Deontic Logic and the Relationship Between Prohibitions and Positive Commandments – Lecture 6

[Rabbi Michael Abraham] We’re basically at the final stage of this topic, and I want to present, really just briefly, not to get too deeply into formalizations, but enough to show what the significance of all this actually is. I think it has an interesting significance specifically in these books on logic. We have two goals. We always say at the beginning of every book that we have two goals: one goal is import, the second is export. Import means importing contemporary or logical techniques in order to analyze halakhic topics. Export is an attempt to export halakhic insights in order to solve existing problems in other fields. Now here it seems to me that there’s mainly export more than import, because the import doesn’t help much. Meaning, and this is a common phenomenon in logic a lot of the time, there are people who are formalophiles, meaning people who, when someone formalizes some topic, go into a high because they see it being written with formulas instead of words. So wow, this is really Torah and science, for them it’s an amazing achievement. Most of these things are worth nothing. I mean, most of them are basically just translating into mathematics what is written in Hebrew, you’re just writing X instead.

[Speaker B] Fine, it’s a language.

[Rabbi Michael Abraham] But sometimes mathematical language helps. In physics too, for example, mathematics is used as a language, but without the mathematics you couldn’t do almost anything. Because translating into mathematical language has enormous power. It gives you things you can’t do in ordinary language, or almost can’t do in ordinary language without the formalization. And that’s the test. Meaning, in a place where you do a formalization that helps you do things you couldn’t do without it, it has value. If you just translated from Hebrew or English into mathematics, then it’s just a translation, so what’s so interesting about that? Therefore I think formalization has value in the area of import only where the formalization helps you do something you couldn’t do without it. Then the translation has value, because then you understand why it’s worth doing; it’s useful in some sense. And here, in this context, I think the benefit is very slight in the sense of import, but specifically in the sense of export it’s very significant. There are many problems people struggle with, and from a halakhic perspective—I don’t even really need formalization to understand it—the whole thing just doesn’t get off the ground. I mean, sometimes it’s simply mistaken discourse; you see it immediately. But this applies not only to Jewish law—that’s what’s nice here. You solve problems; it’s not that Jewish law doesn’t suffer from these problems, but from Jewish law I understand why in the realm of morality too they’re not doing it right. So there too, these problems aren’t really real problems. And I’ll start with what I already spoke about a bit at the beginning of this topic. We’re basically talking about three deontic operators. That means three actions or three concepts or deontic expressions. Deontic means obligation— theories of obligation, of norm. These are forbidden, permitted, and obligatory. Okay? So we have this as obligation, which is obligation, okay? Permitted, which is P, and forbidden, which is forbidden. Okay? These are the three concepts: obligatory, permitted, forbidden. Okay? These are basically the three basic markings in deontic logic. Now the big problem is that since these things don’t talk about facts—I spoke at the beginning about the naturalistic fallacy, about how you can’t derive norms from facts. Now regarding facts, we know the relations between things. If you say that something X implies Y, then you know that not-Y implies not-X. Meaning, relations between facts we know, and logic generally deals with factual statements. Logic and logical relations deal with factual statements. Now you know that if both X is true and Y is true, then in particular X is true. Okay? That’s a relation between facts. Now what do we do when we talk about logic? Some things are similar—deontic logic, yes, deontic logic. Some things, if both there is an obligation to do X and there is an obligation to do P, then in particular there is an obligation to do X. But the question is whether there are relations between claims, more sophisticated relations between deontic claims. And there’s a very basic question here: in what language do you even deal with this? How do I test relations between these statements? How do I prove things? For that, what’s called in logic semantics is needed. Meaning, you need semantics; that’s the syntax. Syntax is the form, meaning the formalization of the concepts is something formal. Form means form in English, right? So now I want to know what their semantics is, what the meaning of the matter is, to give it some semantic interpretation so that I can work with it. Now there is a brilliant idea that was found—I don’t know who first found it—that makes it possible to find relations between deontic claims. And in this context people use what is called modal logic. So let me briefly explain what modal logic is. Modal logic originally came to describe how we talk about concepts of necessity. Meaning, a logic of necessity and possibility. Meaning, it is necessary that X. That’s not the same as saying it is true that X. It is true that X—say it is true that now it is night. Okay, that’s a true statement. Is it necessary that it now be night? I don’t know. The world could have been built differently so that now it wouldn’t be night. I don’t know. So it doesn’t have to be a necessary statement even if it’s true. There is a difference between saying something is necessary and saying something is true. Now how do I express necessity in terms of facts? Because necessity too is actually something factual, but not at the simple level. When you say that the Holy One, blessed be He, is a necessary being, what is the difference between saying that and saying that He exists? There is a difference; He exists in some sense a bit differently from the way I exist. Meaning, I can’t imagine a state in which He does not exist. How do you express that logically? What is the meaning of that? So for this they invented what is called modal logic. Modal logic means that I look at all possible worlds. Hypothetical worlds—they don’t exist—but I define a collection of possible worlds, there are lots of them. Okay? A necessary thing is something that exists in every possible world.

[Speaker B] That’s the modal interpretation. Meaning, to say that something is necessary means to say that it exists in every possible world.

[Rabbi Michael Abraham] How do I know that I’ve scanned all the possible worlds? No, this isn’t empirical, you can’t scan them because there are no such worlds, it’s only hypothetical.

[Speaker B] I’m only giving an interpretation to the statement. So can I say that the set of all possible worlds is our world? And that’s it? No, you can’t say that, because the set of all possible worlds is everything possible. What do you mean? There could be a world that isn’t like ours and is still possible. There could be a world in which there is one less person than in our world; that is possible.

[Rabbi Michael Abraham] But there are lots of worlds whose possibilities I haven’t thought of. Fine, you don’t need to think of all of them. This isn’t a detailed description of them, it’s only an interpretation. I just want to explain what one does with it. It’s only an interpretation of how to explain the concept of necessary. Necessary means: in every world you can imagine—let’s call it a possible world—this thing will exist. There is no possible world in which it does not exist. That’s what it means to say that the thing is necessary. True even if I don’t know?

[Speaker B] If I don’t know that—after all, among the worlds I haven’t imagined, maybe suddenly I’ll imagine some world where it won’t be so.

[Rabbi Michael Abraham] But you’re looking at it empirically, you’re asking how I’ll know—will I go through all the worlds? No, this isn’t empiricism. It’s a question of semantics. Meaning, I’m giving meaning to the concept “necessary.” What is the meaning? In every possible world—I can’t know what all the worlds are—but if I say something is necessary, then I have said that in every possible world it holds. When I say that two plus two equals four, then I say this is necessary. There cannot be any imaginary world whatsoever in which two plus two is not four. There could be a world in which a body doesn’t fall to the earth because there is no force of gravity there. Theoretically there could be such a world, a different physics. Gravity is not a logical necessity. It is a physical reality; that’s how our world is built. There could have been another world in which there was no such law, some other law, or no law at all. Okay? So, for example, that I cannot say must exist in every world I can imagine—gravity need not exist. But two plus two equals four must hold in every world. Okay? When I say that the Holy One, blessed be He, is a necessary being, what that means is that there cannot be a world without a creator. Let’s say that’s what I’m really saying; that’s the interpretation of the concept that the Holy One, blessed be He, is a necessary being. In every imaginable world, no matter how imaginary. By the way, this is an interesting question, because this interpretation with respect to the necessity of the Holy One, blessed be He, I’m not sure really holds up. Meaning, I can imagine a world that exists without the Holy One, blessed be He, without a creator. Yes, theoretically. Theoretically that could be, and then the question is whether that means He is not a necessary being, or whether the modal interpretation is not good for describing that necessity. But there are many philosophical questions behind the formalization here, questions worth discussing, but I’m not going to do that here. So, the modal interpretation. Say, a triangle—in a triangle, in a triangle there is an angle of eighty-six degrees. That is not necessary; not every triangle has to have such an angle. But there are such triangles. What does that mean? That there are possible worlds in which there are triangles with an angle of eighty-six degrees. At least one such world exists. Okay? Among the worlds one can imagine, there are infinitely many such worlds. Okay? That is the meaning of the concept “possible.” All right? So the concept “necessary” means that it exists in all worlds; the concept “possible” means that there is at least one world, or there are worlds, in which it holds. That’s what it means to say that the thing is possible. Now what’s the advantage of this interpretation? The advantage of this interpretation is that now I can prove, on the basis of the interpretation—and this is where I’m getting to it—it’s not an empirical question of how I know whether something is necessary or not. It’s not a way of knowing whether something is necessary or not; on the contrary. First I know that it’s necessary, and now if it’s necessary, then that means it will be so in every possible world. So what good is that? What does that add? It adds something in order to find relations between claims. For example, the modal claim—say, “it is necessary that X” implies “it is possible that X.” Fine? What is S S P? Never mind. So if it is necessary that X, that implies that X is possible. Sounds reasonable, right? If it’s necessary, then certainly it is at least possible. Now how do I do that in terms of worlds? I say: very simply, there it comes out immediately. This process is a process of inclusion, right? Here it means that X holds in every possible world, so in particular it is obvious that there is at least one world in which X holds. Therefore the necessary implies the possible, but not the other way around. The possible does not imply the necessary. But “not possible”—it is not true that “possible that X” implies “it is not true that necessary that X.”

[Speaker B] Meaning, you can prove it, but is this just ordinary logic that you’re drawing now?

[Rabbi Michael Abraham] What do you mean?

[Speaker B] How is this logic different from ordinary logic?

[Rabbi Michael Abraham] This logic talks about concepts like necessity and possibility; in ordinary logic there are no relations between them. You have to generate those relations and show them. In order to show that, you need to find some interpretation of necessary and possible. The modal interpretation is one possible interpretation. And then, in terms of that interpretation, you can show things. Sometimes I’ll show you more complicated things that you won’t be able to grasp in a simple intuitive way. And still you can show them using this interpretation. And what’s its idea? Its idea is that I translate—and this is the important point—that I translate concepts of necessity and possibility into concepts of facts. These are theoretical facts, but they’re still just facts. Meaning, instead of saying that X is necessary—I don’t know what “necessary” is, I don’t logically understand what “necessary” is; intuitively I understand it, but what do I do with it logically? I don’t know, I don’t know what to do with “necessary.” So let’s translate. It means that in all possible worlds this holds; that is, this is a fact. Facts I know how to handle. Therefore I am basically translating the concepts necessary and possible into collections of facts. Basically into a fact—a fact that is a collection. Doesn’t matter. Okay? And with facts I know how to deal. Now this point serves us also in the context of deontic logic. So we want to find the relation between these concepts, and there too I basically use deontic logic and say as follows: suppose there is some world, our world, and I want to know whether in our world there is an obligation to do P. P is some act, say giving charity. Fine? Is there an obligation in our world to give charity? So what do I do? I translate it by a modal translation. I basically say: let’s take all the perfect worlds. W1 numbered, call it W1, one, two, three—there are infinitely many worlds, or many worlds, doesn’t matter how many—perfect ones. What’s the difference between them? This world has a hundred inhabitants, that one has a thousand inhabitants. That doesn’t touch its moral perfection. Okay? They differ, they are different worlds. But whichever world it is, if it is morally perfect, fine? then P must hold in it. That means that in world W1 there is an obligation to do P. Because in all the perfect worlds equivalent to world W1—it’s a series of worlds—in every such world P holds. So once again I have translated the concept “obligation” into simple facts, namely, P occurs. “P occurs” is a simple factual claim; I know what to do with that in logic. Okay? And now I use—or “P is permitted” means there are worlds in which P happens. That parallels possibility. Right? “P is permitted” means that in some worlds it holds, and in others it may not hold. Obviously if it holds in all of them and is obligatory, then it is also permitted. Again, you can prove in exactly the same way that if O of P then that implies I of P. Meaning, if it is obligatory then certainly it is also permitted. How do I know? Because if it exists in all worlds, then certainly there are worlds in which it exists.

[Speaker B] You translated it into facts? So then it’s an ordinary logical relation.

[Rabbi Michael Abraham] Exactly, so it’s just simple inclusion. It’s inclusion of sets of facts. Okay? So this modal meaning, I’m saying this only very briefly, but that is basically the move. This modal meaning basically allows me to find relations between modal claims, because I have in fact turned the non-modal—the deontic—claims. I turned the deontic claims into collections of factual claims. Okay? Now this is a little surprising, because there are all kinds of points here that maybe we’ll see later, where it turns out that there’s some problematic leap here. After all, we spoke about the naturalistic fallacy—that you can’t base norms on facts. And here I’m basically translating a norm into collections of facts. How can it be that you can translate a norm into a collection of facts? Something here can’t be right; there must be something normative even in the language of translation.

[Speaker C] There’s a definition here of—

[Rabbi Michael Abraham] A perfect world—perfect, exactly. The point at which the normative dimension enters into the translation is that I’m running only over perfect worlds. Now for that I need to decide that this world is perfect. That decision is a judgment, meaning a normative decision. Okay? I don’t run over all existing worlds; from among all the existing worlds I focus only on the perfect worlds. That focusing is a normative act; it is not a factual act. And now I run over facts within that world. So this interpretation supposedly turns everything into facts, but not really. And maybe we’ll see later that perhaps some problems come in here—that what we thought we were gaining with this translation, we may not really be able to gain, because we are in fact smuggling the normative dimensions in here through the back door. Meaning, this is not a translation into pure facts alone. Okay. So these points now give us several relations that I was speaking about intuitively. So, for example, O of P is fully equivalent to F of not-P—that’s negation. Okay? That R there. So “it is obligatory that P” means “not-P is forbidden.” Okay? That’s one relation. “P is permitted” means it is not true that there is an obligation of not-P. Okay? What “P is permitted” means is that there is no obligation of not-P, meaning P can also happen. Okay? This is very parallel to possible and necessary, because obligation is necessity and permission is possibility. Basically the parallel is quite natural. Okay? Even though there are some differences, it’s a natural parallel. Therefore there is this relation, and a third accepted relation, say, which we spoke about, is that O of P implies I of P. Okay? Meaning if there is an obligation then certainly it is permitted. Because if in all worlds it holds, then certainly there are worlds in which it holds. All these things can be proved by means of the modal interpretation. Meaning, run over the worlds and you’ll see that, say, if it is obligatory that P, then what does that mean? That P holds in all perfect worlds. Right? That means that in all worlds not-P does not hold. That means there is a prohibition of not-P.

[Speaker C] Didn’t you say it’s a bit hard to move between obligation and prohibition through negation?

[Rabbi Michael Abraham] Wait, right now I’m describing ordinary deontic logic. This is exactly where the corrections we learn from Jewish law will come in. Okay? But this is how it’s presented in every essay or book on deontic logic; you’ll see it presented as simple. This is where they start. Okay? Of course, already these things are not correct. That’s what creates a large part of the problems. So yes, for example, I just showed you why “it is obligatory that P” is equivalent to “not-P is forbidden.” How do I do that? “Not-P is forbidden” means that in all the perfect worlds there will not be P, right? Or there will be not-P. Okay? That is called prohibition. “It is obligatory that P” means that in all perfect worlds P holds. Say there is an obligation to give charity; that means that in all perfect worlds people give charity. Fine? What does a prohibition on not giving charity mean? Right, so the prohibition on not giving charity means that in all perfect worlds there is no person who does not give charity. Okay? Which again is a translation into facts. Now since giving charity and not giving charity, P and not-P, are ordinary negations, not deontic negations, they are factual negations, then I know what to do with them, right? So here I am able to use factual negations in order to generate an inversion between deontic operators. Okay, that’s the advantage of this translation. It’s a very beautiful idea; someone who doesn’t know it may not appreciate how brilliant it is.

[Speaker B] What’s the advantage of the translation?

[Rabbi Michael Abraham] The advantage is not of the formalization but of the move to deontic logic. The advantage is that I know what to do with P and not-P. I know that wherever there is P there won’t be not-P, okay? At the level of facts. If people give charity, that means it is not true that they do not give charity; at the level of facts the relation is simple. How do we get from that a relation between obligation and prohibition? Obligation and prohibition are concepts that are not factual. It’s very simple now, according to the modal interpretation. Because if obligation means that in every—“it is obligatory that P,” in every—that means that in all worlds P holds, and “not-P is forbidden” means that in all worlds it holds—or rather, does not hold, sorry— not-P. Fine? Now look at each perfect world individually. The relation between P and not-P is factual, so that I know. If P holds, that means not-P does not hold, okay? So I can thereby also infer the relation between O and F.

[Speaker B] It all begins and ends with the fact that you turned norms into facts.

[Rabbi Michael Abraham] Right, exactly. That’s the whole idea, and it’s a brilliant idea. Meaning, this whole idea that allows me basically to prove whatever I want in deontic logic is thanks to this modal interpretation. Meaning, thanks to the fact that I manage to turn it into facts.

[Speaker B] And that fits with the material relation.

[Rabbi Michael Abraham] So as I said, it works only because we quantify, because we scan only the perfect worlds. Now the moment we scan only perfect worlds, we have already inserted deontics inside here. You need to decide, from among all the existing worlds, what a perfect world is. So a perfect world is already a deontic judgment, meaning already something normative. Here the normative dimension actually enters, and we’ll see later whether that creates problems or solves the problems. Just a moment. Okay, so that’s the general idea. Now there are several basic problems in deontic logic—there are many, but I’ll just give a few examples so you can get an impression of what’s at issue. Say, saving a life on the Sabbath, okay? I want to describe this in deontic logic, this clash between saving life and the Sabbath. So I say: in the perfect world, basically, in the perfect world from the standpoint of the commandment of Sabbath observance, in every perfect world no one desecrates the Sabbath, okay? On the other hand, in every perfect world a person who is in danger is saved, right? Because “and live by them,” meaning there is an obligation to save—“do not stand idly by your neighbor’s blood,” “and live by them,” not “do not stand idly by your neighbor’s blood.” So in every perfect world a person in danger is saved. Now how do I present in deontic logic the obligation to save a person at the price of desecrating the Sabbath? After all, in a perfect world from the standpoint of Sabbath there are no Sabbath desecrations.

[Speaker B] That’s not Sabbath desecration?

[Rabbi Michael Abraham] No, we’ll get to that afterward with a solution, but first I want to present the problem. I have no way of presenting the problem in standard deontic logic. Because in a perfect world there cannot be a world in which we desecrate the Sabbath or fail to save—meaning, one of the two. So a world in which either of those options occurs is by definition not a perfect world. A world in which we will have to fulfill—manage to fulfill—both norms would be perfect with respect to both norms, but there is no such world. Okay? Unless it’s a world with no Sabbaths, but… But there are supposed to be perfect worlds that include Sabbaths.

[Speaker B] A world with no Sabbaths is a world with no human beings.

[Rabbi Michael Abraham] Yes, a world with no human beings—that really could be a perfect world. They always say at the university that without students it could be perfect. Who needs them there? Without patients, without patients in a hospital, right. So that’s one possibility. Or I don’t know—say, a positive commandment overrides a prohibition, right? A positive commandment overrides a prohibition. So you have a positive commandment to eat matzah and a prohibition against eating new grain, okay? And now you have no matzah from old grain. So the positive commandment to eat matzah overrides the prohibition of new grain, and so you bake matzah from new grain. But again, when I want to describe this in deontic logic, then the perfect world with respect to eating leaven—sorry, with respect to eating matzah—is a world in which everyone eats matzah. In that perfect world, no one violates the prohibition of new grain. But there cannot be a world that is perfect with respect to both these norms. There is no such world. Before I discuss the question of what to do, there is no such world. Meaning, I cannot discuss the question in terms of ordinary deontic logic. Another example: what happens with a prohibition linked to a positive commandment? All these concepts, by the way, also exist in morality, not just— I took halakhic examples, but this is true in morality too. There is a contradiction between—if we once spoke about Sartre, right?—with the student who came to him in occupied Paris and was torn about what to do. His mother had been left alone in Paris and was already elderly and needed help. The father was collaborating with the Nazis, the son—the young man’s brother—had been murdered by the Nazis, the woman was left alone. Now he is torn: should he go to de Gaulle, join de Gaulle, the Free French army, fight the Nazis, or remain in Paris to help his mother? That’s an example—it’s not halakhic, it’s a moral question. There are two values here, both positive values: to fight evil and to help your mother. Okay, what do you do in such a case? Conflicts don’t exist only in Jewish law; conflicts also exist in morality. The same with a prohibition linked to a positive commandment. When you have stolen, there is a commandment to return the stolen object; that’s morally true too, not just halakhically. Okay, I’m using halakhic terms, but it’s true in morality too. Okay, so now let’s talk about a prohibition linked to a positive commandment. So I want—a prohibition linked to compensation, no—

[Speaker B] Doesn’t matter, returning stolen property, what exactly is it?

[Rabbi Michael Abraham] The question is how you present the obligation. And this is an even deeper question than the previous one. In the previous question we said that after we solve the problem that a positive commandment overrides a prohibition, then I’ll arrange it, I’ll create a perfect world in which if there is such a prohibition that gets violated, it is only when a positive commandment overrides it. Fine? In every other situation it won’t be a perfect world if I violate the prohibition. But here you have no way to present it at all; no solution will help. In the case of returning stolen property, after all, in a perfect world there are no thefts. How will you present this norm, the obligation to return stolen property? There is such an obligation, one of the commandments in the Torah, right? An obligation to return stolen property, or a moral obligation to return stolen property. How do you present this obligation in deontic logic?

[Speaker B] In a perfect world there is no such obligation.

[Rabbi Michael Abraham] In a perfect world there is no theft.

[Speaker B] Who said it has to be a perfect world?

[Rabbi Michael Abraham] Because if we’re not talking about a perfect world, then you have no way to present the obligation to return stolen property. So show me a deontic logic in which you can also handle this obligation. After all, the goal of deontic logic is to handle all the obligations that apply to us, right? Among other things, we have an obligation to return stolen goods; it’s one of the commandments. Okay, now how do you present this in deontic logic? This is an obligation that by definition exists in an imperfect world, right? It is an obligation that is born when I am in an imperfect world.

[Speaker B] Why are you talking about an imperfect world?

[Rabbi Michael Abraham] I’m talking about a world that has people in it. What?

[Speaker B] A world that has people in it—even if it’s not perfect—about it

[Rabbi Michael Abraham] You can

[Speaker B] present the—but

[Rabbi Michael Abraham] you don’t have a logic that fits, because deontic logic

[Speaker B] works only in terms of perfect worlds.

[Rabbi Michael Abraham] I don’t know what to do with deontic logic when I don’t translate it into perfect worlds. So I have a logical problem; I don’t have a problem of what to do with it. I understand what it means that one must return stolen property. But my problem here is now a mathematical problem, a logical problem. That is, how do I build a logic that can also handle this kind of problem in a non-perfect world? It’s a scientific problem, not a religious problem. Yes, okay, so the question is how you translate these things. Now there are all kinds of additional things, for example conditionals, deontic conditionals. A deontic conditional—for example, in deontic logic you can prove that if it is obligatory that if P then Q—returning on the Sabbath—if you stole, return it, okay? It is obligatory that if P then Q; all of that is the obligation. Okay? So let’s formulate it differently: how do I symbolize the obligation to return stolen property? There are those who want to symbolize it this way, but if you symbolize it this way you can show, in terms of possible worlds, that this also holds, and it is equivalent to this. How do I know? Because if it’s an obligation, that means that in every world where there is P there is also Q, right? Let’s move from there. Because in every world, if P holds then Q holds; there cannot be a world in which there is P and not Q, because it is an obligation, so in every perfect world, if P holds then Q holds. Okay? So what does that mean now? That basically if it is obligatory—suppose now that P is obligatory—then that means that P holds in every world. Now from here it follows that in every world where there is P, Q also holds, so that means that Q also holds in every world. Meaning that this is equivalent to this; this statement is equivalent to that statement. In terms of possible worlds you can immediately see it. Although here, for example, you can see why this interpretation is useful: if I had asked you this without that interpretation, it would not have been so simple to arrive at the fact that saying this is really the same as saying that. On the contrary, in a moment we’ll see that intuitively it’s not true at all. But in deontic logic that’s what comes out, and it can be proved easily. I already heard that. Okay, now come on: if that really is the correct symbolization of the obligation to return stolen property, then it means that if there is an obligation to steal, then there is an obligation to return. There is no obligation to steal; rather, if a theft happened, then you must return it, right? So there is something problematic in this symbolization. At most, maybe you could symbolize it this way: P implies that Q is obligatory. If P happened—not if P is obligatory, but if P happened—then there is an obligation regarding Q. Meaning: if you stole, then there is an obligation to return. Not that there is an obligation that if you stole then you return it. Now, the statements are similar, and that is the advantage of mathematics, because in mathematics you see that even though the statements are similar, you can immediately see what the difference is between them. That is, it’s completely clear why this is different from that. When you say it in everyday language it’s harder to see the difference between them. Okay. So this is actually a more reasonable symbolization of the obligation to return stolen property, because basically I start from a fact, not from an obligation, and derive an obligation from it. Okay. And then it may still not solve my problem of how I present this within a framework of perfect worlds, because if P happened and it is theft, then the world is not perfect. Okay. So it doesn’t really solve the problem—the problem is still there—but in terms of the symbolization of what I mean when I say the obligation to return stolen property, this is a more reasonable symbolization than that.

[Speaker B] Unless you say that there is no obligation not to steal. Why? It says, “Do not steal.”

[Rabbi Michael Abraham] Correct, but doesn’t that mean there is a prohibition against stealing?

[Speaker B] Where is there?

[Rabbi Michael Abraham] In Jewish law—what is “Do not steal”? What do you mean? Morally too there is a prohibition against stealing, and also—

[Speaker B] There is an obligation to return the stolen item.

[Rabbi Michael Abraham] There is also a prohibition against stealing—“Do not steal,” what do you mean? And “he shall return the stolen item that he stole”—that is a positive commandment that detaches the prohibition. So that, for example, is another case. I’ll show you why the conclusion is actually very problematic. One example: on a Jewish holiday there is a positive commandment to eat a meal, the holiday meals. If one eats, then one recites a blessing. Right? Now, can you derive from this that there is in fact an obligation to eat? Fine. And if one eats, there is an obligation to recite a blessing. Okay. Can one derive from this that on a Jewish holiday there is an obligation to recite a blessing? Why not? Seemingly yes. Really? No, it can’t be. In terms of the interpretation of perfect worlds, you can prove that these two imply that. Okay. But it is obviously not true. There is no commandment on a Jewish holiday to recite a blessing. On a Jewish holiday you will recite a blessing; in every perfect holiday world you will recite a blessing, but it is not true that there is a special commandment of blessing on a Jewish holiday. There is no such commandment. Meaning, this does not correctly describe the meaning of the commandment. It describes what will happen. What will happen is that always, on every Jewish holiday, I will recite a blessing. That is true, obviously; practically speaking, that is what will happen in every perfect world. But that does not mean there is a commandment to recite a blessing. So here—

[Speaker B] That already directly undermines the modal interpretation, because it means that there could be—

[Rabbi Michael Abraham] A situation that holds in every perfect world, and nevertheless it will not be an obligation.

[Speaker B] It will not be defined as an obligation to recite a blessing on a Jewish holiday, even though it will hold in every perfect world, because there is no commandment to recite a blessing on a Jewish holiday. The commandment is that if you ate, then there is an obligation to recite a blessing, and there is an obligation to eat. Those are the commandments in the Book of Commandments. Such a commandment does not appear in the Book of Commandments. Someone who fulfills it has not fulfilled a commandment—I mean beyond the commandment of Grace after Meals; that commandment, yes, but it is conditional. What? On the condition that he ate. Yes, exactly. So there isn’t—maybe there isn’t a commandment to recite a blessing on a Jewish holiday. There is the commandment of Grace after Meals if you ate. You did not fulfill two commandments if you recited the blessing after eating. There is something else that is not conditional. What? There is a commandment to recite Shema every morning. Okay. Is there a commandment to recite Shema on a Jewish holiday? No. Yes, well—

[Rabbi Michael Abraham] It’s the same idea.

[Speaker B] Yes, but it’s more so, because it’s not an “if,” because here the “if” is: if morning comes out on a Jewish holiday, then you are obligated.

[Rabbi Michael Abraham] Correct, but the Jewish holiday is a date. It’s like there is no commandment to recite Shema on a Tuesday, so you could say there is a commandment—just as there is on Tuesday, there is also on a Jewish holiday. Meaning, I think it’s a bit different from here.

[Speaker B] No, it’s different, it’s different.

[Rabbi Michael Abraham] So perhaps there is room to say that there is a commandment to recite Shema on a Jewish holiday, simply as a date; on every date there is a commandment. So that’s one example; there is another example, yes, that’s—

[Speaker C] But in my opinion you need to distinguish between the obligation to eat and “if P happens,” because not always if P happens then you must recite a blessing. For example, once in Ashkenaz, as I understand it, menstruating women did not recite Grace after Meals according to some customs, so even though they are obligated to eat on a Jewish holiday, they do not recite the blessing.

[Rabbi Michael Abraham] Fine, but that’s not important; it’s an exceptional case. But I’m saying, leave aside that exceptional case—let’s say that indeed anyone who eats—

[Speaker C] Needs to recite a blessing; it’s not enough that you ate, it has to be that you ate and that this condition holds.

[Rabbi Michael Abraham] So let’s talk about a system in which there isn’t that invention. Even then it does not follow; there is no obligation to recite Grace after Meals on a Jewish holiday. Why not? You can say that effectively, if there is an identity between the obligation to eat and—then that identity is an identity in practice, in facts. Factually, in every perfect world they recite Grace after Meals. There is an obligation to recite a blessing. But that does not mean there is a positive commandment to recite a blessing on a Jewish holiday. Therefore I say there is some jump here from facts to norms that does not actually reach the norm. It reaches “in every perfect world, call it the fact,” but that does not mean there is such a commandment.

[Speaker C] And therefore this equivalence between saying “there is a commandment” and saying that in every world it happens is true only in one direction. If there is such a commandment, then in every perfect world it will happen.

[Rabbi Michael Abraham] But if in every perfect world it happens, it is not certain that there is such a commandment.

[Speaker D] Why, why, why is there this separation between commandment and obligation? Why not? Because if you leave it as an obligation, it’s an obligation. No, commandment, obligation—what’s the difference? Commandment and obligation.

[Rabbi Michael Abraham] There is no obligation, no—

[Speaker D] All the same, there is an obligation to recite a blessing because there is an obligation to eat.

[Rabbi Michael Abraham] No, there is no obligation to recite a blessing; it will simply happen, not that there is an obligation to recite a blessing.

[Speaker D] It will happen; practically, there is no obligation either.

[Rabbi Michael Abraham] The obligation is to recite a blessing because you ate, not because it is a Jewish holiday. Correct? You are not fulfilling two commandments when you recite the blessing; you are fulfilling one commandment, Grace after Meals. You are not fulfilling “the commandment of Grace after Meals on a Jewish holiday.”

[Speaker B] Yes, but the obligation—the obligation holds; the commandment does not hold.

[Rabbi Michael Abraham] Not the obligation; the fact holds. What? Not the obligation—the fact necessarily holds. But to say that the fact necessarily holds is not identical to saying that there is an obligation. That is exactly the point. You keep identifying them, but I—and that is what I want to show. Even though the fact will hold in every perfect world, that does not mean there is such an obligation. This identification assumed by deontic logic is not really—really not correct. That is, it does not fit our deontic intuitions. Another example—someone working on this issue gave the following example: if there is an obligation to go out to the May Day parade in the squares of Moscow. Now there is also an obligation that if you are walking in the street and you see someone in distress, you need to save him—the law of “do not stand idly by your neighbor’s blood,” like the Good Samaritan. Okay? Now Moishele did not fulfill his obligation to go out to the May Day parade. Yankele was there on that street and was in distress. So of course Moishele did not save him because he was not there. But he did have an obligation to march there. And whoever marches there and sees someone in distress is obligated to save him, so in fact he has an obligation to save him. Now, does the fact that he did not go out to the May Day parade mean that he will also be sued for not saving Yankele? This is the Grace after Meals example, right? It’s the same thing. But it’s more intuitive because it’s moral. You say, what—does he also have a claim against him for why he didn’t save Yankele? No. If I had been there and hadn’t saved him, you could have claimed against me. And it’s true that in practice, in every perfect world, I would have had to save Yankele—but that does not mean they can come to me with complaints that I didn’t save Yankele because I didn’t go out to that parade. Okay? So that is another example. There is yet another example, what is called contrary-to-duty, CTD. That is, what happens if someone—basically this is like returning stolen property but a more sophisticated case: the rapist and the seducer. Meaning when someone raped a young woman or something like that, then “she shall be his wife,” okay? And afterward “he may not send her away all his days.” So basically the moment he committed one prohibition, an obligation fell upon him to marry her; after the obligation to marry her took effect, a prohibition fell upon him to divorce her. Again, it is a bit like returning stolen property, basically, okay? But with more stages. There too, the same thing: you have no way to present this in a perfect world, because in a perfect world no one rapes, and if he marries then he does not divorce—meaning there is no—therefore there is no way to present this kind of obligation in deontic logic.

[Speaker C] Why does it have to be in a perfect world? What? Why do you need to formalize all these things into a perfect world?

[Rabbi Michael Abraham] How else would you formalize it? How would you do deontic logic without the interpretation of perfect worlds?

[Speaker C] No, why not just present it the way we say it?

[Rabbi Michael Abraham] So then what is the relation between O and P? How would you do the calculation? How would you prove claims? You prove claims with the deontic interpretation; there is no other way—or at least I don’t know another way—to prove these claims. We have intuitions about them, of course, but if you’re looking for a way to prove them, then you need something systematic—show it in a formal way, give it to a computer to prove. The moment you talk about sets of facts, the computer can immediately check containment.

[Speaker B] Meaning all the transition from norms to facts becomes possible only in perfect worlds. Yes.

[Rabbi Michael Abraham] And you need that transition in order to be able to handle deontic operators. Without it you can’t handle them. Okay? Again, the problem is not a substantive problem in moral theory, in theory. In moral theory I know how to deal with these things. The problem is a formal problem, a mathematical problem. How do you build a logic that will manage to deal with this sort of claim, or this sort of problem? Okay, it’s a technical problem, not—not a moral problem.

[Speaker B] In the world of mathematics, is there such a branch, the concept of deontic logic?

[Rabbi Michael Abraham] Yes, in logic it is a branch of logic. I wouldn’t say there is a huge, huge amount of work on it, but there is—there are groups of people in the world who work on deontic logic. There are articles and books written on it, yes. Now there are all kinds of paradoxes that come out of it. Well, it’s a bit—some formalizations, and I’m not sure I’ll have time to get to them. For example, I think, the claim—the claim that O of P implies O of P or Q. Okay? Because if P is true, then P or Q is also true, okay? So if in all worlds P holds, clearly in all worlds O of P or Q also holds, because in particular P holds, right? Now from this you can somehow derive that either it is obligatory that P or it is obligatory that Q—that is already not true. If there is an obligation that Q—in short, all kinds of problems of this type are created because of the modal interpretation. Not only because of it, but many of them are because of it. Now the claim—the fundamental claim—there are various other paradoxes here; I won’t get into all of them now. The most basic claim, I think, is the claim against the fundamental identity. In fact, when we look at the relations between deontic acts, we said that O of P is equivalent to “it is not true that F of not-P.” Okay? It’s the same thing. To say that it is obligatory that P is to say that it is not true that it is forbidden—wait—that not-P is forbidden. Okay? That not-P is forbidden. This basically means that one of them is redundant. Whatever you want to write with F you can write with O; just change the predicate’s direction, change the negation, turn a positive into a negative, a negative into a positive. You can write F of P; instead of that you can write O of not-P. Okay? And then it is simply redundant. Meaning, to say “obligatory” and to say “forbidden” are two—one of the terms is unnecessary; you can use only one. And here, as Oren rightly noted earlier, this is the first point from the analysis we did: from Jewish law it comes out that this is not true. Because there is no way to express, say, if I speak of this as a positive commandment and this as a prohibition—yes?—there is no way, in fact, to express a positive commandment in terms of a prohibition. This identity is not correct. Now many of the paradoxes of deontic logic come from this identity. And this identity is not correct. The claim is—without getting into all the formalism—but what this basically means is that, in fact, people who deal with moral theory are mistaken in that they think unlike Jewish law. That is, it’s not that Jewish law is special; rather moral theory should also have worked this way, and the fact that they do not understand that there is a difference between an obligation and a prohibition means they are missing something, and they arrive at paradoxes. That means that even in morality, to say that there is an obligation to do something is not the same as saying that there is a prohibition against not doing it, or vice versa. Because the fact that the paradoxes are created in morality as well basically means that the halakhic conclusion we reached—that there is an unbridgeable gap between prohibitions and positive commandments, that you cannot translate one into the other, that saying there is a prohibition against doing labor and saying there is an obligation to cease—that is not the same thing. Right? That’s Maimonides in the sixth root. It means that this is not equivalent to that, right? That is basically what it means. Now the claim that in the moral world too, anyone who identifies them will run into problems, will run into paradoxes, and therefore this is proof that in the moral world too we really ought to speak in this kind of double language, in the language of prohibitions and in the language of obligations. This is basically—I’ll give an example, maybe—what? No, the examples aren’t like that. The examples I can give, say, are—for example, I’ll give you a legal example, a legal implication. You can talk about this in the legal world; you can talk about it in various things, in the game of chess, doesn’t matter. It’s an interesting question in soccer. We once talked about it—not me—I once heard some lecture in a pub in Tel Aviv. We went to hear it with that same friend with whom we talked about abortions. So it was a lecture by two lecturers from the Open University during the last World Cup; it was a lecture on the philosophy of soccer. There were some interesting things there, and there were arguments there. So the question is how to relate to a foul in soccer. After all, today—intuitively—today basically a foul is one of the coach’s techniques. He tells you: commit a foul here, commit one there. That is, usually when we commit a foul—

[Speaker B] Say in basketball—

[Rabbi Michael Abraham] There it is very true, yes, it’s outside the game. But it’s as though the one who committed a foul is a criminal. Meaning, over there it isn’t really an offense; it’s one of the rules that whoever commits a foul gives the ball over—that is, the other side gets the ball.

[Speaker B] He still has more—

[Rabbi Michael Abraham] Fouls left to give, yes, he still has more fouls to give. It’s a terribly funny kind of language when you look at it from the basic point of view. What do you mean? Someone who committed a foul violated the rules of the game. But in soccer and basketball it’s not like that. A foul is part of the rules of the game; it’s exactly like returning stolen property. Meaning that if someone committed a foul, then the ball passes to the other side. That is the rule. It does not say that it is forbidden to commit fouls. By the way, in the Israeli law book—as Chaim Cohen writes in a book called The Law—he writes there that there is no prohibition against stealing. It says, the thief’s punishment is such and such. Sort of, yes. There is no prohibition against stealing, or the murderer’s punishment is such and such. Not everyone agrees with that interpretation, but that is the language of the law. The language of the law is like that. Meaning this too is a kind of contrary-to-duty: an obligation that is actually defined through what happens if you did it, but there is no prohibition against doing it; rather, if you did it, then the result will be such and such. Okay. Now we talked about this—I think I once had an argument about it with someone from the Hebrew University, Alon Harel, a legal scholar from the Hebrew University—whether there are positive commandments in Israeli law. So I argued that there aren’t; there are only prohibitions. What do you mean? Is there a commandment to pay taxes or serve in the army? There is. So I told him no: there is a prohibition against not paying the taxes you owe, or against not serving in the army. What’s the difference? So he says to me, what difference does it make? The commandment to pay taxes is the same thing as the prohibition against not paying taxes. Right, it’s that identity. Right? I said, what are you talking about? To say that there is a commandment to pay taxes is not the same as—

[Speaker B] There is no punishment for a commandment.

[Rabbi Michael Abraham] Right. There is no punishment for a commandment, and there is no reward for refraining from a prohibition. Okay? Meaning basically, again, in practice you can say that one is punished for neglecting a positive commandment, but that simply loses the distinction between a positive commandment and a prohibition. The truth is that it really is only prohibitions. What do you mean? Now why, in law, when you ask a jurist, will he not agree with me? Because he assumes this identity. From his point of view, what’s the difference? In the language we spoke of earlier, he is basically saying that the difference between a positive commandment and a prohibition is an operational difference. That is, when what is required of you is to do something—say, pay taxes—then that is a positive commandment; that is the definition of a positive commandment. Or to serve in the army—that is a positive commandment. If what is required of you is not to murder, that is a prohibition. Meaning his criterion is an operational criterion. When I say that the criterion is not operational, in that I am saying this is incorrect. Understand? It is the same thing. Since basically this means that there can be an obligation to do P that appears as a prohibition on not-P, or as a positive commandment on yes-P, and that is not the same thing. Meaning that the fact that both of them are actions does not mean that it is necessarily always a positive commandment. It could be the performance of a prohibition or the performance of a positive commandment. And that is exactly what it means to say that this identity is not valid. Now you will ask, so what practical difference does it make? I don’t know—regarding the betrothal of a woman. Meaning in Jewish law there are practical differences regarding whether you receive reward or punishment, whether you must spend all your money on it or only up to a fifth of your money. Meaning in Jewish law there are practical consequences to these things, and therefore in morality or in law it is hard to feel this. But I claim that it is true there as well. Even though you can’t feel it, even though it makes a practical difference regarding the betrothal of a woman, it makes a practical difference regarding paradoxes. Because if you assume this identity, you run into all sorts of paradoxes. And in order to solve them you need to give up this identity, and therefore this means that this identity is not correct. Even though it is hard to put your finger on what exactly the difference is. Intuitively you need to understand that it is different to say that I want from you a desirable state, or that I want to prevent you from being in an undesirable state—as I discussed there in Maimonides in Friday’s class. Okay? So this is basically a kind of proof that even in the legal world or the moral world it is incorrect to identify these things; it is simply an incorrect assumption of deontic logic, and it solves various problems or paradoxes.

[Speaker C] In the moral world is there something that counts as an obligation? Meaning, because you could put the whole moral world under the category of forbidden? Even “do not stand idly by your neighbor’s blood”?

[Rabbi Michael Abraham] I think so, yes. For example, charity is clearly to me a positive commandment. There is no prohibition against not giving charity.

[Speaker C] Yes, of course not. You would say that it is an obligation, or—

[Rabbi Michael Abraham] That it is something proper but not really obligatory?

[Speaker C] No, it’s what is called a moral obligation.

[Rabbi Michael Abraham] A moral obligation means—that is the difference between a moral obligation—

[Speaker C] And a halakhic obligation: that this is what is proper to do. What is proper—that is a moral obligation.

[Rabbi Michael Abraham] By the way, you could also say that there is an obligation to donate a kidney, and an obligation to give—I don’t know what. There are obligations at different levels. There are levels in prohibitions too; there are prohibitions—

[Speaker C] Punishable by stoning, punishable by karet, simple prohibitions.

[Rabbi Michael Abraham] There are levels of prohibition and levels of obligation.

[Speaker C] Now in the moral realm, then if in the Ten—

[Rabbi Michael Abraham] Commandments, but charity—that is, a practical thing—

[Speaker C] An act, and therefore it is a positive commandment and not a prohibition.

[Rabbi Michael Abraham] But it is a positive commandment. A moral positive commandment is something that we call proper, but it is a moral obligation. It’s just that if you did not do it, you are merely immoral, but you are not a legal criminal; one cannot imprison you. But the moral world itself is simply softer than the legal world. So what we call “proper” in this context is basically the equivalent of obligation in the moral context. Now, true, there are different levels of obligation, but just as there are different levels of prohibition, there are obligations in Jewish law too. There is a positive commandment that carries karet—there are two like that—and there are positive commandments that do not carry karet. There are prohibitions punishable by court-imposed death, prohibitions punishable by karet, prohibitions punishable by lashes, and prohibitions that don’t even have that. So there are different levels of prohibition and of obligation, obviously. So the full model is much richer. Okay? Now that is one point. A second point that we learn from Jewish law is that, in fact, when I speak about contradiction—and this too cannot be described in terms of perfect worlds—I speak about contradiction, and then I say: a positive commandment overrides a prohibition. What do we do in such a situation? After all, there cannot be a perfect world in which both the prohibition against eating new grain and the obligation to eat matzah are both fulfilled, because in a world where I do not now have produce from the old grain, then either I violate the prohibition or I neglect the positive commandment. There is no perfect world from the standpoint of the prohibition and from the standpoint of the positive commandment. So first of all, the perfect worlds of a prohibition and the perfect worlds of a positive commandment are two different worlds. These are the worlds of fear and the worlds of love, in Nachmanides’ language. Right? Nachmanides says that positive commandments are on the side of love, prohibitions are on the side of fear. The perfection of love and the perfection of fear are two perfections that do not follow from one another. These are the worlds, the positive states and the negative states. We discussed this—even though in terms of performance some are positive action and some are passive omission, that doesn’t matter; you have this on both sides. Okay? But that is exactly the meaning of what Nachmanides says: you cannot speak about a perfect world from the standpoint of positive commandments and from the standpoint of prohibitions. So here, for example, is a solution to this problem of a positive commandment overriding a prohibition. Why did the problem arise? Because the assumption was that the same set of perfect worlds would be perfect both with respect to prohibitions and with respect to positive commandments. And that is not correct. Perfect worlds with respect to prohibitions are worlds in which no one is in a negative state. Perfect worlds with respect to positive commandments are worlds in which everyone is in a positive state. Now these are not the same worlds. You can perhaps say that there is an intersection between the two sets of perfect worlds, such that in that intersection everyone is not in a negative state and is also in a positive state. Maybe, maybe there is such an intersection, maybe not. But the problem no longer arises at the level of presentation. The same thing, incidentally—there are also clashes between one positive commandment and another: the question whether a positive commandment overrides another positive commandment, not only whether a positive commandment overrides a prohibition. Or prohibition against prohibition—say, because it doesn’t depend on performance, so take for example “do not stand idly by your neighbor’s blood.” That is a prohibition fulfilled by positive action, right? Now say that to jump into the river to save my friend involves violating the Sabbath. Okay? So that is prohibition against prohibition, because this is a prohibition of positive action and that is a prohibition of passive omission. There are clashes also between prohibition and prohibition or between positive commandment and positive commandment. So what happens with the perfect worlds there? So the conclusion is basically that you need to create a series of perfect worlds for each prohibition. And there is another index—I erased the index—and there is another index; meaning for each and every commandment there is a set of perfect worlds from its point of view, in which that commandment is fulfilled or that prohibition is observed. Meaning it becomes very detailed. You cannot speak about the same perfect worlds. And here exactly comes in what I said: that you cannot translate norms into facts, because you assume the perfection of the world, but with perfection now you need to enter in and understand: perfection in what respect? All these paradoxes in deontic logic do not enter the question of perfection; they assume as if perfection is obvious and now we are only in the realm of facts. Let’s see whether the facts hold or do not hold. But it is not like that. You need to look at the question of which worlds you selected, which worlds you are looking at, what your criterion of perfection is. There are many worlds; among them you look only at the perfect ones. What is perfection? What is the perfect? Another thing, this time in the opposite direction, in the halakhic world. In the halakhic world, in the end, after I reach a conclusion—say there is danger to life on the Sabbath. So danger to life overrides the Sabbath according to Jewish law. Thus, in the halakhically perfect world, when there is such a situation one should save. There is a perfect world. True, in that world you will desecrate the Sabbath, but there is no problem with that, since Jewish law determines that in order to save a life one desecrates the Sabbath. Okay? So in the halakhically perfect world, one will in fact desecrate the Sabbath. Now this basically means the following: in the halakhic world—and I think also in the moral world, and this is a solution to another set of paradoxes, there just isn’t enough time here to get into all that—but in the halakhic world one must distinguish between two sets of such operators. There is a set of theoretical operators, such as, say, an obligation to save lives and a prohibition against desecrating the Sabbath. Perhaps there is an obligation to save lives on a Torah level and a Torah-level prohibition against desecrating the Sabbath, meaning doing labor on the Sabbath. Those are two—let’s say they mark two—two acts. Okay? Two symbols. In practice there is no connection between those two. Okay? But in practice, at the bottom line, we will desecrate the Sabbath. Right? Meaning there is a deontic obligation to desecrate the Sabbath in such a case. Right? If I say that there is an obligation to save a life on the Sabbath and a prohibition against desecrating the Sabbath, right? Now I say: when you take both of them together, in the end there is one halakhic answer as to what must be done. What must be done is to desecrate the Sabbath. Now here on the practical plane—what do we do? Not on the plane of which commandment applies in such a situation. One question is which positive commandments and prohibitions apply to this situation. I say: two. One is the obligation to save him, the second is the prohibition against desecrating the Sabbath. Fine? But now Jewish law moves me—okay, I identified all the obligations relevant to this situation, fine? I pass it to the halakhic computer. The halakhic computer tells me what has to be done in a situation where there is a contradiction between two—two such norms. In this case, say, a positive commandment overrides a prohibition, or whatever, danger to life overrides the Sabbath. So we have criteria for what overrides what, meaning how one resolves the problem. The result of this criterion is not a commandment. The result of these criteria is a practical directive. Right? The commandments are in the theoretical realm. In the theoretical realm, when I am on the Sabbath and I see someone for whom I need to desecrate the Sabbath in order to save him, in the theoretical realm there is a commandment to save him and a prohibition against desecrating the Sabbath. I have collected all the commandments relevant to this situation. Okay? That tells me nothing about what I must do. Right? Therefore this is not even a contradiction. There are two directives here. Now the question is how I move to the practical plane. What do I do? Not which commandment is upon me and which prohibition is upon me, but what do I do? The translation between “there is a prohibition upon me” and “I am forbidden to do it,” or between “there is an obligation upon me” and “I am required to do it,” is an incorrect translation. That is another mistake of deontic logic. After all, to say that there is an obligation upon me or a prohibition upon me does not mean that I must do it. First I have to collect all the obligations and prohibitions that apply to the situation, and then decide what I am required to do. Therefore there is an additional set of operators that says “obligatory to do” and “forbidden to do” on the practical plane, not which commandment and which prohibition exist. And here ordinary deontic logic does hold. Because if according to Jewish law I have an obligation to save someone, then obviously I have a prohibition against not saving him. A practical prohibition, not a prohibition in the formal sense, but in practice, if I am required to save him then clearly I am forbidden not to do it, right? Meaning all deontic logic holds on the practical plane. But it does not hold on the theoretical plane, the Torah plane, the plane of prohibitions and positive commandments. Meaning that between the operators OT and FT there is no deontic relation. Between these operators there is. So in fact there are two sets of operators: one set satisfies deontic relations and the second set does not satisfy deontic relations. Now the operator E can also be expressed on this plane, right? When we say “permitted,” it means there is neither obligation nor prohibition. And that is called permitted, so in any case it is redundant. Meaning there are only—there are only two independent operators on the theoretical plane. On the practical plane there is only one. Just this or F, I don’t care, but you can express one by means of the other because the identities hold. So in total there are three operators that one must work with halakhically. It is prohibition, positive commandment, and prohibition-commandment, and the practical directive. Obligation or prohibition of the opposite, which is the same thing. Okay? And that’s it. With this you can lay everything out. Now what still has to be done in order to complete the picture is to create a set of rules that takes me from the collection of norms that apply to the situation to the answer of what must be done in practice. For example, if I have a positive commandment and a prohibition, then the rule is that the positive commandment overrides the prohibition. If I have a positive commandment against a prohibition and a positive commandment, then the positive commandment will not override a prohibition-and-positive-commandment. Right? There can be situations in which there are ten—yes, “a man plows one furrow and is liable for it on account of six prohibitions.” Okay? And there can be a situation in which six commandments apply in the same situation. Sometimes they will clash, sometimes they will fit one another, or more than one another. Right? You may fulfill two positive commandments but violate three prohibitions. There can be all kinds of things of that sort, a great many things. Therefore it is very important to make the distinction that deontic logic does not make—and this is another mistake of deontic logic—the distinction between the theoretical plane and the practical plane. On the practical plane all of deontic logic is correct. Some of the paradoxes arise because I identify it with these operators, and that is not correct. The relation between these and that is a relation of calculation. One has to perform a calculation. And that calculation has various algorithms in Jewish law. Here, I’ll show you—where’s the table, just so you get an impression. We put a table here. Basically we define twelve—twelve states. There is OT, FT, and OD, three operators. Each one either on P or on not-P. Let’s say that P is an act and not-P is an omission. Okay? And with negation outside and without negation outside. That makes twelve, right? There are four possibilities times three operators. Fine? Now basically we have twelve such types, and we need to summarize twelve such possibilities, to go over all the commandments in the Torah in a given situation. I have a situation, say someone is in mortal danger and I need to save him. A given situation. I go over all six hundred and thirteen commandments and mark what each one says about that situation. Or they may say nothing, but I find which of them do say something; there might be ten that speak about that situation, or one or two or none, doesn’t matter. Okay? Each of them can say either negation, or OT of not-P, or FT of not-P, or any of the twelve combinations. Fine? I collect all these twelve combinations, and now I ask what happens when, for example, negation of OT with negation of P together with this of negation of P—what in fact does Jewish law say to do in such a case?

[Speaker D] What does this have to do with the six hundred and thirteen commandments? It has to do with the way of a halakhic decisor, let’s call it that. A halakhic decisor has things that are not related to the six hundred and thirteen commandments.

[Rabbi Michael Abraham] We are talking about a halakhic decisor.

[Speaker D] But wait, but a halakhic decisor—for example, “just as it is a commandment to say something that will be heard, so too something…”

[Rabbi Michael Abraham] No, no, let’s talk right now—

[Speaker D] Wait, there is public need, there is—all this is part of the halakhic decisor’s considerations. No, it’s not related.

[Rabbi Michael Abraham] Right now I am talking about the theoretical core of Torah-level Jewish law. Fine? After all, I begin with a toy model; I start with a simple example to see how the business works. Afterwards you have to insert all the extra-halakhic and rabbinic considerations and emergency enactments and all sorts of things—human dignity and many things. I am speaking right now—I want to see how the logic of Torah-level Jewish laws works. So I say: what is a halakhic decisor actually supposed to do? A halakhic decisor is supposed to go over all six hundred and thirteen commandments, right? All these three operators—after all, there are six hundred and thirteen of them. Because each commandment can appear as this, this, or this. Okay? With negation and without negation inside and outside, meaning twelve possibilities for each commandment. For any given situation you have to go over all the commandments and collect them all. And then you need a table that takes you from these to that. Okay? Basically from the commandments and transgressions to the question of what the practical directive is. That table, of course—there is a set of many such tables, not infinitely many by the way, but many. Because you need to decide what happens when there is a pair of norms. So that is twelve by twelve, right? You need to say: this is this table. Twelve by twelve: what happens when there is such a norm and such a norm—what is the result? Here it says what the result should be. And for that there are completely clear answers in Jewish law, for all the cases. So there are answers. But of course in situations where there are two prohibitions of this type plus a positive commandment of that type, let’s say. What do you do in such a case? Or three positive commandments of this type, one positive commandment of that type, and two prohibitions of this type. What do you do there? Now, so we built here a table for pairs, a table for triples, a table for quadruples, for groups of four. Okay, we got as far as groups of four because it already starts becoming terribly complicated, and all in all most—no paradoxes and no contradictions.

[Speaker B] Yes, so did you present this to logicians who deal with ethics?

[Rabbi Michael Abraham] We wrote an article, didn’t we? We wrote an article. We wrote an article—let them look. Yes, and at the end of the article, it appears there too, the tables.

[Speaker B] So it needs to be exported.

[Rabbi Michael Abraham] We did publish it. We did. If you export it by writing an article—here in the article it also appears, these tables. So fine; I wanted not to get too deep into the formalism, but I wanted to show basically how this business can actually influence thinking in fields that are not halakhic. That is, in the end, precisely the halakhic resolution lets us notice things that in moral or legal contexts people pass over without even noticing that there are two different things here. Jewish law in this sense is much more sensitive. But it is not unique. People think it is unique; it is not. That is, the basic claim in our logic book in general is that there is nothing unique about Jewish law. Jewish law works exactly like any other normative system. Many times there are situations where in Jewish law you see things that you do not see elsewhere, so you can export them. Meaning you can see that this solves certain problems there, and basically show that the ignoring of the finer distinctions into which Jewish law enters is what creates the problems. Okay.