Deontic Logic and the Relationship Between Prohibitions and Positive Commandments – Lecture 1
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Table of Contents
- Deontic logic and the problem in formalization
- Russell, Principia Mathematica, and type theory
- Formalization in the social sciences and the example of “emotional intelligence”
- The teaching method: formalism versus examples
- Norms versus facts: Aristotle, indicative and imperative
- Positivism, verification, and metaphysical claims
- Maimonides’ eighth root: warning, command, and negation of obligation
- Language and thought: positive commandment and prohibition, Arabic, Whorf, and counting systems
- David Hume’s naturalistic fallacy and the bridge between fact and norm
- The foundations of deontic logic: obligation, prohibition, permission, and equivalences
Summary
General Overview
The text presents deontic logic as a logic of norms, focusing on the relation between prohibition and positive commandment, and argues that the formalization of normative statements carries hidden assumptions that can create paradoxes or conceal problems instead of solving them. It illustrates this through the analytic attempt at formalization in mathematics and philosophy, through a critique of Russell’s solution to the paradoxes by means of type theory, and through an example from the social sciences involving “multiple intelligences,” where redefining a concept changes its results. It then distinguishes between facts and norms, and between indicative statements and imperative statements, brings Maimonides’ eighth root as a linguistic-logical distinction between a warning and the negation of an obligation, and connects this to David Hume’s naturalistic fallacy, according to which one cannot derive a norm from facts without a bridging assumption. Finally, it presents the accepted basis in deontic logic of obligation, prohibition, and permission, and the equivalences between them, and declares that these underlying assumptions are not correct in Jewish law, and that specifically a halakhic deontic logic would look different and would not suffer from the familiar paradoxes.
Deontic Logic and the Problem in Formalization
Deontic logic is a logic of norms rather than of facts, and it attempts to formalize statements like forbidden, obligatory, and permitted, and derive conclusions from them. Logical formalization looks persuasive, like a mathematical proof, but the pitfalls lie in the move from everyday phrasing to formal phrasing, because formalization assumes underlying premises. Mathematics does not solve philosophical problems but at most helps solve them or else successfully hides them, and the crucial problem is exactly what was translated into the mathematical language and which assumptions were absorbed in the translation. The claim is that in deontic logic the accepted formalization is problematic, and that when one builds a halakhic deontic logic, different assumptions emerge and therefore a different formalization, in which the known paradoxes do not appear—not because the formalization “solved” them, but because it exposes what was flawed in the regular formalization.
Russell, Principia Mathematica, and Type Theory
Bertrand Russell and Whitehead wrote Principia Mathematica as an attempt to ground mathematics on a consistent, paradox-free foundation, with the ideas mainly attributed to Russell. In the introduction, type theory is presented as a solution to self-reference paradoxes by means of a hierarchy of levels: every statement can refer only to statements lower than itself, and therefore cannot refer to itself. The text presents examples of self-reference paradoxes such as the barber who shaves all the men who do not shave themselves, the Protagoras and law student paradox, and the liar paradox, and notes that all this was written before Gödel’s theorem, and that Gödel’s theorem was “a major blow” to the book. Russell’s solution is described as an analytic solution that prevents the problem only by forbidding it from being presented in the language, and is therefore compared to a “Stalin-style solution,” where you simply eliminate whoever raises the problem, and the underlying assumption behind it is that every philosophical problem stems from vagueness in language.
Formalization in the Social Sciences and the Example of “Emotional Intelligence”
The text describes the popular thesis of “multiple intelligences” as one that expands the concept of intelligence so that people who are not mathematical-scientific geniuses will also be considered geniuses in other kinds of ability, and presents this as the dream of the politically correct and postmodern equality. It argues that the methodological problem is that in the process of conceptualization, one distills features out of an existing intuition about intelligence, and then discovers that those features fit both Einstein and Maradona, which indicates that the distillation was incorrect and that essential features were missing. The result is that the logical “achievement” after the definition is trivial, and the real substance lies in the assumptions built into the conceptualization process itself, similar to the hidden assumptions in the process of formalization in logic.
The Teaching Method: Formalism versus Examples
The text presents a hesitation about how deeply to enter into formalism, because formulas make things harder for some learners, and suggests postponing the formalization to the end, after the ideas are already clear. It distinguishes between “correct” teaching of mathematics in a top-down approach from assumptions to conclusions, and “successful” teaching in a bottom-up approach that starts with examples and generalizes, and argues that a lecturer who leaves the examples to the teaching assistant causes nobody to understand.
Norms versus Facts: Aristotle, Indicative and Imperative
Aristotle divides statements into claims that are judged as true or false, and statements that are not claims, such as questions and commands. Statements of fact are descriptive claims, whereas normative statements such as “it is forbidden to murder” are not facts but express obligation and a judgment of what is proper and improper, and the text assumes that deontic logic assumes that norms are claims in the sense that one can relate to them as true or false even if they are not factual. The distinction is illustrated through the difference between “it is forbidden to murder” as a norm and “according to Israeli law it is forbidden to murder” as a factual description of a legal system. It also connects this to the ideal of scientific neutrality and to the dispute in anthropology between living inside the tribe for internal understanding and observing from a distance “like ants,” and argues that the attempt to turn non-scientific domains into science empties them of meaningful content.
Positivism, Verification, and Metaphysical Claims
Positivism identifies true claims as factual claims that can be decided empirically, and therefore sees claims of morality and metaphysics as claims with no way of being verified and with no content, or even as nonsense. The text notes that a positivist can also present geometrical statements as conditional claims such as “in Euclidean space, the sum of the angles is one hundred and eighty degrees,” and raises the criticism that positivism itself rests on assumptions that are not always visible to it because they seem agreed upon. It presents an attempt to derive morality from a basic premise like “what is hateful to you, do not do to your fellow,” and argues that the problem remains in the transition from “if-then” to objectivization in relation to someone who does not accept the premise or claims that “for me it is not hateful.”
Maimonides’ Eighth Root: Warning, Command, and Negation of Obligation
In the eighth root, Maimonides rules that “it is not proper to count the negation of an obligation together with a warning,” and defines a warning as one of the two parts of a command: positive commandments command doing, and prohibitions command not doing. Maimonides quotes “those who speak in the craft of logic” and argues that in Arabic there is no term that groups command and warning together, so they are forced to call both by the name “command,” while in Hebrew the inclusive term is “decree,” and the Sages called every commandment “the decree of the King.” Maimonides distinguishes between “no/not” of warning and “no/not” of negation of obligation, which is a description of a state such as “so-and-so did not eat last night” or verses such as “And no prophet arose again in Israel like Moses,” and rules that prohibitions that are merely negation are not counted among the negative commandments. Maimonides explains that a warning is always in the future tense of command, which cannot be in the past and does not enter into narrative, whereas negation can appear in past, future, and present as part of an indicative sentence with subject and predicate.
Language and Thought: Positive Commandment and Prohibition, Arabic, Whorf, and Counting Systems
The text uses Maimonides’ claim about Arabic to demonstrate how language influences distinctions in thought, similar to examples attributed to Whorf about the many words for snow among Eskimos and to Hebrew examples such as “harvesting dates” and “picking grapes.” It also brings the example of one-two-many tribes such as the Pirahã, in which there are “one, two, many,” and argues that the absence of mathematical concepts makes it difficult to understand the relation between close numbers. In the halakhic context, it argues that the distinction between positive commandment and prohibition is not merely active versus passive, and that there are positive commandments that require not doing and prohibitions that require action, so these are two kinds of demand and not only two kinds of action. It also presents a debate within the discussion about rabbinic prohibitions, decrees, and safeguards, and examples from selecting on the Sabbath, ritual handwashing, and the decrees of shaving and laundering on the intermediate days of a festival.
David Hume’s Naturalistic Fallacy and the Bridge Between Fact and Norm
David Hume argues that one cannot derive a norm from a fact, and therefore moving from facts to a normative conclusion requires an additional assumption that bridges between the levels. The example is the move from “the chair is blue” to “the chair is beautiful,” or the move from naturalistic morality such as “murder causes suffering” to the conclusion “it is forbidden to murder” without the normative assumption that “what causes suffering is forbidden.” The text shows how arguments for halakhic change, such as qualifying women for testimony on the basis of social-factual change, fail logically without a connecting assumption such as that the original disqualification stemmed from lack of education. It presents evolutionary naturalism as a mistaken claim when it moves from a description of the development of moral feeling to the determination that something “really is forbidden,” because an additional normative assumption is required that whatever does not aid survival is morally forbidden.
The Foundations of Deontic Logic: Obligation, Prohibition, Permission, and Equivalences
Deontic logic divides normative claims into three basic operators: obligation, prohibition, and permission, and tries to determine the logical relations among them. The text presents a standard deontic identity according to which “it is obligatory not to murder” is equivalent to “there is a prohibition against murder,” so that prohibition can be expressed through obligation with an internal negation. It also presents “permitted” as the state in which there is neither obligation nor prohibition, and argues that the equivalences make it possible to reduce the system so that the obligation operator together with negation is sufficient to express both prohibition and permission. It states explicitly that this central equivalence “is not correct in Jewish law,” and marks this as one of the fundamental differences because of which a halakhic deontic logic would require a different formalization.
Full Transcript
[Rabbi Michael Abraham] I’d like to begin a new topic, which actually, in the class before Passover, the class on Passover, that was also some kind of introduction to this topic. And this topic is deontic logic, whose focus is the relation between prohibition and positive commandment. Deontic logic is a logic of norms, meaning that instead of the logic of facts that we usually use, there’s a somewhat different logic that deals with relations between normative claims. And this is a relatively new topic in the world of logic, where people are trying to create a formalization of deontic sentences, normative statements: forbidden, obligatory, permitted, things of that sort, and to understand what the relations are between these statements and how one can derive one statement from another. Of course, as in every area of philosophy, logical formalization hides behind it various underlying assumptions, and that is both its strength and its weakness. On the one hand, when something looks like a logically or mathematically structured argument, and you can prove it, it sounds terribly convincing. It can’t be otherwise—we proved it, so it must be true. But usually, if there are pitfalls—and there can be pitfalls—they lie in the transition between the everyday formulation and the formalization, meaning the formal form we give to the statements, because the process of formalization contains various assumptions within it. And therefore, although ostensibly we’re dealing with mathematics or logic, we can still find problematic things. If the logic itself is done correctly, then the problem is not in the logical process, but in the assumptions embedded in the formalization. Now, this is true of many things. There’s one field I’m very fond of—philosophy—not many philosophers like it all that much, but it’s really a field of analytically formalized philosophy, meaning the attempt to demonstrate philosophical problems with mathematical tools. It’s much clearer, meaning it has an advantage because you really see before your eyes what the assumptions are, what the conclusion is, and you can think about things clearly. The disadvantage of this field is that the assumptions underlying the formalization are not always visible.
[Speaker B] That you need to know logic and mathematics?
[Rabbi Michael Abraham] Not only that. But yes—even if you know logic and mathematics, you have to be aware of the assumptions underlying the formalization, and many times the problem is there; almost always the problem is there. So in fact mathematics doesn’t really solve problems, but at most helps solve them or alternatively hides problems successfully. I think I once spoke about Bertrand Russell’s theory of types. There’s a mythical book in mathematics called Principia Mathematica. There are three volumes like that, written by—
[Speaker B] By—I don’t know if there are two people in the world who read it—
[Rabbi Michael Abraham] Russell and Whitehead wrote it, and it’s the kind of book that is all formulas, only formulas. As opposed to—there everything is written mathematically, there’s almost no English in it. Don’t worry, I didn’t read it either. I went over the introduction, saw the theory of types, leafed through the book a bit, because I used to be very fascinated by formalism. For me it was really—so I tried, but very quickly I gave up. In any case, in the introduction there he deals with paradoxes of self-reference, and he tries to solve those paradoxes analytically, in classic Bertrand Russell fashion. I don’t know whether it’s accepted somehow to think that the main content there is Russell’s. Whenever you have a pair of co-authors, usually there’s someone who wrote it and someone who just helped him, formulated it. Landau and Lifshitz in physics—whoever knows—so it’s well known there isn’t a single idea there from Lifshitz and not a single word there from Landau. Lifshitz wrote it and Landau said what to write. So I don’t know what the division was there between Russell and Whitehead, but I think people usually attribute the ideas to Russell. So he proposes solving the problems of self-reference by means of a new language. Maybe I’ll give an example: the barber who cuts the hair of all the people who do not cut their own hair. The barber of Seville. He used to cut the hair of all the people who do not cut their own hair. Now the question is: does he cut his own hair? Because if he cuts his own hair, then he belongs to the group of people whom he doesn’t cut, right? Because after all he doesn’t cut people who cut their own hair. So if so, he doesn’t cut his own hair. So if he cuts his own hair, then he doesn’t cut his own hair. But if he doesn’t cut his own hair, then he belongs precisely to the group that does get cut by him, so then he does cut his own hair. And so on. Or, I don’t know, a somewhat different example: Protagoras, the law lecturer. I no longer know why this is specifically attributed to Protagoras, but that’s always how this paradox is presented. He taught a law student and made a condition with him that he would pay him if he won his first case. A sign that he had succeeded. So if he wins his first case, then he owes him tuition. Fine, he finished his studies, and of course doesn’t pay. So his lecturer sues him for not paying. So now they come to court and the judge has to decide: if the lecturer is right, then the student lost the case, so he has to pay. But if he lost the case then he doesn’t have to pay; he only has to pay if he won the case. And so on. There are others. The liar paradox, of course, is the father of all self-reference paradoxes. By the way, this was written before Gödel’s theorem, and Gödel’s theorem basically turns the liar paradox into an actual building block in logic. So Bertrand Russell—this book was written before Gödel’s theorem. Gödel’s theorem was one of the biggest blows that landed on this book. But Bertrand Russell proposes solving self-reference paradoxes by means of a new language. He calls it the theory of types, where in that language there is a rule that divides statements in the language into different types, different hierarchical levels. Every statement belongs to some type, some level in the hierarchy, and there is a rule that every statement may refer only to statements lower than it in the hierarchy. So obviously it also cannot refer to itself.
[Speaker B] And that also solved the problem in set theory, that was—
[Rabbi Michael Abraham] Brought—
[Speaker B] There—
[Rabbi Michael Abraham] In the introduction there, that was brought in part in order to… In any case, the claim is that if you build a language in which every statement can refer only to statements that belong to a lower type, then you’ve essentially prevented the problem of self-reference in the language, because self-reference cannot occur. A statement cannot refer to statements that belong to its own level in the hierarchy and of course in particular not to itself. So ostensibly he solved the paradox; this is a classic analytic solution to paradoxes. Except that clearly such a thing is not really a solution. Why? Because basically what he does with that language is simply forbid presenting the problem within the framework of the language. This is a Stalin-style solution to problems in philosophy. Meaning, whoever raises the problem gets his head chopped off, and the problem is solved. In other words, this language basically says: you are forbidden to present this kind of problem; it’s illegal in the language. So everything is fine, we solved the problem. But the problem is a real problem; it’s not a problem in the language. If analytic philosophy—and this is the assumption of analytic philosophy—is that every problem is fundamentally rooted in some kind of vagueness, lack of clarity, or lack of precision in language, then if we define a more precise language, that won’t happen. Leibniz’s dream, for example, was to create a precise mathematical language in which paradoxes would not appear, meaning it would be completely consistent. He failed—or rather, he never managed; it’s not that he failed, he didn’t manage at all to create such a language. And Bertrand Russell tried. Principia Mathematica was an attempt to create such a language. In fact, that was the goal of that book: an attempt to build all of mathematics on some foundation in which everything would be consistent and no paradoxes would appear. The foundation was basically set theory; he chose set theory as his basic infrastructure. In the end he failed. Gödel’s theorem showed that he failed. Meaning there is a paradox also within Principia Mathematica. In any case, this introduction, which speaks about the theory of types, is also that kind of solution. Because in mathematics, if we really formulate mathematics in a language of that kind in which paradoxes are not presented, that’s an important mathematical achievement worthy of note. Because the goal in mathematics really is to create a language free of paradoxes. But as a solution to a philosophical problem, it doesn’t help. Because if I have a philosophical problem, the fact that you manage to create a language in which the problem cannot be expressed only means that you have presented an incomplete language, a partial language. It’s like someone trying to write a poem in the language that Bertrand Russell or Leibniz would have managed to create—he wouldn’t get very far. Some kind of mechanical robotic poem. Meaning you can’t. A poem has to be something more alive, rounder, less sharp in that yes-or-no sort of way. So one has to know what can be done with mathematics and what cannot be done with mathematics. The problem is always the formalization. Meaning, the problem is always how you translate the contents that in the end you’re actually interested in into mathematical language. And once there is a problem in the contents and it doesn’t appear in the mathematical language, then you haven’t solved the problem, you’ve simply shown that the language does not represent the contents correctly, that’s all. That is not called solving the problem. I once spoke about—when we spoke about definitions—I spoke about the problem I see in the development of this concept called emotional intelligence, if you remember. So I talked about it; it’s exactly the same problem. The concept of emotional intelligence has become very popular in recent years. Yes, it’s politically correct in the field of science or pseudo-science, and basically what they want to say is that there are all kinds of intelligences. And therefore even people whom traditionally we would regard as stupid—that only means they don’t have one kind of intelligence but they do have another kind. So there is motor intelligence and emotional intelligence and all kinds of intelligences, and not only Einstein is intelligent, right? Or not only the classical geniuses, the mathematical, scientific ones—not only they are geniuses. There are all kinds of other intelligences, and you can be a genius in all sorts of ways. You understand why this is the dream of the politically correct crowd.
[Speaker C] And vice versa. What?
[Rabbi Michael Abraham] That intellectual geniuses can also be stupid in other areas.
[Speaker C] They can be, and sometimes that’s even more important. Yes, נכון.
[Rabbi Michael Abraham] In short, it’s more perfect equality. We people really enjoy equality, the idea that no one is better or worse. In the postmodern world that’s wonderful. So it’s no surprise that this thesis of intelligences developed so nicely. What bothered me there was the method, because ostensibly if you listen to someone talking about multiple intelligences—you can read this all over the internet today, it’s very widespread—they present a definition of the concept of intelligence, and you really see that many different kinds of ability fit that definition. Meaning, true, there are various kinds of ability that traditionally were not understood as a type of intelligence, and they too are seen as intelligence. They simply satisfy the characteristics of intelligence as well, not only scientific or mathematical ability or whatever other sort. So what’s the problem? So my suspicious mind always wakes up there—wait a second, something here isn’t logical. Meaning, you start from the point that Einstein is a genius and Maradona is talented with his feet. And then suddenly you arrive at the conclusion that they’re both geniuses. So something happened along the way here. What happened? What happened is—how did they do that? How does one do such a thing at all, in the social sciences? How do you do conceptual development in the social sciences? It’s not mathematics; you don’t produce concepts out of themselves. In the social sciences you produce concepts in a different way. What do you do? You take people who have an intuitive concept of what intelligence is. And all of us more or less do. You try to distill from that concept what the characteristics are. Meaning, why do people call something intelligence? Okay? So I find, I don’t know, six or seven characteristics and I write the characteristics down. Now I say, fine, so now that’s my definition of intelligence. So now let’s see what fits that definition. And then suddenly you discover that Maradona is a genius too. Right? And you probably agree—and he doesn’t understand at all what the problem is. Yes.
[Speaker D] Not to mention Messi.
[Rabbi Michael Abraham] By now he has already declined from his greatness. Yesterday. Yes. In any case, the claim is that the problem that lies here behind the process of formalization, or conceptualization—let’s call it conceptualization, not formalization; it’s not formal but it is conceptualization, you’re creating a concept—is that your translation into the concept is simply incorrect. Meaning, you took a concept that in our intuition Einstein fits and Maradona does not fit, distilled its characteristics, and lo and behold, the characteristics fit both Maradona and Einstein. What does that mean? It only means that that distillation was an incorrect process. You probably omitted some of the characteristics of the concept. Meaning, the process of conceptualization did the work for you, not the achievement. The achievement is the easy part. Meaning, the achievement is obvious: once those are the characteristics, then it’s true, both Maradona and Einstein fit them. You hid it in the process of conceptualization just as in the process of formalization in logic. Therefore, many times a process of formalization has behind it various assumptions that are actually the interesting thing, or the thing that has the real substance, because once you’ve already formalized, from that point on it’s all mathematics. Meaning, okay, there’s nothing new here. Sometimes it can be sophisticated, but it’s not—one plus one equals two. The question is what “one” is and what “plus” is. And many times that’s the problem. Now in deontic logic too, suddenly. I thought something in the process of formalization didn’t look right to me, the accepted process of formalization in deontic logic, and after I started thinking about it a bit I found that Jewish law—or if one does a halakhic deontic logic—it looks different from ordinary deontic logic. Meaning, there are different assumptions there, and that has to find expression in a different formalization, and it seems to me that all the paradoxes I know in deontic logic do not appear there. But in this case it wasn’t the formalization that solved the problem; rather, I can show what was flawed in the regular process of formalization, or what needs to be changed in the assumptions at the basis of the regular process of formalization in order to produce a different deontic logic in which the paradoxes don’t appear, meaning there aren’t those problems. Now I’m a bit hesitant as to how far to go here into formalism. It’s not terribly complicated, but it does involve some formulas, and not everyone is comfortable with those things. So maybe I’ll do it more toward the end, meaning I won’t do it now. What?
[Speaker B] You need a whiteboard here.
[Rabbi Michael Abraham] Yes, we once worked here with a board. It was one year or two years that there was a board here, when we talked about a fortiori reasoning. Yes, exactly. So maybe I’ll do it at the end after the ideas are already clear, because usually there are two ways to teach mathematics. There’s the correct way and there’s the successful way, and they always cancel each other out.
[Speaker B] I have no problem, I just don’t know how to record the board.
[Rabbi Michael Abraham] We’d have to switch to video. Yes. In mathematics, if you teach top-down, from the assumptions to the conclusion, that’s the correct way, but it’s the unsuccessful way, because then nobody understands anything except for some kind of mutants whose minds are built mathematically, so they understand. But a normal person—you need to work bottom-up, meaning give examples and then generalize them and explain the general idea. If you start from above—and that’s how a pure mathematician thinks—give me the rule, and then the examples are already obvious, they follow automatically, so there’s no need, that’s for the teaching assistant. A lecturer who leaves all that to the teaching assistant—nobody understands him. Meaning, he has to do that in the lecture as well. So maybe we’ll do that here too, but first I want to explain what this is about. Okay, so I’ll begin with a distinction that is important to begin with, between norms and facts. If we’re dealing with deontic logic, which is a logic of norms, then we need to understand what norms are as distinct from facts. After that we’ll see that the process of formalization makes use of—that is, it moves from the level of norms to the level of facts, and that’s how it solves the problem. That’s basically what people do in deontic logic. So first let’s try to understand the difference between these two things. We know statements in language of different kinds. Already Aristotle speaks about this, that there are statements that are claims and statements that are not claims. A statement is a claim only if it has to be judged in terms of truth or falsehood. Meaning, it’s dark outside now—that’s a claim. Why? Because it’s a statement that is either true or false. Also, it’s light outside now—that’s a claim too; in this case a false claim, while the previous statement was a true claim. But a statement that stands the test of truth or falsehood is a claim. Okay? What is a statement that is not a claim? For example, pass me the salt, please. Pass me the salt, please is not a claim. It’s not a true statement and it’s not a false statement either; there’s no point speaking about truth or falsehood. Or a question, or a command, or things of that sort—these are statements that are not claims, but they are statements.
[Speaker B] He’s making claims against me.
[Rabbi Michael Abraham] Yes, exactly. In any case, claims too can be discussed, or divided, into several kinds of claims. There are factual claims and there are claims—although philosophically one can argue whether they are claims or not, and there are disputes about this—that are not factual claims. For example, when I say it is forbidden to murder. If I look at that sentence, it does not belong to the domain of facts. It is forbidden to murder—that is a norm, not a fact. Right? On the other hand, there are people who jump one step further and say: fine, then in that case there’s really no true and false here. You think it’s forbidden to murder, he thinks it’s permitted to murder, one society is like that, another society legislates a different law, this is basically arbitrary, there’s no truth or falsehood here. So actually it isn’t a claim at all. What would someone who thinks that yes, it’s true, murder is forbidden, say to such a thing? Meaning, the true statement is “it is forbidden to murder”; whoever says it is permitted to murder is mistaken, a false statement. So he will have to say that there is such a thing as claims even though they are not factual claims. Meaning, this is a claim that can be related to in terms of truth or falsehood even though it does not deal with facts but with norms. Okay? So when we speak about deontic logic, in a certain sense we are assuming that there are claims that are not facts. Because if they aren’t claims, there’s no point in creating a logic of them. Logic deals with relations between claims. Okay? So on the one hand these are claims, but they are not factual claims; this is a different logic, as we will see. So there is basically some assumption here that there is another kind of claim, namely non-factual claims. Now one can somehow give this a kind of factual meaning. I can say that it is forbidden to murder means that one who gazes upon the idea of the Good sees there the ethical “fact,” in quotation marks, that it is forbidden to murder. Because there is something objective standing behind this matter that murder is forbidden. Okay? And then in a certain sense I have turned the norm into a fact. But that is an ethical fact, meaning one can say this is a bit of a play on words. All I really want to say is that there is truth and falsehood here, and that it is not arbitrary. Turning it into facts is already another question; you can call it a fact, but that’s just a label. Okay, now when I say, for example, according to Israeli law it is forbidden to murder—what is that? A factual claim or a normative claim, or is it not a claim at all?
[Speaker B] A factual claim, a factual claim, right?
[Rabbi Michael Abraham] But if I say it is forbidden to murder? A normative claim, a normative claim. What’s the difference? When I say that according to Israeli law it is forbidden—
[Speaker B] To murder, I’m not saying that murder is forbidden; you’re saying that Israeli law forbids murder.
[Rabbi Michael Abraham] I’m simply describing facts. Look in the law books and see whether it says there that murder is forbidden or not. I’m not expressing a position. Meaning, a normative claim usually carries some kind of evaluative charge. You’re saying proper, worthy and unworthy—I need to be careful with true and false here—rather proper and improper. Meaning, this is how one ought to behave and this is how one ought not to behave. A descriptive claim, Israeli law forbids murder, does not express any judgment. It’s simply a description. I may agree with that law, I may not agree with that law; it’s simply something descriptive. So in fact statements of fact are descriptive claims, and normative statements are claims that express judgment or obligation or contain normative weight, let’s call it that; they are loaded claims, not neutral claims. When you describe, you are neutral, like science is often perceived as something that is supposed to be neutral. The scientist is not supposed to be involved in the subject he is studying. That doesn’t always happen, but that’s the idea. Because you are simply supposed to describe what’s happening there. You know, at the beginning of sociological and especially anthropological research—more than modern sociology—there was a major debate about how it should be done. The original approach was: let’s live inside the tribe being studied, let’s try to get into their heads, and then we’ll understand better how the whole thing works. Others said that’s not science; that’s immediate impression. Science is supposed to be that you sit on top of the hill, you don’t know who they are at all, you understand nothing, and you watch them like ants. Meaning, you document what they do and you explain what they do, you compare it with other populations, and you try to produce a neutral description of human phenomena. That’s how you create scientific anthropology. Okay, now in the case of anthropology, I think the second group was right from the standpoint of those who want to make it into a science, but the first group was right because it isn’t a science. Meaning, many times the failure stems from trying to turn a field that by its nature is not suitable for scientific treatment into something scientific, and then the price you pay is a heavy price. You basically empty it of the interesting and useful contents in it, and focus only on things that are in fact very superficial and sometimes trivial, because those are the only things you can say in a completely independent way, not conditioned by worldviews, and that can then be scientific. Mathematics—we are all neutral there, meaning mathematics, what is true is true, it doesn’t depend on worldviews, ostensibly. Even there there are disputes, but ostensibly it doesn’t depend on worldviews or on anything. But in the social sciences, certainly in the humanities, it isn’t like that, and therefore there the involvement of the person is in my view necessary in order to do good research, but you have to be aware of it. That this will suffer from problems of bias, meaning that you really are not producing science here. I wrote in one of the posts about qualitative research, which is one of the things people are trying to do now. It amuses me not because it’s wrong to do it—I think on the contrary, that’s the right thing to do. What amuses me is only that they call it a scientific tool. Meaning, it’s the right way to deal with fields that science is not a good way to deal with. There’s nothing you can do. There are apparently fields—or at least they haven’t yet found the good scientific way to deal with them. So one has to acknowledge that reality and use other tools. And that’s perfectly fine; there’s no need to be embarrassed. One just shouldn’t take the scientific pretension and insert it where it doesn’t belong. So also in the context of norms and facts, the difference is that factual statements are descriptive statements, indicative statements, and normative statements are imperative statements. You shall not murder, or it is forbidden to murder. Even “it is forbidden to murder” basically hides behind it a kind of command, right? Basically, “it is forbidden to murder” means that in some sense there is a command not to murder. It’s just another way of describing the same thing. And therefore one can speak here about the relation between imperative statements and indicative statements. Maybe a few more distinctions concerning claims before we get into the matter. There are various claims; there are various approaches. Positivism, basically—if we call them by their name—recognizes only factual claims as claims. Because factual claims are claims for which you have an empirical tool to determine whether they are correct or not. How can you determine whether “it is forbidden to murder” is a true statement? We have no way. Even someone who thinks murder is forbidden—meaning he is not a moral relativist, he doesn’t believe in moral relativity, but thinks it really is forbidden to murder, and whoever says it is permitted to murder is mistaken—still cannot give me a criterion. Meaning, he cannot give me tools like we have in the observational sciences. He cannot tell me what I am supposed to do in order to become convinced that it is forbidden. I understand that it is forbidden, but if someone doesn’t understand it, I have no way to show him, to give him some tool—okay, observe this and this, if you see such-and-such it will turn out that murder is forbidden, if you see such-and-such it will turn out that murder is permitted. Meaning, you have no means of verification—with a v. Yes. You have no way to clarify or test whether this claim is true or false. So the positivist says that if so, then it is not a claim. He says more than that. The logical positivist even said that in that case it is nonsense. Meaning, for example, all the claims of metaphysics, from the positivist’s point of view, are nonsense. When you say there is God…
[Speaker B] I don’t understand that. So on that level, “the sum of the angles of a triangle is one hundred and eighty degrees”—is that a factual claim according to the positivist? Yes. Why not? Because in the end it rests on two or three assumptions…
[Rabbi Michael Abraham] No, the claim is not that. A real positivist will tell you that the claim is that in Euclidean space, the sum of the angles is one hundred and eighty degrees.
[Speaker B] In Euclidean space. Yes. So I’ll say that in moral space, murder is forbidden.
[Rabbi Michael Abraham] What is the assumption that leads to that?
[Speaker B] Basic assumptions. What?
[Rabbi Michael Abraham] Of morality. For example?
[Speaker B] That you can define murder as forbidden.
[Rabbi Michael Abraham] Fine, okay, so that’s a basic assumption. Why can’t that be a basic assumption?
[Speaker B] No, there’s no problem, but—
[Rabbi Michael Abraham] Almost everything is basic assumptions. Fine, if you say the whole business is basic assumptions…
[Speaker B] Are there things that aren’t basic assumptions? What?
[Rabbi Michael Abraham] Here too there’s a basic assumption. I say the time now is 9:19. How do I know? I saw it. There’s a basic assumption there too—but who says that what I saw really exists? Here too there’s a basic assumption, it’s just that here it somehow seems completely obvious, so to speak, agreed upon by all of us, so we skip over it. Meaning, it’s obvious that if I saw it, then that’s how it is. You’re right that in principle you could reduce everything to basic assumptions. So that’s why the positivist sees metaphysical claims as claims that really don’t claim anything. Not as claims that I can’t check whether they’re true or false. If I can’t check, then they have no content. Because all their content is the possibility of checking them. What is content? Content means they claim something about the world. If they claim something about the world, then let’s see whether it holds in the world or not. If they don’t claim anything about the world, then they aren’t a claim. So for example, he’ll say that the claim that there is God, or that there are angels, or fairies, or whatever you want, these are not false claims and not true claims either—they simply aren’t claims at all, because I have no way whatsoever to check whether they’re correct or not. There’s no way. And again, the question of what counts as a way by which one can or cannot check—this is a very interesting and very difficult question, and in my opinion the positivists have no answer to it. But that’s the view.
[Speaker B] I have an idea. Factual claims yes, in the world—in the world of, say, moral arguments. There’s a basic assumption: “What is hateful to you, do not do to your fellow.” From there you can derive logically a great many things: murder is forbidden, theft is forbidden, this is forbidden and that is forbidden.
[Rabbi Michael Abraham] Yes, but you’ll derive it—you won’t really be able to derive it, because if someone says, “That isn’t hateful to me,” then for him it isn’t hateful, and you won’t be able to tell him, “Fine, but murder is still forbidden for you.” In other words, you still remain with an if-then, just like with Euclidean space. Meaning, if your assumptions are such-and-such, then yes, of course, that follows—that’s just simple logic. But you won’t arrive at any objectification of these claims. In other words, they won’t receive objective meaning, they won’t enable you to argue against someone who holds a different position.
[Speaker B] But, like, he’ll say—
[Rabbi Michael Abraham] “I don’t care if they kill me”? Yes. If it doesn’t bother me that they kill me, then in that regard the rule “what is hateful to you…” doesn’t apply. Meaning, it doesn’t dictate the move to “what is hateful to you, do not do to your fellow.” That doesn’t seem to people nearly as self-evident as “through two points exactly one straight line passes,” which somehow we all agree on. That’s why I said that sometimes there are assumptions. What? Fine, but I’m saying it’s less so—even people who agree with that understand that it’s not on the same level of certainty as “through two points exactly one straight line passes.” They think it’s terribly dangerous and terribly important, of course, to behave that way, but the level of certainty you have in it, the degree of truth, the feeling is that it’s not the same thing as “through two points exactly one straight line passes,” even though that too can’t be proven; it just somehow seems obvious to us. And therefore I say this is one of the failures of positivism—that it doesn’t feel that very often it too imports all kinds of assumptions into its outlook, only they seem so obviously true to it that it doesn’t count them as assumptions at all. But then again, if you already allow what you regard as an assumption to enter as an assumption, and that’s legitimate, then you open the door to everything, as you said earlier. And that is exactly the problem with logical positivism. In any case, for our purposes: there are claims that are factual claims, and at root they are descriptive claims; and there are claims that are judgment claims, and they are not descriptive claims in the simple sense. You can call them descriptions of morality, but they do not describe some fact that I can observe. They do not deal with the ordinary world, the physical world we know. One of the interesting places where the distinction between these two kinds of sentences comes up is in the eighth root principle of Maimonides. Maimonides writes there, in the eighth root principle, that one should not count the negation of an obligation together with a prohibition. Meaning, in the root principles—the question of what enters the enumeration of the commandments and what does not—he says: the negation of an obligation, a prohibition, that is a negative commandment; the negation of an obligation does not enter the count of the negative commandments. What exactly is the negation of an obligation? “Know that a prohibition is one of the two parts of a command.” Meaning, there are two types of commands, one of them is a prohibition, and that is because you command the commanded person to do one thing or not to do it. You can command him to do something—a positive commandment—and you can command him not to do something—a prohibition—those are the two parts of a command, and that is our topic: positive commandments and prohibitions. Just as you would command him to eat and say to him, “Eat,” or command him to keep away from eating and say to him, “Do not eat”—not “you will not eat” as a description, but “do not eat.” “And in the Arabic language there is no term that includes both of these notions together.” That’s a claim about Arabic; I don’t know Arabic, but he claims that in Arabic there is no common term for both of these kinds of commands. You know, there’s an interesting book by Whorf—I don’t know if you know it—he examined the influence of language on thought. The examples people always give, yes, are that Eskimos have thirty words for snow, all kinds of types of snow; every nuance has a different word. We’ll see two types of snow, and as far as we’re concerned, it’s snow. It won’t even seem to us that these are two different kinds. The Eskimos, because they live in such a world, their distinction is much sharper, so they create a word for every shade. But once you create a word for every shade, that also helps you distinguish between those two kinds of snow. I, who don’t have that word in my language, simply won’t distinguish—it’s snow as far as I’m concerned. What?
[Speaker B] You harvest dates one way, and you pick grapes another way.
[Rabbi Michael Abraham] Yes, right. Distinctions like that exist in many languages, distinctions of that kind, and clearly linguistic richness helps us distinguish, and of course the distinction also creates linguistic richness. I spoke not long ago about the one-two-many system, about those tribes that count one, two, many. Maybe because they live in pairs, life itself dictates it. Maybe, I have no idea. So they could understand that 10 is more than 2, but it was very hard to explain to them why 8 is more than 6. Meaning, that’s already closer, and there you need the mathematical concepts to help you make the distinction too. Where the distinction is obvious, people understand such distinctions. Meaning, language is not everything, but language helps a great deal; it increases your resolution. Okay, so in Arabic there is no distinction between a positive commandment and a prohibition. Think about the fact—and we’ll see later—that in everyday thinking too there is really no distinction between a positive commandment and a prohibition, not only in Arabic, and this trips up deontic logic. I’m already dropping hints for later, but this distinction is what trips it up. I think the halakhic distinction between a positive commandment and a prohibition will manage to create a deontic logic that won’t suffer from all the problems ordinary deontic logic suffers from, because we grew up with the fact that there is such a distinction, and it is somehow obvious to us. There are many people to whom this is not obvious. In other words, it’s all the same thing—what difference does it make whether you are commanded to steal or commanded not to steal? This is a positive command and that is a positive command too; all the rest is only what is demanded of me. Right? Is an action demanded of me, or is an omission demanded of me? It’s active versus passive. What? It’s active-passive. Yes, but all in all the demand is always a positive demand. The demand is positive; it’s just that what it demands from you is sometimes doing and sometimes not doing. Yes? If someone is running at constant speed, then stopping—is stopping an action or is stopping a non-action? You can always argue; it’s not always clear what counts as action and what counts as non-action. Okay, but the demand is an active demand. In Jewish law there are two kinds of demands. A positive commandment and a prohibition is not only a question of activity versus passivity; they are two different kinds of demand. Their deontic logic is different. And this is a distinction people don’t understand. Someone who didn’t grow up inside the world of Jewish law does not understand this. People think they understand the difference between a positive commandment and a prohibition—they do not understand it. They do not understand. By the way, even people in the halakhic world, when you sharpen the point for them, they haven’t thought about it. It’s just that this is how we grow up inside this language. They don’t think about it, so they immediately translate positive commandment and prohibition into action versus omission—but that is incorrect. This does not stand the test of Jewish law. There are positive commandments that require me not to act; there are prohibitions that require me to act. So in what sense is this a prohibition and that a positive commandment? There is something here where the demand itself is an active demand or a passive demand—not the act demanded of me. There is a negative demand and a positive demand. It seems to me that this is what Maimonides means when he speaks here about the two parts of a command. So in Hebrew there is a common word for this: command. It has two parts—commandments, or commandment: positive commandments and prohibitions. In Arabic there isn’t—there’s no common word; it’s simply two things. So on the one hand you can—there isn’t—
[Speaker B] In Arabic is there a word that tells you, “Don’t do such-and-such”?
[Rabbi Michael Abraham] No, there is—but it’s not the same word as the word for “do such-and-such.” They are not both called a commandment.
[Speaker B] Rather, it’s simply considered two different categories.
[Rabbi Michael Abraham] Meaning, yes. So in that sense, on the contrary, Arabic is like the Eskimos. They see these two things as completely different; they don’t understand at all what is similar between them. Okay, so this both helps them and doesn’t help them, because there is something similar here and also something different. They distinguish more easily that it’s different, but they don’t distinguish that these are two species of the same genus—that there is also something similar. Or at least it is harder for them to distinguish that.
[Speaker E] Suppose I demand that you do something, and I demand that you not do something.
[Rabbi Michael Abraham] Let’s say, something like that.
[Speaker E] But they won’t see that as a commandment?
[Rabbi Michael Abraham] No, no, on the contrary—they won’t put it that way. They won’t say “I demand.” In Hebrew I’d say, “I command you not to steal,” or “I command you to observe the Sabbath.”
[Speaker D] But—
[Rabbi Michael Abraham] An Arab would say, “I command you to observe the Sabbath,” and “I-something-you” I don’t know what for “not to eat pork.” It’s a different word. He won’t use the same word. For him these are two different semantic fields. He doesn’t see that these are two branches—it’s harder for him to understand that they are two different branches of the same thing. Two species within the genus called commandment. “And the logicians have already mentioned this, and said—this is their wording”—I don’t know whether he means the mutakallimun, “the speakers,” or whether he simply means those who speak about the craft of logic.
[Speaker F] By the way, in my opinion—
[Rabbi Michael Abraham] Also—
[Speaker F] With rabbinic commandments we are like Arabic.
[Rabbi Michael Abraham] There are—
[Speaker F] There’s a rabbinic positive commandment to light Hanukkah candles, but there is… separating refuse from food is Torah-level, and food from refuse is rabbinic.
[Rabbi Michael Abraham] The rabbinic prohibitions—the commandments are commandments by definition, obviously, but they are decrees. Rabbinic decrees are prohibitions; they are safeguards so that you won’t violate them.
[Speaker F] Fine, but—
[Rabbi Michael Abraham] They themselves are rabbinic prohibitions. No—
[Speaker F] That’s not correct. Also selection—the labor of sorting—is forbidden by Torah law. Now, Torah law forbids sorting with a sieve and sifter. And now the rabbis made a safeguard for you; they didn’t give you a prohibition just so you wouldn’t come to the sieve-and-sifter prohibition—they gave you hand-sorting.
[Rabbi Michael Abraham] Obviously, but that safeguard is—
[Speaker F] A rabbinic prohibition.
[Rabbi Michael Abraham] Now if I sorted food from refuse on the Sabbath, what did I violate? I didn’t arrive at sorting refuse from food; after all, they prohibited this so that I wouldn’t sort refuse from food, so that’s the safeguard involved. But I didn’t get to sorting refuse from food—I sorted only food from refuse. So what did I violate? I violated the rabbinic prohibition of sorting food from refuse. The fact that it’s a safeguard is the rationale of the law—that’s the reason they prohibited it. But now, practically speaking, it’s forbidden, and it’s like a rabbinic prohibition. You’re right that the newly instituted rabbinic commandments are probably—and there is also a very interesting discussion about this in the first root principle between Maimonides and Nachmanides—they are probably positive commandments. The author of Halakhot Gedolot claims there are seven such commandments; he counts seven rabbinic commandments. Maimonides attacks him: what do you mean, why don’t you count all rabbinic commandments? There are millions. So Nachmanides wants to argue in one of his explanations that he counts only the newly instituted commandments, not things that are a fence or safeguard for another commandment. And the newly instituted commandments, it seems to me, are all apparently positive commandments—but there too there is discussion. For example, ritual handwashing. Is there a commandment to wash one’s hands, or is there a prohibition on eating without washing one’s hands? You can interpret it this way or that way; it’s not clear. Okay? There is no commandment to wash one’s hands. If you didn’t wash your hands, nothing happened. But if you ate without washing your hands, you violated a prohibition. Now that is a newly instituted commandment; it is not a decree.
[Speaker B] Refuse from food is Torah-level?
[Rabbi Michael Abraham] Refuse from food is Torah-level, and food from refuse is rabbinic.
[Speaker B] If it’s immediate use and…
[Rabbi Michael Abraham] No, fine, I’m not getting into that. The Shulchan Arukh brings that this is the view of many medieval authorities—not all, by the way—the view of many medieval authorities that the three requirements in sorting all combine. Meaning, each one separately still remains Torah-level; you need all three for it to become rabbinic.
[Speaker B] And then it’s permitted—if you have all three it’s permitted?
[Rabbi Michael Abraham] What? No. If you have all three it’s rabbinic, as far as I remember. If you have all three it’s rabbinic, because on the contrary, the other positions say that one is enough. Say, you sorted food from refuse but you did it with a utensil. Fine? So is that rabbinic or actually Torah-level? Torah-level.
[Speaker B] But if you have the two, is it permitted?
[Rabbi Michael Abraham] No. So what do you mean by rabbinic?
[Speaker B] There’s no rabbinic, only between—
[Rabbi Michael Abraham] I’ll look again, but I don’t think so. If you have all three is it permitted? No. Close to the meal is a different matter—that’s a different leniency; that’s not sorting at all, you’re eating. I need to check; I don’t remember anymore. But it seems to me that in the Shulchan Arukh these three requirements combine in order for it to be rabbinic. But fine, I’ll look; I no longer remember. In any case, there they combine, meaning none of them has a status on its own. There are medieval authorities in whom one of them has status on its own. So the Shulchan Arukh—Maimonides in the eighth root principle says, “And the logicians have already mentioned this, and said…”
[Speaker B] What? The speakers—kalam.
[Rabbi Michael Abraham] I know, so I was debating whether he means the mutakallimun or whether he means those who speak in the field of logic, those who deal with it, the investigators of logic. I don’t know. In Arabic, mutakallimun literally means speakers, yes, that’s clear. “And they said—this is their wording: however, command and prohibition have no term in the Arabic language that gathers them together, and we were compelled to call them both by the name of one of them, namely command.” Basically, command in its essence means a positive commandment. But since we have no term that connects positive commandments and prohibitions, we call both of them command. Okay? “And now it has already become clear to you that prohibition belongs to the matter of command.” How has this become clear? Maimonides wrote it. Meaning, Maimonides claims that unlike what is reflected by the Arabic language, in essence it really is one matter. It is two different species within one genus. The genus is norms, normative statements—what is forbidden and what is permitted, or commands—but within that genus there are two species: positive commandments and prohibitions. But they belong to one genus. Okay? There is something shared between them. “And the famous word in the Arabic language that is assigned to prohibition is the word ‘la’”—that is, “do not.” “And this matter itself exists without doubt in every language, namely, that you command the commanded person to do something or not to do it.” It doesn’t matter whether you have a separate word or not; clearly there are two kinds of commands here. “If so, it is clear that positive commandments and prohibitions are both complete commands—things we were commanded to do, and things we were warned not to do. The name of the thing commanded to be done is positive commandment, and the name of the things warned against is prohibition.” Meaning, one species is called positive commandments, the second species is called prohibitions. “And the name that includes them both in the Hebrew language”—where there is a shared word for both—“is gezeirah,” decree. “Gezeirah” is before me. Maimonides claims that the word gezeirah basically means a normative statement, under which there are two subcategories: positive commandments and prohibitions. So positive commandments and prohibitions are two things. In Arabic, where there is no word like gezeirah, the word mitzvah itself serves for both meanings.
[Speaker D] Why doesn’t Maimonides say here “commandment” but rather “decree”? What?
[Rabbi Michael Abraham] Because there is also “commandment” in Arabic—sorry, Arabic. He claims that using the word “commandment” to describe a prohibition too is a borrowed usage; it’s not really correct. The word “commandment” applies only to positive commandments. But since they have no common word for both, they use the word “commandment” for both meanings. In Hebrew there is an independent word. We have already taken over from Arabic and use the word “commandment” in both contexts. In Hebrew, really, one should have said “decree”—that’s what Maimonides claims. By the way, all this is in translation. This thing was written in Arabic. I don’t know—he probably wrote that word in Hebrew, because otherwise how could you write this passage that Maimonides wrote here in Arabic? You can’t. This passage you simply can’t write in Arabic. It’s interesting—there are all kinds of interesting logical loops here. In any case: “And likewise the sages called every commandment, whether positive or negative, a royal decree.” Fine? Interesting. I don’t know where the use of the term “commandment” began to include also a prohibition—“negative commandments.” In the Talmud there are, I think, such expressions, right? It’s not something that came from Arabic.
[Speaker F] “Negative commandment”?
[Rabbi Michael Abraham] It’s not something we took from… it seems to me—I’d have to check; I don’t remember—but he claims that somehow this is really an influence from Arabic. In principle one should have said “decree,” not “commandment.”
[Speaker B] There are 613 commandments in the Talmud. How—613?
[Rabbi Michael Abraham] Ah right, that all 613… does it say “commandments” there?
[Speaker B] What, in Makkot?
[Rabbi Michael Abraham] Rabbi Simlai, yes, Rabbi Simlai there at the end of Makkot. It’s not organized… yes, there’s also in Kiddushin… I don’t know, I don’t remember, we’ll have to check. No matter. It’s an interesting question about halakhic jargon—whether all this is really taken from Arabic. That would surprise me very much if that’s so, because this is what we use all the time today. We speak about positive commandments and prohibitions—these are all commandments. “Decree” is not the expression we use. Still, all this until now is just an introduction: what is a commandment. But in this root principle Maimonides is coming to say what the negation of an obligation is—and that it is not a commandment. So Maimonides says: “However, the negation of an obligation…”
[Speaker B] For a prohibition you don’t get lashes for it if… when a positive commandment overrides a prohibition.
[Rabbi Michael Abraham] Well then, where is “commandment”?
[Speaker B] The question is whether it says “commandment.”
[Rabbi Michael Abraham] Yes, we’re talking about… obviously there is a difference between a prohibition and a positive commandment in the Talmud; that isn’t an Arabic invention.
[Speaker B] “Do not do” appears.
[Rabbi Michael Abraham] Yes, but the question is whether both are called “commandment.” Here—
[Speaker B] I found it: Rabbi Simlai expounded that 613 commandments were said to Moses: 365 prohibitions corresponding to the days of the solar year—
[Rabbi Michael Abraham] —and 248 positive commandments corresponding to the limbs of a person. So here it says “commandments.” Fine, so if so, then an influence of early Arabic. Yes. Fine. “However, the negation of an obligation is another matter: that you negate a predicate of a subject, and there is in it nothing at all of the matter of command. As when you say: so-and-so did not eat yesterday, and so-and-so did not drink the wine, and Reuven is not Shimon’s father, and the like—behold, all this is the negation of an obligation; it has no scent of command in it.” Meaning, the sages say in the Talmud that a prohibition is indicated by “beware,” “lest,” and “do not,” right? You need key words that indicate whether we are dealing with a prohibition. “Beware,” “lest,” and “do not.” And of course “do not” itself—for him he doesn’t even mention that; it’s obvious. Yes. But Maimonides says… This is, by the way, an interesting explanation for why the sages really did not mention “do not” itself, but only “beware,” “lest,” and “do not.” I usually understood it as because “do not” is self-evident; they came to say that besides that, “beware,” “lest,” and “do not” too. But perhaps not. Perhaps because “do not” also serves in the negation of obligation, not only as a prohibition. Whereas “beware,” “lest,” and “do not” are always prohibitions. Then that would be an interesting explanation for that rabbinic statement. I don’t know if it’s right, but maybe. In any case, he says that when we use the word “not,” sometimes in fact—or in my language I would say—it is an indicative sentence, not an imperative sentence. In other words, the “not” does not instruct me not to do something; it describes a negative fact. Okay? It is basically a descriptive sentence. So it’s a sentence that… what? Describes? No, instructs. It’s a command. Obviously. There is a word “not” that commands, and there is a word “not” that negates command. Exactly for that reason you need a root principle. Because in Hebrew there is the same word, which sometimes serves as a prohibition and sometimes serves as a negation of command, Maimonides devotes a root principle to this—the eighth root principle—saying: notice, not every time it says “not” is it a prohibition. Okay? Then he says: “And the word by which they mostly negate in Arabic is the word ‘ma,’ not ‘la.’ And they also negate with the word ‘la,’ or with the word ‘laysa’”—never mind. In short: “However, the Hebrews mostly negate with the word ‘not’ itself, by means of which they also prohibit.” Here again Arabic distinguishes between these two things: negation of obligation and prohibition are different words. In Hebrew both are done with “not.” Okay? Again, like the Eskimos. It’s a linguistic sensitivity. And this sensitivity also helps thought. We need to pay attention. What?
[Speaker B] In Hebrew there is “al,” which is command—“al” means “do not do.”
[Rabbi Michael Abraham] “Beware,” “lest,” and “al”—all three. Okay. In Hebrew “not” serves for both meanings. You’re right that it’s not only “not,” but “not” serves for both meanings. And apparently—I don’t know again, I don’t know Arabic—but he says that in Arabic they use separate words for this. Fine. “And they also negate with ‘ein’ and its attached pronouns such as ‘eino,’ ‘einam,’ and ‘einkhem,’ and the like. However, negation in Hebrew is with the word ‘not,’ as in: ‘And there arose not again a prophet in Israel like Moses,’ or ‘God is not a man, that He should lie,’ ‘Affliction shall not rise up the second time,’ ‘And no man stood,’ ‘And he did not rise and did not stir from him,’ and many such examples.” All these “nots” are not prohibitive “nots,” but negating “nots.” Now, fine, this is simple enough, but Maimonides says there are things that look like a prohibitive “not,” but are really the negation of an obligation. And this is a kind of intermediate level—a sentence that is halfway norm and halfway fact. For example: “Now the difference between prohibition and negation has already become clear to you, in that prohibition belongs to the matter of command, and exists only in the mode of command equally.” Fine? Now he says this: “And all this is self-evident to anyone who exerts himself a little.” Anyone who tries a bit will understand these distinctions. “And since this is so, it is not fitting to count…” Ah, perhaps I skipped an important sentence here actually. “Now the difference between prohibition and negation has already become clear to you, in that prohibition belongs to the matter of command, and exists only in the mode of command equally. I mean to say that just as command always pertains to the future, so too prohibition.” Both are called, as it were, future tense. “You shall not do” can be a description that you will not do, and it can be an instruction: do not do. So it sounds like future tense, but it is really a command. “And it is impossible in language for there to be command in the past, and likewise prohibition. And there is no way to insert command into narrative.” Narrative is an indicative sentence, a descriptive sentence. And command is a normative sentence, okay? And these are two different things. The future description, “you will not eat”—that is description. But “do not eat” or “you shall not eat”—that is command. Okay? This is indicative and that is imperative. “For narrative requires a subject and a predicate, whereas command is a complete utterance.” Behold, “Do not eat”—you don’t need a subject there. There is no subject that you need to mention, subject and predicate. Rather, “Do not eat,” meaning murder is forbidden. This is not a sentence built in the form of subject and predicate.
[Speaker E] The command itself is subject and predicate?
[Rabbi Michael Abraham] So Maimonides says there is no subject and predicate here. I think that’s just another way of saying the same thing. “And prohibition too does not enter narrative.” A prohibition is also not a narrative; it is an imperative sentence, not an indicative sentence. “Not so negation. For negation enters narrative and negates in the past and in the future and in the standing tense”—that is, the present. There is an interesting linguistic discussion here. Now what does he mean? “And all this is self-evident to anyone who exerts himself a little. And since this is so, it is not fitting to count negative commandments that are negations among the prohibitions in any way whatsoever. And this is a demonstrative matter requiring no witness beyond what we mentioned from understanding the meanings of the words so as to distinguish between…” Anyone who understands the linguistic difference between prohibition and negation needs no further testimony, proof—it is obvious. But of course Maimonides writes this because there are people who do not understand it. So he says: “And this was hidden from others than us,” which here of course means the author of Halakhot Gedolot. “Others than us” here is always him. “To the point that he counted ‘She shall not go out as the slaves go out,’ and did not know that this is negation, not prohibition.” What is “She shall not go out as the slaves go out”? That’s interesting. It’s not like “There did not arise in Israel a prophet”—that’s not the same thing; there it’s obvious, everyone understands that it’s only negation. But “She shall not go out as the slaves go out” is a halakhic instruction. It is a halakhic instruction. What do you mean instruction? The maidservant does not go free by loss of tooth or eye. So what does that mean? It means that you remove from the maidservant the law of going free by tooth or eye. Okay? But there is no command here. It does not forbid you to knock out her tooth or eye, nor does it forbid you to free her. The law that grants freedom this way does not exist for a maidservant; it exists only for a male slave. So you negate the obligation, and that is negation of obligation. So it is not a prohibition.
[Speaker B] You can’t free her through tooth or eye because you violate “you shall work them forever.”
[Rabbi Michael Abraham] Fine, but you don’t violate “She shall not go out as the slaves go out.”
[Speaker B] You violate—
[Rabbi Michael Abraham] “You shall work them forever,” perhaps—that is, if it’s a Canaanite slave. Yes yes, by tooth and eye this is a Hebrew maidservant. That’s a Hebrew slave.
[Speaker B] But if someone did free her, she really did go free.
[Rabbi Michael Abraham] Ah, you’re saying then “you shall work them forever” doesn’t apply. Yes, because it’s Hebrew. Never mind. Even if there is “you shall work them forever,” still that’s not the prohibition of “She shall not go out as the slaves go out.” “She shall not go out as the slaves go out” is not a prohibition. “You may not ignore”—what? “You may not ignore.” That is a prohibition.
[Speaker B] That would be a prohibition.
[Rabbi Michael Abraham] Yes. Even though it says “you may not,” which looks somewhat descriptive. There are things even more extreme on the side of positive commandments too: “Therefore the children of Israel do not eat the sciatic nerve to this very day.” That is just a descriptive sentence. But the sages—Rashba already speaks about this in his aggadic explanations on Berakhot. Rashba notes this; he doesn’t give a very convincing explanation there, but he points out that sometimes the sages received something as a positive commandment even though it is not formulated as a positive commandment. In any case, here he says: when you negate an obligation from a certain situation and from a certain person, that is essentially a sentence that you do not count as a prohibition. Because that sentence, in a certain sense, is a descriptive sentence, not a command sentence. It describes what is written in the lawbook, but in essence it comes to tell you a fact, not to command you. The “not” here functions linguistically as a descriptive “not,” not a commanding “not.” Okay? So in that sense it does not enter the count of the commandments. So here in this Maimonides there really is a very sharp distinction between norms and facts, and even a kind of intermediate level of negation of obligation, which ostensibly deals with norms, but negates the norm not in the normative sense but in the factual sense. In other words, it says: it is not true that this norm applies here. This is the factual negation of a norm.
[Speaker D] Is that the only example he gives?
[Rabbi Michael Abraham] No no, there is another example. Which other one? Yes.
[Speaker B] But earlier you told him that he also includes commandments that are not norms, that he can include commandments that are just, as it were, a topic—or laws of impurity—but perhaps there is no obligation to become impure or become pure or something like that.
[Rabbi Michael Abraham] Yes, where they are not commandments of anything. They define a procedure. No, this defines a procedure. Here you define nothing; you say this norm does not apply here. Fine. It does not apply. You can call this a detail within the law of release by tooth and eye. So there is a detail that for a Hebrew maidservant it does not apply. And that detail is described—the word “not” that describes that detail is not one that negates by way of command, but one that negates by way of description. It is not a “not” that comes as a prohibition, like “do not do.” You cannot say “beware, lest, and do not free this maidservant by tooth and eye.” If it were written like that, it would be a prohibition. Whoever freed her by tooth and eye would have violated a prohibition. Understand? But here whoever frees her by tooth and eye did not violate a prohibition; rather, there is simply no commandment to free her by tooth and eye.
[Speaker B] Yes, but Maimonides himself defines commandments that are only procedures and have nothing normative in them, so why can’t Saadia Gaon do that? Halakhot Gedolot. Ah—
[Rabbi Michael Abraham] Halakhot Gedolot. No, because with prohibitions he can’t do that. The prohibition here is a negating prohibition, not a commanding prohibition. You count a prohibition only if there is “beware,” “lest,” and “do not”—only with prohibitions. There is no such thing with commands; there are no key words with positive commandments. With prohibitions there is “beware,” “lest,” “do not,” and “not.” But within “not” you have to be careful that it is not a negating “not” but a commanding, normative “not.” Okay, so this is basically the distinction between facts and norms, and between imperative sentences and obligating sentences. Now the next step. There is what is called the naturalistic fallacy, or the is-ought fallacy, of David Hume. Basically, Hume argued that you cannot derive a norm from a fact. In other words, if something is—I don’t know—the chair is blue, therefore the chair is beautiful. The claim that the chair is blue is a factual claim. The claim that the chair is beautiful is a judgment claim—in this case aesthetic, not ethical, but never mind, it’s the same principle. The claim is that you cannot derive a norm from a fact. You cannot derive a norm from a judgment. For the argument to be valid, you need to add another assumption: for example, that what is blue is beautiful, or that what is colored in some way is beautiful. You can complete it in various ways, but you need to supplement it with another assumption. What is the nature of that additional assumption? It is an assumption that connects the plane of facts with the plane of norms. In other words: what is blue is beautiful. Yes, the fact is such-and-such. Meaning, you must have within the premises themselves some normative dimension if you want the normative conclusion to follow from the premises. If in the premises there are only facts, and in the conclusion there is only a norm—the conclusion is a norm—then clearly the argument is a null argument. In other words, it is invalid. You don’t even need to check where the problem is; there is a problem. It’s worth checking in order to see where, but even without checking you can know there is a problem. It cannot be. In other words, a norm can never be derived from facts. Now these things come up in many contexts. Again… what? Derived only from facts? Yes. The context in which Hume deals with this is the question of morality. That is, naturalistic conceptions of morality are conceptions that say a thing is immoral because it causes pain, or because it creates such-and-such a problem. Hume says: that is a null argument. Because the fact that something causes pain is a fact. But who says that something that causes pain is forbidden? So let’s add the assumption that whatever causes pain is forbidden. Now I ask you: but why is that true? When you try to ground your moral claim, you bring an argument that grounds the moral claim—you won’t succeed. Because if the claim is a factual claim, I know how to ground it: I simply look. I see whether the fact is true or false. If I could derive a norm from a factual claim, then no problem—I could also ground a normative claim. How? I would establish that the fact is true, and then derive the norm from that fact. The problem is that you cannot derive norms from facts, and therefore you cannot ground normative claims.
[Speaker B] Is that his argument in the name of Ben Elazar at the end of Kiddushin, that “In my life I have never seen a deer as a dryer of figs, or a lion as a porter,” and all sorts of things like that—is that a naturalistic link?
[Rabbi Michael Abraham] It’s a naturalistic link if you don’t supply another assumption. It’s like saying—someone who says murder is forbidden because murder causes, I don’t know, suffering, or it creates a lack in the family to which the murdered person belongs. That’s a good argument even though logically it’s a null argument. Why? Because it is obvious to everyone that causing suffering is forbidden. You simply skip over an assumption that is self-evident—
[Speaker C] You’ll skip over it.
[Rabbi Michael Abraham] Exactly. So you need to fill in assumptions that are self-evident, and then the argument will be a fine argument. Never mind. But many times we skip over them not for nothing. Let me perhaps give you an example to sharpen the point. Suppose there are various arguments in favor of changes in Jewish law. For example, validating women as witnesses. I don’t know if that’s already… yes. Let’s say, for the sake of discussion, women once were not educated; today women are more educated, and therefore they should be accepted as witnesses. There are many arguments of this sort. That argument is a null argument. Why is it a null argument? On its face—even before I check the details at all—because its premises are facts and its conclusion is a norm, a halakhic norm in this case. The factual premises are that women once were not educated—that is a fact. That women today are educated—that too is a fact. Okay, how do you derive the norm from those facts? In order to derive the norm, you still need to add another assumption.
[Speaker B] That the reason they were disqualified was… exactly.
[Rabbi Michael Abraham] An assumption that ties the norm to the fact. Namely, that the reason women were disqualified from testimony is because of the fact that they were not educated. If you add that assumption, no problem. But of course that is precisely the assumption that will be very hard for you to defend. How will you prove that the sages really disqualified women for that reason—or that the Torah, the sages, because this is Torah-level—disqualified women because of that? And since it’s hard to defend that, very often we simply hide the problematic claim and treat it as kind of self-evident—and sometimes it even works. In other words, we simply skip over the greatest minefield.
[Speaker F] Does reality changing matter even when we know the reason? What? Shaving on the intermediate days of a festival. We know that the reason they decreed the prohibition of shaving on the intermediate days was so that one would not enter the festival looking disheveled. Now, even though we know that is the reason and people shave, there is still a prohibition.
[Rabbi Michael Abraham] According to those decisors who hold it is forbidden.
[Speaker F] Those who rule that way—that’s the discussion. No, we know the reason why it was forbidden.
[Rabbi Michael Abraham] Very good, but those who rule that way perhaps really think that way. But there are others who rule differently, who say that because that is the reason, today it is in fact permitted. Or the reverse—perhaps it is even a commandment.
[Speaker B] It seems to me that all shaving—what happened with shaving—what—
[Speaker F] That’s it.
[Rabbi Michael Abraham] That is exactly what prevents… Or laundering on the intermediate days of the festival.
[Speaker F] It’s a fact that there are those who disagree.
[Rabbi Michael Abraham] You asked the question. Laundering on the intermediate days of the festival—there too, I think he brought that Rabbi Mazuz writes that today it is permitted to launder on the intermediate days. Because it is not the laundering that was forbidden—machine washing, in a washing machine. In any case, the naturalistic link… the naturalistic fallacy stems from this gap between factual claims and normative claims. Basically these are two completely different planes, and you cannot move from one to the other. In other words, in order to move from one to the other you need a bridge that carries you from one to the other. The principle?
[Speaker F] What does “naturalistic” mean?
[Rabbi Michael Abraham] What is it? “Naturalistic” means this: naturalism is a factual approach, meaning that you ground the norm in facts. And grounding a norm in facts is a fallacy, so that’s why it’s called the naturalistic fallacy. In other words, naturalistic moral theories are, for example, people who say: it’s immoral to murder because it’s not beneficial for evolution, because if you murder then we won’t survive. A society that permits murder is a society that won’t survive. That’s the naturalistic fallacy. You’ll hear a great many people claiming that this is actually the basis of morality. So they can say that, as a matter of fact, that’s how the moral feeling developed that murder is forbidden, but they cannot say that therefore murder is really forbidden. Because if it’s not beneficial for survival, so what? Who said that one ought to promote survival? You have to assume a normative premise that says that whatever does not promote survival is morally forbidden. But where does that come from? Does that also come out of evolution? Where does it come from? Therefore you can’t bypass this issue. It’s very easy to get confused about this, even though it seems like a clear distinction, but in many contexts we see people getting confused about it. So that’s the naturalistic fallacy. Now I want to maybe begin the topic of deontic logic; it’s taken me much longer than I thought. Basically, deontic logic deals, as I said before, with the logic of normative claims. Normative claims are divided, fundamentally, into three types. If we’re talking about commandments, then yes, Maimonides divided them into two types: positive commandments and prohibitions, and of course there is also permission. In other words: it is forbidden to do such-and-such, one is obligated to do such-and-such, and one is permitted to do such-and-such. Those are the three deontic operators, meaning the three basic deontic concepts, the basic deontic actions, or deontic directives. And deontic logic deals with how we find connections between deontic claims. For example, when I say that there is an obligation not to murder, that means there is a prohibition against murder. Right? In other words, if I say that obligation is O, obligation, right? Then O of not-X means F forbidden, right, F of X. In other words, there is a deontic identity between the obligation not to murder and the prohibition against murder. Basically, in other words, you can do without one of them. Once there is such an identity, I can dispense with one of them, right? Because every time I want to express a prohibition, I can express it by means of the operator of obligation; I just put the negation inside. Instead of “it is forbidden to murder,” I’ll say “there is an obligation not to murder,” and that’s all. With the negation operator and the obligation operator I can generate prohibition.
[Speaker B] Every time we don’t want to, do we make a blessing?
[Rabbi Michael Abraham] What? I talked about that in— we dealt with that in the email. Yes, the question whether commandments require intention is also said with respect to prohibitions. The well-known case of the scribe from Bnei Brak, who says that one has to have intention regarding “do not round off the corners of your head” and “do not keep a hired worker’s wages overnight.” Yes, so afterward we had some argument by email, because the Ari, of blessed memory, claims that yes, one must also have intention regarding prohibitions. Fine, that seems to me a strange thing. In any case, there are three types, but really they are not actually basic types. In fact, two are enough, because if I have obligation and permission, I can express prohibition. The obligation not to do something is the same thing as the prohibition against doing it. That is a standard deontic assumption. By the way, that is not true in Jewish law, I’m already telling you now. This identity, for example, is one of the differences between ordinary deontic logic and halakhic deontic logic, but I’ll talk about that later. Another assumption, or another operator, is the operator of permission. It’s marked as P. I don’t know what the P is in English, why permission is called P—do you have any idea? P as what? Possible. Ah, possible. Okay. So permission means that there is no obligation concerning it and no prohibition concerning it, right? That is what is called permitted. When you say that act X is permitted, that means that there is no obligation to do it and no prohibition against doing it, or no obligation to do its opposite and no prohibition against doing its opposite. Do whatever you want. Okay? That’s what it means for something to be permitted. If so, it turns out that permission is also actually unnecessary. In fact, all three of these can be reduced to one. Once I have the concept of obligation, and the operator of negation, I can do everything. Say, an obligation that X—so I say there is an obligation to put on tefillin, fine. If I want to say it is forbidden to put on tefillin, then I say O of not-X. There is an obligation not to put on tefillin; that is the prohibition against putting on tefillin. If I say that it is permitted to put on tefillin, then I say: it is not true that there is a prohibition against putting on tefillin. And I already reduced prohibition earlier, so it’s the negation of O, and inside that the negation of X. Right now I won’t do the full formalization here, but the principle is clear. So in practice, these deontic equivalences basically tell me that these three concepts are not really independent. In other words, I can reduce two of them to one. That is, P cannot ground the other two, but both O and F can ground the other two. Therefore one can choose one of them and build the entire deontic logic with it. That is the basic infrastructure of deontic logic. It creates various problems. It creates various problems, because you can show all kinds of paradoxes that arise in deontic logic. I’ll perhaps do that after I solve everything, because then it’ll be easier for me to show it with both the breakage and the repair—that is, the problem and its solution. So that’s why I said: I’ll do the formalism at the end. But that’s the idea, the basic idea of deontic logic. Let’s continue.