters in the barrel. Okay? If he assembles an incorrect answer, he gets an electric shock. Okay? Let’s say we have infinite time; there is no time limit. Okay, so in the end the claim is that he could perhaps answer every question he receives with an answer.

[Speaker B] And he has an infinite capacity to learn from the shock. Yes, exactly.

[Rabbi Michael Abraham] So the claim is that in the end he could get to a state where he communicates with you in Chinese. And the question John Searle asks is whether this man really understands Chinese. Now, to any normal person it’s obvious that he doesn’t, but a person involved in artificial intelligence will tell you yes. Because for him, understanding Chinese means communicating in Chinese. Meaning, the mental operations that underlie the input-output system don’t interest him. Obviously the computer doesn’t imitate that, but that doesn’t matter to him. That’s why, for example—and this is actually a very interesting point about abstraction, I hadn’t thought of it—he speaks, for example, about the intelligence of a computer, or the intelligence of a bird, or I don’t know, of another animal. And they rank them; there are rankings of what kind of intelligence different animals have and where they are positioned relative to humans, how much IQ a monkey has and how much IQ a pigeon or a dolphin has. To me that’s absurd, because none of these creatures has IQ. The use of the concept of intelligence in those contexts is a very technical use that doesn’t really capture its true meaning.

[Speaker B] So what you’re saying is that artificial intelligence is a meaningless concept?

[Rabbi Michael Abraham] No, it’s a meaningful concept, but it isn’t intelligence. Meaning, never mind, it’s just terminology. Artificial intelligence. Yes, I’m saying it’s terminology because there is value in engaging in this field. I’m not claiming the field is worthless; it has meanings, it has implications. But I’m just saying that many times those who work in this field take the concept—which is of course a useful and efficient concept, and good to work with—but they take the concept as if it expresses an essence. And then they basically say that a human being is also some kind of… But it’s not that. It’s a completely different kind of creature. And in an extreme form you can talk about the intelligence of water. I talked about this, yes, the intelligence of water: it solves equations that no physicist knows how to solve, the Navier-Stokes equations. These are very complicated equations of continuous flow; no physicist knows how to solve them except in entirely trivial cases. Meaning, beyond that nobody knows how to solve them. Even computer simulations aren’t simple to do with those equations, though the computer maybe can, and the water itself solves all the problems. Put the water in any situation and it will somehow flow. So when it flows somehow, it is ostensibly solving the Navier-Stokes equation—there, factually, it knows how to flow. Now it’s clear to all of us that that’s nonsense. Here even people in artificial intelligence wouldn’t say that the water has intelligence, but essentially there is no difference between that and a computer. The computer doesn’t think either. The computer is simply a machine, like water, that is constructed in a way that symbolizes our thinking, because we built it. We didn’t build the water, or the laws of gravity, or whatever governs the water. Here we build it, and therefore it’s easier for us to talk—or more natural for us to talk—in terms of intelligence. And so this, for example, is a case of an abstraction that is very useful, but on the philosophical level it isn’t an abstraction at all, it’s an illustration. Meaning, the concept of intelligence itself is an abstraction, and we’re making it into an illustration. We’re trying to translate it into something more concrete. We often view that as abstraction. It’s illustration. So on the technical level it’s a very useful abstraction—it’s a fact that you can produce machines by analyzing what kind of intelligence you want, and how much intelligence, and what is required for such-and-such a level of intelligence. There are all sorts of theorems in computability: what is needed, what kind of network can do this kind of operation or that kind of operation. Meaning, these things are very useful. But they are useful only because we succeeded in making some kind of abstraction of the concept of intelligence. But in this case, in my view, it’s not abstraction; it’s illustration. Meaning, the concept of intelligence itself is an abstraction, and we’re trying to give it a concrete expression. And that brings me back to an aspect I spoke about last time: many times—or almost always—abstraction and illustration are two things constantly playing on the field against one another, but when we relate to them, many times we call illustration abstraction. Why? Because at the base of the illustration sits an abstraction that we don’t even put on the table. When we build a computer, the computer is an illustration of the abstract concept of intelligence; we’re trying to give it a concrete expression. But in order to do that, we had to take a mode of human operation, which is also something concrete, and try to abstract from it the modes of operation, the intelligence, the concept, detached from a concrete person in a concrete situation, trying to understand the forms of thought that appear in our brain or in our intellect. After we’ve done that abstraction, it’s possible to make a different illustration of it and then build a computer. That’s why many times illustrations are really only the second part, the final part of the work. First of all, you have to do some kind of abstraction. And I spoke about Aristotle and logic—he abstracted the forms of human thinking, which later made it possible for us to make an illustration by means of a computer, or what in technology is called an implementation by computer, of the abstract mechanisms that Aristotle arrived at through his abstraction. Therefore abstraction and illustration are concepts that are opposite on the one hand, but very confusing. And many times when we encounter an illustration, we call it abstraction because it’s the result of abstraction. Meaning, you can’t make a different illustration if in the background you haven’t already performed an abstraction. Because after you’ve done the abstraction, you’ve discovered some more general concept, and then you understand that the concept you started from is really only one illustration of that abstract concept, and you can also make another illustration of it—but for that, you had to arrive at the abstract concept. I spoke about theory and model in mathematics. Yes, there is a theory—group theory, or set theory, or various spaces—all these are theories, and there are certain models, each one of which is a model for the theory. Meaning, all the propositions of the theory hold for it. Numbers, for example—the numbers we’re familiar with are a model, not a theory. Number theory is a theory; it doesn’t deal with numbers. It can also deal with other entities, as long as they satisfy certain basic rules. Numbers are a model of that thing, and so numbers too can be described by number theory.

[Speaker C] Okay, but abstraction also has to derive from some concept. Meaning, abstraction isn’t floating in the air; it comes from something.

[Rabbi Michael Abraham] I’ll get to that in just a moment—whether it comes from something or hits upon something—but in a moment I…

[Speaker C] …will talk about that today.

[Rabbi Michael Abraham] No, I don’t know if it’s three levels; in a moment I need to sharpen that a bit more. So the claim, basically, is that we have opposite processes of abstraction and illustration, but usually we do both things. Meaning, we don’t arrive from some abstract thing and look for illustrations of it. The things in our world are always concrete. In order to make an analogy from one concrete thing to another concrete thing, you have to abstract the first concrete thing, and then make another illustration of the abstract thing. And then there is an analogy between the two concrete things, because they are both illustrations of the same abstract thing. Let me give you an example of the trickiness involved here. In Maimonides, regarding the laws of building, just now I remembered this. In the laws of building, Maimonides speaks, for example, about making cheese—someone who makes cheese—as a derivative of building. Okay? And also making a tent is a derivative of building. Now the question is: what connection is there between making cheese and making a tent? What similarity is there between these two things? Making cheese is producing a block of cheese from milk, or from cheese particles if you like, and a tent is stretching a tent-sheet. What similarity is there between these two actions? No connection at all. Now Rabbi Isser Zalman, in an essay in Even HaEzel—the Kehillot Yaakov cites him—an essay of Rabbi Isser Zalman, where he argues that the primary category of building—and maybe this too we’ll talk about as abstraction, I hadn’t thought about it, electricity on the Sabbath and building, those are also interesting abstractions—building is basically building a house, what we’re familiar with. What is a house? You take, say, bricks, collect them together into a structure, and that structure contains within it a space. You create a space, and the structure that defines it is a structure built out of bricks. Meaning, the primary category of the labor of building is gathering parts in a way that creates a space. That process is called the primary category of building. Okay? Now that can have two derivatives. One derivative is when you gather parts in a way that does not create a space. So it’s not the primary category, because it’s something not entirely like the primary category, but it’s sufficiently similar to be prohibited by Torah law, and it’s called a derivative. Okay? How do you do that? Making cheese is such a case. You gather parts; it doesn’t create a space. You collect the parts and some kind of structure is created. That structure is not a space; you don’t use it the way you use a house, but you take parts, gather them together, create a structure—so that’s a derivative of building. Now a tent is the reverse. There is no gathering of parts in a tent, but there is creation of a space. The blanket, for example, that you spread above, is not gathered from parts; you place it above and it creates, encloses, some kind of space. So creating a space without gathering parts is also a derivative. Now something very interesting comes out: each of the derivatives resembles the primary category, but there is no similarity at all between the two derivatives themselves, because the primary category has two characteristics whose combination together—not the similarity between them, but their combination together—creates the primary category. Now if the resemblance of derivative A is in characteristic A, and the resemblance of derivative B is in characteristic B, then there is no similarity between the derivatives, even though both are derivatives of the same primary category.

[Speaker E] And why can’t you come and say that it’s cumulative? The moment you gathered parts and created a space, that’s what it has to be. There is no such thing as creating a space without parts, and there is no such thing as—

[Rabbi Michael Abraham] You could have said that, but the Talmud doesn’t assume that. The Talmud claims that there are primary categories and there are derivatives that can be merely similar to the primary categories and not identical to them. What is identical to the primary category is a primary category. Maimonides distinguishes between… there is the Kalkalat Shabbat at the beginning of the Mishnah of Tiferet Yisrael—he has a work there about primary categories and derivatives on the Sabbath, principles of the prohibited labors of the Sabbath, among them about primary categories and derivatives. There he discusses somewhat the question of how you define a primary category and a derivative, how similar it has to be. But this already appears in Maimonides himself: there are things that are quasi-primary categories, and there are things that are derivatives in the prohibited labors of the Sabbath—things that aren’t exactly the labor that was done in the Tabernacle, but the similarity is strong enough that the thing is not considered merely a derivative, but rather a…

[Speaker G] …primary category, a quasi-primary category.

[Rabbi Michael Abraham] Because it has all the characteristics. Even though it’s not the same labor, all the essential characteristics appear there, so it’s a quasi-primary category. Therefore a derivative is always when the similarity lacks an essential characteristic—not a nonessential characteristic—and yet, of course, there are still enough essential characteristics for it to count as a Torah prohibition and not a rabbinic prohibition or something entirely permitted. In legal language, what is called “and/or.”

[Speaker E] What do you mean? Meaning either all the parts together…

[Speaker H] …or one of them.

[Rabbi Michael Abraham] After you add the derivatives, it’s and/or. The “and” is the primary category and the “or” is the derivatives. Yes, exactly.

[Speaker I] What’s the practical difference? In this definition, what is “gathering parts”? Connecting parts?

[Rabbi Michael Abraham] So, that’s the claim of Rabbi Yitzhak Ze’ev HaLevi. He says that’s basically the definition of the labors. What?

[Speaker I] Isn’t it just accidental that you need to gather parts in order to have a space?

[Rabbi Michael Abraham] What does “accidental” mean? This is the labor called building a house—that’s where we started. It’s true that the Tabernacle wasn’t built out of bricks; that doesn’t matter. They gathered parts there in a different way. They gathered the sockets with the screens and with—never mind—but that too was gathering parts in a way that enclosed a space, okay?

[Speaker J] So making a tent was the labor—they wouldn’t have learned it from making cheese?

[Rabbi Michael Abraham] No, obviously not. In this conception there’s no connection. Therefore the concept of similarity, which many times is perceived by us as a transitive concept—meaning, if A is similar to B and B is similar to C, then A is similar to C—that’s not true. It could be that A is similar to B in parameter X, and B is similar to C in parameter Y, and therefore you cannot infer that A is similar to C. The concept of similarity is not transitive, okay? Even full similarity with respect to one of the parameters—no, complete full similarity is transitive, yes, but something can be fully similar in one characteristic and lacking another characteristic. Now here, yes?

[Speaker H] Once you talked about the opposite example—winnowing and throwing and spitting—where one derivative is fused from two primary categories.

[Rabbi Michael Abraham] Right, that’s a fusion, right. That’s a fusion, and it’s really very interesting. Actually I hadn’t even thought of talking about these things, but maybe it’s worth discussing them more broadly, because there really it’s the opposite situation. What happens there is—after all, the Jerusalem Talmud brings it. One who spits four cubits is liable, liable because of winnowing—and some versions say because of throwing. It’s not clear whether it’s winnowing or throwing. Now ostensibly there is no connection between winnowing and throwing, right? Winnowing is where you winnow the grain and the wind blows away the chaff and the kernels fall down, a kind of sorting, yes? That’s winnowing. Winnowing, sorting, and sifting are basically three ways of separating. Therefore they are considered three primary categories only because all three were done in the Tabernacle; that’s the Talmud in Klal Gadol. So that’s winnowing. And throwing is taking something in the public domain and throwing it four cubits, as distinct from someone who carries four cubits in the public domain. Throwing is a derivative of carrying. Now regarding spitting—someone who spits on the Sabbath—it says in the Jerusalem Talmud that he is liable because of winnowing or throwing, depending on the version. So the Mishnah Berurah in Bi’ur Halakhah cites Rabbi Menasheh of Ilya, a disciple of the Vilna Gaon. He argues that this is a fusion of winnowing and throwing. It’s not two versions; it’s both together. It’s a fusion of winnowing and throwing. And basically the claim is—and the way I noticed this logical point is that there is an interesting logical point here. The truth is that in general we need to talk about primary categories and derivatives in this context; really I need to add that, I’ll make myself a note. What happens is that in the primary categories of tort law, for example, or in most places where there are primary categories, they have derivatives. From the fact that there are primary categories, it follows that there are derivatives—as the Talmud says in Bava Kamma. Now sometimes there is a derivative of one primary category, but sometimes the derivative belongs to two primary categories. In Bava Kamma 6, “their common denominator”: his stone, his knife, and his burden, which he placed on top of his roof and they were blown by a normal wind—or someone who takes manure out into the public domain—there are several examples there. And the Talmud shows that you can’t learn it from any one of the primary categories alone; you need to make a “common denominator” argument. There are two teachers here, the common denominator. There too there is a very interesting logical issue. The interesting thing is that in the primary categories on the Sabbath there is no derivative that is a derivative of more than one primary category. I don’t know of one. In the Talmud certainly there isn’t, and I don’t think there is an example in the medieval authorities (Rishonim) or the later authorities (Acharonim) either. At least I’ve never found one.

[Speaker K] There is no derivative of two?

[Rabbi Michael Abraham] One that needs a common denominator in order to learn it, that needs two primary categories?

[Speaker L] No.

[Rabbi Michael Abraham] In tort law there is; in other places there is.

[Speaker L] Why in tort law do you always call that a derivative? The common denominator—you sometimes call it that.

[Rabbi Michael Abraham] It may be a common denominator or a derivative.

[Speaker L] Why? It’s a derivative of two primary categories.

[Rabbi Michael Abraham] There there is no practical difference between a primary category and a derivative; only in the case of pebbles there it’s a derivative of a primary category with its same kind, so there it’s a practical difference whether it’s a primary category or a derivative. But on the Sabbath there is a practical difference, because for a primary category and its own derivative you incur one liability. In tort law that’s not relevant. But plainly it is a derivative. What is learned from a primary category is a derivative; what is learned from two primary categories is even more of a derivative, because you certainly can’t define it as one of the primary categories. At most you could define it as another primary category, but there is no other primary category.

[Speaker L] There is an attempt among the later authorities (Acharonim) to define it as the common denominator being something obligating. The common denominator obligates.

[Rabbi Michael Abraham] No, that’s what I mentioned before—Rozovsky there, the Brisker approach. In any event, the claim is that on the Sabbath there is no derivative of two primary categories. Just interesting—I discussed this with a very interesting Jew and didn’t hear an answer from him. He tried a few things, but not successfully. In any case, the only example I found is Rabbi Menasheh of Ilya, that spitting according to the Jerusalem Talmud—if that’s really what Rabbi Menasheh of Ilya claims—that it’s a combination of winnowing and throwing. Why? Because in winnowing you see—why do you need both? You can’t learn spitting from throwing. Why not? Because the assumption is that in spitting the wind takes it. It’s not the force of the spit itself, otherwise it would be like throwing. Rather, you expel it from the mouth and the wind takes it—at least for the four cubits you need the wind, because without that you don’t have the force to do it four cubits. So that’s how it works. You can’t learn it from throwing, because in throwing your force carries it the four cubits; here your force doesn’t do it, the wind does. From winnowing there is no real similarity to throwing from which to learn it. But from winnowing you can learn that if the wind is a partner in the action, that doesn’t detract, right? You don’t need to perform the action by yourself; you can activate the wind, because that’s what you do in winnowing, and the action is still attributed to you. The combination of both together creates spitting. Basically winnowing teaches… it’s not similar to throwing, not really. If I had to decide, it’s a derivative of throwing, not of winnowing. Winnowing only teaches you that even if you throw in a way that is aided by the wind, it’s still throwing.

[Speaker M] Maybe in winnowing, using a normal wind wasn’t something defined as his direct force? No. Whereas in tort law it is?

[Rabbi Michael Abraham] Correct. There is the Talmud—and the opposite—in the Talmud in HaKones, where the Talmud says “winnowing and the wind assists him.” There Rav Ashi says that this is indirect causation, and indirect causation on the Sabbath is liable because the Torah prohibited intentional craftsmanship, but in tort law not. There it’s in the opposite direction. What? Tosafot there in the case of the scatterer in Bava Batra—Tosafot talks there, or the Jerusalem Talmud, I don’t remember, Jerusalem Talmud.

[Speaker L] Tosafot on winnowing and on…

[Rabbi Michael Abraham] The Talmud makes that distinction. The Talmud gives four answers there, and Rav Ashi, the last one, says there is a difference between the Sabbath and tort law. On the Sabbath it is “the Torah prohibited intentional craftsmanship,” and there “intentional craftsmanship” is a stringency, not like usually where it goes leniently—that you’re exempt for an unintentional act or for a labor not needed for its own sake. There it’s a stringency, that indirect causation is liable, like Rashi there, the Rosh and Rashi. And in tort law, indirect causation is exempt, as in all of Torah. So it’s not something trivial that when you do something with the wind you’re liable. Plainly it’s indirect causation. Fine? Now from winnowing you learn that yes. And this is a dispute between Rashi and the Rosh there—whether from winnowing you can learn for all cases. Rashi claims that from there we learn that indirect causation is liable because the Torah prohibited intentional craftsmanship on the Sabbath. According to the Rosh, it’s only in winnowing, because that’s the normal way to do winnowing, so you can’t learn from it something general. But this Rabbi Menasheh of Ilya apparently goes with Rashi and not with the Rosh. And then the claim is basically that from winnowing you learn only that the assistance of the wind does not exempt. He says that it’s still your labor. But basically the labor you are doing is the labor of throwing, not the labor of winnowing. Fine? Because you are moving it four cubits in the public domain; it’s just that your own force doesn’t do it, rather with the help of the wind. So winnowing shows that that’s okay. So here you see a fusion of two things, but it’s not an equal fusion like in building, which is a fusion of creating space and gathering parts. Here it’s basically throwing. Winnowing only comes to remove an objection: what is unique about spitting? That the wind assists it. Winnowing proves that this doesn’t matter—meaning, even if the wind assists it. But in principle it’s a derivative of throwing. If I go back to… look, now I’m drifting a bit—but if I go back to the Talmud on page 6 there in Bava Kamma about the derivative of two things, after all the Rosh there brings… there are those who say two methods; I argue there are three methods as to how to relate to his stone, his knife, and his burden, which he placed on top of the roof and they were blown by a normal wind and caused damage. So it’s a derivative of fire and pit. Right? Since they caused damage after coming to rest. It’s a derivative of fire and pit together. So the Rosh there brings: there are some of the great ones who said that it’s a derivative of both, and therefore here you have both the exemptions of fire and the exemptions of pit. Meaning exemption for vessels and exemption for hidden objects. Okay? And he argues that the entire law of pit applies to it. Meaning this is a derivative of pit. So what about fire? Fire does exactly the same work as here. Fire just says that the fact that it got here by means of the wind—you didn’t dig the pit; you put it up high, and the wind brought it down. The fact that the wind took part here doesn’t interfere. But when you ask me: a derivative of which primary category of damage is this? It’s pit, because it caused damage after it came to rest; it did not cause damage while moving. So here fire only removes an objection or a weakness, but essentially it resembles pit, okay? Exactly the same thing with winnowing.

[Speaker I] Who says that this objection is also removed in the case of hidden objects? What? Who says that the objection is removed there too if there is an exemption of fire? I didn’t understand. If fire has an exemption for hidden objects—

[Rabbi Michael Abraham] Then the Rosh argues that there won’t be the exemption of fire in this law.

[Speaker I] Ah, makes sense—there are the exemptions of fire…

[Rabbi Michael Abraham] …and there are also the exemptions of pit. No, the Rosh argues that the exemption for hidden objects won’t apply.

[Speaker I] Why? Why is the objection removed in a place where there are hidden objects, where it’s hidden?

[Rabbi Michael Abraham] That’s the question on the Rosh. The simple logical conception is like the great ones regarding fire. The Rosh says no. In a case where you’re only removing an objection, then basically it goes back to being a derivative of pit, and all the laws of pit apply. Meaning, it will be liable for hidden objects, even though ostensibly in the case of hidden objects, if you go back and try to learn it, you won’t be able to prove it, because in the case of hidden objects fire cannot prove it. This is connected to the Brisker Rav that was mentioned before. The Brisker Rav argues that you don’t really learn this from the two sides, but rather from the common denominator, and then the exemptions apply to their own specific laws. On page 5, what the Talmud says there is that you need to learn the exemptions, not the liabilities. And then if the common denominator exists here, then you obligate, you impose liability. Now let’s see the exemptions—and the exemptions aren’t here.

[Speaker K] Okay, someone who transfers from one domain to another within four cubits—that certainly isn’t by means of the wind. So it must be only by his own force.

[Rabbi Michael Abraham] Then there aren’t four cubits, so he isn’t liable. There is no throwing; throwing less than four—ah, from domain to domain? Yes, so what? Then it’s because of throwing. Meaning, throwing is only in the public domain. Throwing is only in the public domain. If you throw from the private domain to the public domain, then the question is where the initial uprooting is, where the placing down is. The uprooting was… the placing down—“something intercepted is considered as though placed down”—so here we need to discuss many other things. It’s not so simple that there would really be liability for throwing there.

[Speaker L] If there really is a derivative of two things, then there is a problem of “we do not derive punishments from legal inference.”

[Rabbi Michael Abraham] That’s also a question in tort law. Tosafot on the spot asks this in Bava Kamma page 2.

[Speaker L] But regarding liability for capital punishment, it’s more of a problem.

[Rabbi Michael Abraham] Tosafot argues that “we do not derive punishments from legal inference” applies in monetary matters too. That’s Tosafot’s assumption there. There are disputes about this. Tosafot’s assumption there—he asks this, after all, “we do not derive punishments from legal inference,” and he says there that he wants to argue that in monetary matters we do derive punishments from legal inference, but there is a dispute on this issue, whether in monetary matters we do derive punishments from legal inference or not.

[Speaker L] Yes, say with this derivative maybe there would be a problem here. It fits with what the Rabbi said earlier—why on the Sabbath don’t we learn from a common denominator?

[Rabbi Michael Abraham] No, the Sabbath is prohibition—what difference does it make? So don’t punish, but learn the prohibition. As for prohibition you can certainly learn it. For prohibition, certainly you can write in the Shulchan Arukh that it’s prohibited. Leave it—don’t execute him—but you need to write that it’s prohibited. The prohibition is certainly learned; otherwise what do you do with the hermeneutical principles by which the Torah is interpreted? You learn through interpretive principles, including the common denominator. With the common denominator, the question is whether “we do not derive punishments from legal inference” also applies. That’s only Maimonides’ position—that with all the interpretive principles, “we do not derive punishments from legal inference” is said. The simple conception is that it applies only to an a fortiori inference. So what happens here isn’t really a fusion of two things, but rather one thing, and the second only removes some objection. And again, these are all kinds of examples of certain types of abstractions, and all these abstractions are made by stripping away characteristics. Or by fusing characteristics—but even fusing characteristics is itself bound up with abstraction. Because if I now take winnowing—how can I learn from winnowing that spitting is also liable? Because I take winnowing and say: leave aside now what is done in winnowing. I abstract away all the specific things that belong to winnowing. What do I see there? That the assistance of the wind does not exempt. That’s a kind of abstraction. I say: let’s abstract from winnowing the fact that here we’re doing selection and our purpose is this, to remove the waste and leave the food—leave all that. Let’s relate only to one element, one characteristic of winnowing: that the wind takes part in the matter. And now I take that and fuse it into something else. So all the processes, all the analogies we make, the generalizations we make, the fusions we make—all these things are bound up with processes of abstraction and illustration. Basically, in the end, I think that the most fundamental operations in the inferences we make are abstraction and illustration. All the analogies, inductions, deductions, all these things that we do are really different combinations of abstraction and illustration. We talked a bit about analogy, right? How do you make an analogy between two chairs or two frogs? Basically by abstracting to something and seeing both as particular cases of it. Again, it’s all the same thing—you see it when you look at it through these glasses. So every inference we make is basically some combination of abstractions and illustrations. It’s up and down, moving upward and downward. Maybe here is the place to add another point.

[Speaker K] One could ask: after all, sifting is sorting is winnowing is sifting—why count them? Wait, winnowing is by means of the wind. And that’s not the answer the Talmud gives.

[Rabbi Michael Abraham] Of course, because the Talmud understands that the essential primary labor is separating food from waste. That’s all; all three do that. Why should I care by what method you do it? Therefore the Talmud really says that in principle it should have been one primary category.

[Speaker K] Fine, but what’s the problem with saying, if—

[Rabbi Michael Abraham] If you go by differences that marginal, then there aren’t thirty-nine primary categories; then all the derivatives should have been primary categories. Because that’s fine—if with marginal differences, then either there could be many other primary categories that weren’t defined at all. But you’re assuming that isn’t so; there aren’t many more primary categories. Whatever resembles it, is it. Rather, what happened is that these three were all in the Tabernacle, says the Talmud, and therefore they are counted as three. Obviously it can’t be completely identical, because otherwise even if it was in the Tabernacle you wouldn’t turn it into three primary categories, right? They cultivated dyes—but they cultivated dye A and dye B and dye C. So maybe sowing galbanum, frankincense, and I don’t know what—each one is a different primary category. Why not? Because the difference there is apparently absolutely negligible, so it doesn’t matter that all of it was in the Tabernacle. So here it’s clear that it’s not true that only separating food from waste is relevant. Obviously the way we do it also has some significance. But that’s apparently a marginal significance. Meaning, were it not for the fact that it was in the Tabernacle, we would say it’s one primary category. So yes, I started to say—there is an American philosopher named Peirce who defines—we talked about analogy, induction, and deduction—he talks about abduction. I don’t remember if I mentioned it; I’m not sure; I think I didn’t. It’s very confusing. What else can there be? After all, analogy is from particular to particular or from general to general, meaning on the same plane. Deduction is from general to particular. All horses have four legs; this thing is a horse, so it has four legs. It’s a particular within the general, so you can derive it. Induction is the movement from the particular to the general. I have particulars and create from them a general rule. What else can there be? What other inferences can there be? Ostensibly that’s everything. Either from particular to particular, or from particular to general, or from general to particular. What else?

[Speaker B] General, particular, and general?

[Speaker K] No—

[Rabbi Michael Abraham] General, particular, and general is not from general to particular; it’s a linguistic form. It’s how the verse is written, in the form of general-particular-general. It’s not a movement of inference from general to particular and from particular to general.

[Speaker B] Yes, there can also be from general to general, which is also analogy—that’s what I said.

[Rabbi Michael Abraham] The particular you’re talking about is analogy—it doesn’t matter whether it’s general. Why? Because general and particular are always relative definitions. When you move from particular to general, the meaning is from a particular to a general of which that particular is a part. If you move to two generals—from all horses to all donkeys: if all horses are mortal, then all donkeys are mortal—that’s an analogy from particular to particular, where the particular is the group of horses. Because relative to donkeys, horses are not included in them; there is no relation of inclusion between them. So it’s not a relation between particular and general, but between general and general or particular and particular—it doesn’t matter. Now what is abduction? Abduction is an interesting point, because when we—think about how science works. By the way, it’s exactly like the common denominator. How does science work? We see examples, say, of bodies falling to earth. I let go of this pen and it falls to earth. This chair too, and this lectern too. Okay, now I say: good, what causes all these fellows to fall to earth? Aristotle said because, of course, they want to return to their source. But in modern thought we say it’s because they have mass, right? Bodies with mass fall to earth. That’s a generalization, and that generalization is basically induction. You take particulars and say: all these are bodies with mass, so I create from this a rule—every body with mass falls to earth.

[Speaker N] Those are laws of nature, induction.

[Rabbi Michael Abraham] In a moment we’ll see—not exactly; in a moment we’ll see. Of course, you can make generalizations in various ways. Who says that’s what they have in common? Maybe what they have in common is that they are white. Say this and this and this—these three are white. So maybe white things fall to earth. Fine, you can test that too and see that this one is brown and still it falls. I can find a common characteristic for all four of these. There is always some characteristic that will be common to whatever objects you collect. You can always find some characteristic. But we nevertheless have some ability to distinguish what is essential and what is nonessential. A miracle in itself—maybe I’ll talk about that later too. That’s ordinary induction. What is abduction? Abduction is an attempt to produce a theory from these facts, when I ask myself why all bodies with mass fall to earth. The statement that all bodies with mass fall to earth is simply a movement from particular to general. I have particulars that I know about, and I produce a law that deals with the whole group, the general. So that really is just generalization, a move from particulars to the general. But when I ask why it falls to earth—and many times through that I arrive at the generalization—the question of why, the movement from the particulars to the theory, is much more complex than the movement from particulars to general. How do you invent a theory? You say there is a force of gravity, and if you enter into the details then there are descriptions of it and gravitons, and you can get into its innards and see how it works—and nobody has ever seen any of that. Nobody has seen it. It is an abstraction, or an abduction, that we make from the cases we see, the concrete cases. We perform experiments in the laboratory, and from that we produce some theory within which there are what are called theoretical entities. Theoretical entities means basically some kind of entities or concepts that are created only in the theory in order to explain the facts we observe. Nobody has seen those entities, but they explain the facts, and through that I hypothesize that they are probably there, that they exist.

[Speaker N] And that’s not certain.

[Rabbi Michael Abraham] No, nothing is certain. A generalization isn’t certain either. In that sense there’s no problem.

[Speaker B] A law of nature isn’t certain either.

[Rabbi Michael Abraham] Nothing is certain. You say: I think all bodies with mass fall. Are you sure? Maybe there is some body with mass that won’t fall? If I haven’t seen it? You can never be sure, ever.

[Speaker B] Certainly not in a mathematical sense.