Deontic Logic in Halakha and Beyond
This transcript was produced automatically using artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.
🔗 Link to the original lecture
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Table of Contents
- Opening of the lecture and its three-part structure — a Torah-oriented introduction on types of commandments, then a move to deontic logic, and finally a connection between the two planes and its implications.
- Mapping four types of positive commandments — an obligatory positive commandment, an existential positive commandment, a prohibition inferred from a positive commandment, and a definitional positive commandment in the style of annulment of vows.
- The common distinction between positive and negative commandments as a practical distinction — positive action versus passive omission — and the difficulty raised by examples like fasting and refraining from labor.
- Examining positive commandments in civil law — taxes and military service as seeming examples, and preparation for the claim that there really are no “positive commandments” in law.
- Study of Maimonides’ sixth principle — why a commandment stated both positively and negatively is counted as two commandments, and what the extra precision in Maimonides’ wording teaches.
- Undermining the practical definition through examples — the Sabbath, Yom Kippur, and “do not stand idly by your neighbor’s blood” prove that formulation determines more than the character of the act.
- A proposed alternative definition — a positive commandment points to a desired state, while a prohibition points to a negative state, regardless of whether this involves action or omission.
- Normative implications of the distinction — coercion, a parapet for a roof, the zero state, and the difference between “not being righteous” and “being wicked.”
- Comparison to Nozick’s philosophy of law — enticement versus extortion as an illustration of an objective zero line separating a positive state from a negative one.
- Conclusion regarding the world of law — law deals only with the categories negative/permitted and is therefore built primarily as a world of prohibitions, without a category of “righteous.”
- Introduction to deontic logic — a distinction between descriptive claims and prescriptive claims, and presentation of the operators of obligation, permission, and prohibition.
- The modal interpretation of deontic logic — normatively perfect possible worlds, and the standard logical relations among obligation, permission, and prohibition.
- Difficulties with ordinary deontic logic — conflicts, contrary-to-duty cases, conditional obligation, and Ross’s paradox, which arise from the accepted modal interpretation.
- Application to Jewish law — the need for two systems of operators: a normative plane of commandments/prohibitions and a practical plane of what one should actually do.
- Enriching the halakhic model — indices for different commandments, conflicts of the type where a positive commandment overrides a prohibition, and examples from Maimonides and from the topic of new grain and matzah.
Summary
General Overview
The lecture sought to connect the world of Jewish law with deontic logic. The point of departure was that the common distinction between positive commandments and prohibitions — action versus abstention — is inadequate. Based on a close reading of Maimonides and various halakhic examples, a deeper distinction was proposed: a positive commandment points to a desirable positive state, whereas a prohibition points to a negative state in which one may not be. On that basis, it was argued that ordinary deontic logic is too sparse to describe Jewish law, and that a richer model is needed.
## Types of Positive Commandments and a Conceptual Introduction
Rabbi Michael Abraham opened by distinguishing among several types of positive commandments: an obligatory positive commandment that can be fulfilled or neglected; an existential positive commandment that can be fulfilled but whose non-fulfillment is not a transgression; a prohibition inferred from a positive commandment, which can only be violated but not fulfilled; and a definitional positive commandment, such as annulment of vows according to Maimonides, which is neither an obligation nor a prohibition but rather lays down a procedure. He then presented the ordinary distinction between a positive commandment and a prohibition as a practical distinction: positive action versus passive omission.
## Why the Practical Definition Is Incorrect
Using Maimonides’ sixth principle, he argued that the practical definition does not hold up. Maimonides rules that when the same norm appears both as a positive commandment and as a prohibition, both are counted, and he even emphasizes that each is counted in its own category. That emphasis seems unnecessary — unless positive and negative commandments are not defined by the character of the act. Examples such as “you shall cease” on the Sabbath, fasting on Yom Kippur, and “do not stand idly by your neighbor’s blood” show that a positive formulation can require omission, and a negative formulation can require action. Hence the criterion is not practical execution.
## A Desired State versus a Negative State
The central proposal is that a positive commandment indicates a desirable state that the Torah wants me to be in, whereas a prohibition marks a negative state that the Torah forbids one to be in. Therefore, “to be wearing tefillin” is not the same as “not to be without tefillin.” Even if practically the same result may emerge, normatively these are two different kinds of instruction. From this follow several implications: by neglecting a positive commandment a person is not “wicked” but rather not “righteous”; a prohibition carries punishment, whereas neglect of a positive commandment generally does not; observing a prohibition can sometimes occur in an empty way, whereas a positive commandment requires positive realization.
## Law, Nozick, and the Absence of Positive Commandments in the Legal World
From there the Rabbi moved to law: in law there are not really positive commandments in the halakhic sense. Paying taxes or serving in the army does not make a person “righteous”; it merely prevents him from being a criminal. Law deals only with negative states and with punishment for them. The comparison to Nozick — the difference between enticement and extortion — illustrated the idea of the “zero line”: there is an objective baseline state, and what is above it is positive or legitimate, while what is below it is forbidden harm.
## Deontic Logic and Its Limits
In the second part he presented the foundations of deontic logic: operators of obligation, permission, and prohibition, and their modal interpretation through normatively perfect worlds. But this model has difficulty handling conflicts, contrary-to-duty cases, and conditional obligations. Paradoxes such as Ross’s paradox also arise because ordinary logic assumes too sparse a system of normative relations.
## The Halakhic Model: Two Layers and Indices
Returning to Jewish law, he proposed a richer model. One must distinguish between a normative plane — which commandments and prohibitions exist — and a practical plane — what I should actually do in practice. On the normative plane, the same act may involve both an obligation and a prohibition, each from a different commandment-index. Thus with eating matzah made from new grain: on the one hand there is the commandment to eat matzah, and on the other hand the prohibition of new grain. The conflict is not a logical contradiction but a normative collision, and its resolution is carried out on the practical plane through decision rules such as “a positive commandment overrides a prohibition.”
## The Conclusion
The conclusion is that halakhic deontic logic must include two systems of operators, and must add indices for different commandments. Only such a model can describe multiple prohibitions applying to one act, permissions and prohibitions from different angles, and conflicting obligations. In Rabbi Michael Abraham’s view, this enrichment is not only useful for understanding Jewish law, but may also solve central paradoxes in general deontic logic.
Full Transcript
One more remark that I won’t be able to go into in detail here, but it’s still worth keeping in the background: there are several kinds of positive commandments. With prohibitions, for example, less so, but with positive commandments there are several types. In principle, take a positive commandment — say, I don’t know, the commandment to put on tefillin. If I put on tefillin, I have fulfilled a commandment; if I do not put on tefillin, I have neglected a positive commandment, meaning this is a kind of transgression, okay? So an ordinary positive commandment — they call it an obligatory positive commandment, “obligatory” in the sense that you are required to do it, and if you do not do it, you have committed a transgression, and the transgression is neglecting a positive commandment.
But there are positive commandments that are not like that. There is a positive commandment called an existential positive commandment. An existential positive commandment means that if you fulfill it, you have a commandment to your credit, and if you do not fulfill it, nothing happened. Meaning, it only works in the positive direction, not in the negative. So that is a positive commandment that can be fulfilled, but cannot be neglected.
A third type is a positive commandment that can only be neglected but not fulfilled. This is called a prohibition inferred from a positive commandment. A prohibition inferred from a positive commandment — for example, if the Torah says, “You may lend with interest to a foreigner” (Deuteronomy 23:21). Right? To someone who is not Jewish, it is possible to lend with interest. It is not commanding you to lend with interest; it is only saying that the prohibition on lending with interest to someone who is Jewish does not apply to someone who is not Jewish, that’s all. So there is no commandment here if you lend with interest to someone who is not Jewish. Excuse me to our friends here, but there is no commandment to lend with interest to someone who is not Jewish. Rather, if you lent with interest to someone to whom it is forbidden, then you have also neglected this positive commandment, not only committed a transgression. So this is called a prohibition inferred from a positive commandment, and that is the third type. It is a positive commandment that can be neglected, but there is no way to fulfill it, okay? For example, to eat produce of the seventh year, during the Sabbatical year — that is not a commandment, but if I do something that is not eating, that is a transgression; for example, commerce in seventh-year produce is a transgression. Because one must eat, but not really “must eat”; rather, one must only eat. Meaning, with a prohibition inferred from a positive commandment, the emphasis is on the “only.” Meaning, you should eat, and if you did something else, then in effect you have neglected that positive commandment; it is a kind of transgression.
And there is a surprising fourth type, which Maimonides adds, and that is a positive commandment that cannot be either fulfilled or neglected. You can’t do anything with it. For example, the commandment of annulment of vows, Maimonides says. Suppose a woman makes a vow; her husband can annul the vow for her, okay? There are all kinds of rules about when and how and so on. There is no commandment to annul vows, no prohibition against not annulling vows, nothing. Meaning, it is not something that obligates you to do something, nor something that forbids you to do something. It only defines the procedure. Meaning, if you want to cancel the vow, this is the way to do it; if you did not do it, the vow is not cancelled. So this too is defined by Maimonides, for some reason, as a positive commandment, but it is a definitional positive commandment. It can neither be fulfilled nor neglected. That is the fourth type.
Okay, that really is just in brief, just so it will be there in the background. I’m returning now to the difference between positive commandments and prohibitions. The accepted explanation is, as I said earlier, the practical definition. That is: does the commandment require me to act? If so, it is a positive commandment. If the commandment requires me not to act, or forbids me to act, then it is a prohibition. Once I asked some professor at the Hebrew University — I spoke with him when I was dealing with this topic — Alon Harel, he was in the news a while back, so I asked him whether, in his opinion, there are positive commandments in Israeli law. He said, “Yes, of course.” So, what do you say? Are there positive commandments in Israeli law?
[Speaker B] The Good Samaritan.
[Rabbi Michael Abraham] The Good Samaritan, yes, following “do not stand idly by your neighbor’s blood,” with Hanan Porat. But let’s leave that aside for the moment; it’s a little tricky. Maybe I’ll comment on that later, but let’s take simpler things.
[Speaker C] What about the obligation of the law—
[Rabbi Michael Abraham] Does it obligate me to do something, or only not to do something? Taxes. Hm? Well, right, the obvious candidates are paying taxes, for example, which you are required to pay, or military service — not everyone is careful to fulfill that instruction, but those are two examples of positive commandments. Okay? Why indeed are those examples of positive commandments? Because of the definition I gave earlier, which from now on I’ll call the practical definition. The practical definition says that the distinction between positive commandments and prohibitions is the manner of performance. Meaning, if you want to fulfill a positive commandment, you have to do an act. If you want to fulfill a prohibition — meaning not violate it — you have to refrain, meaning not do something. Okay? In halakhic jargon this is called that with positive commandments we fulfill them through positive action — meaning I am required to get up and do something — and we violate them through passive omission. That is the expression for inaction.
[Speaker D] Is fasting a positive commandment or a prohibition?
[Rabbi Michael Abraham] Ah, excellent question. Seemingly, according to that view, fasting is a prohibition. Right? Because I’m required not to eat. Okay? Excellent example; I’ll get to it later. It’s even timely — Yom Kippur is coming up soon. So actually my purpose in that conversation with Alon Harel was to explain to him that in my opinion there are no positive commandments in Israeli law, and I’ll try to explain why I think so. But in order to clarify this point, I want to use a principle that appears in Maimonides.
Before his Book of the Commandments, where he counts all the commandments, the positive and the negative — it is divided into positive commandments and prohibitions — before the book there are fourteen principles. In general the number fourteen is very dear to Maimonides. A lot of things with him are fourteen. The Mishneh Torah — “yad” is fourteen — fourteen books, there are fourteen interpretive rules, yes, all kinds of things. In any case, in the introduction to this book he lists fourteen rules that guide him when he comes to determine what counts as a commandment, how the commandments are classified, what enters the count and what does not enter the count; sometimes commandments are split, sometimes several details are combined into one commandment. So you need all kinds of rules.
And Maimonides worked with a very strong sense of reflection; I spoke a bit about this once in the series when I discussed the introduction to Jewish law. Maimonides really was exceptional in this respect — he gives a full account, Nimrod would have been delighted with him, he gives a full account of his methodology. Meaning, he really gives the rules, with the reasons, with everything needed — truly with amazing reflection. I don’t think there is anything comparable to it, really; I think his whole enterprise has no equal, even globally. But within these fourteen rules, there is the sixth rule, the sixth root, as it is usually translated into Hebrew. So I’m reading it here; you see it in bold. Quotations are always bold in this text.
The sixth rule — wait, where is it? Yes? The sixth rule: “A commandment that contains both a positive and a negative form should have its positive element counted among the positive commandments, and its negative element counted among the prohibitions.”
Maimonides says the following: sometimes in the Torah there are commandments that involve a certain duplication, except that one time it is formulated in active language, like a positive commandment, and one time it is formulated in passive language. For example, there is a commandment to cease on the Sabbath, and not to do labor on the Sabbath. “You shall cease” on the Sabbath is the language of a positive commandment, right? And “do not do labor on the Sabbath” is a prohibition. Or earlier they mentioned fasting, so say there is a commandment to afflict oneself, and there is a prohibition against eating. Okay? The content overlaps, but the formulations are active in one case and passive in the other.
Now, Maimonides’ rule — and this is in the ninth principle, which I did not bring here — Maimonides’ rule is that if the Torah repeats the same thing several times, it is not counted several times; it is counted once. Suppose the Torah says ten times to keep the Sabbath: there is one positive commandment to keep the Sabbath, not ten. Okay? That is the ninth principle. The sixth principle — and don’t ask me why he placed it earlier — is a qualification of the ninth principle. He is basically saying: if the duplication is between a positive commandment and a prohibition, that is not considered duplication. Meaning, here we do count both commandments. Everything I said in the ninth principle applies only when there are two positive commandments or two prohibitions. But if the overlapping content is formulated once as a positive commandment and once as a prohibition, then we count two commandments.
But Maimonides takes the trouble here to say something else as well, and Maimonides is generally precise in his wording, so when we infer things from his wording, it is not hair-splitting — unlike other close readings, which very often are hair-splitting — because Maimonides really was precise in his language, and the rule is that one has to pay close attention to what he writes. And here, in this case, notice that he added another point: not only that when there is this overlap between a positive commandment and a prohibition we count two commandments, he added something else — that the positive commandment is counted among the positive commandments, and the prohibition is counted among the prohibitions.
Fine, you’ll say, “Well, okay, obviously — what? If we count both, then the positive commandment belongs with the positive commandments, and the prohibition belongs with the prohibitions… what? Why did he need to add that? Just say we count both of them, that’s all; why add all this detail?” So the answer to that — I won’t read the continuation, the continuation is just examples he brings — let’s try for a moment to think, say, about the commandment to keep the Sabbath. There is a commandment to cease on the Sabbath; that is a positive commandment. And there is a commandment, “do not do any labor” — yes? There is a prohibition against doing labor on the Sabbath. So how would we define these commandments according to the practical definition I gave earlier? As with fasting on Yom Kippur, say, what you asked earlier — same thing. What do you say?
[Speaker D] Prohibitions.
[Rabbi Michael Abraham] Right? They are both prohibitions, because why should I care that you formulate it in the language of “you shall cease”? In the end, what you require of me is not to do labor; you require omission from me, not action, right? So in effect that is a prohibition. Therefore Maimonides sees fit — and we need to understand why — but therefore this is not trivial. When Maimonides says that we count two commandments here, that is not enough; he has to add: the positive commandment is counted among the positive commandments, and the prohibition is counted among the prohibitions. And what that basically means is that the definition that distinguishes a positive commandment from a prohibition is not the practical definition. If the definition were the practical definition, then both of these should have been prohibitions, and the same applies to fasting on Yom Kippur and many other examples.
Let’s perhaps bring a few more examples. For instance, there is the commandment: “Do not stand idly by your neighbor’s blood” (Leviticus 19:16). The Good Samaritan was mentioned earlier; we once discussed that it isn’t exactly the Good Samaritan, but “do not stand idly by your neighbor’s blood” means that if you see, say, your fellow drowning in a river, you have to save him. Okay? Now, “do not stand idly by your neighbor’s blood” in formulation is a prohibition, okay? But what does it require of you? Not not to stand, but to do something, right? So in effect, according to a practical definition, we should have counted it as a positive commandment. But no — all the enumerators of the commandments count it as a prohibition, not as a positive commandment. Here it is not even a double formulation as on the Sabbath, so this is actually a better example, because on the Sabbath there are both sides: there is also the positive commandment to cease, and also the prohibition against doing labor. Here there is only the negative side — “do not stand idly by your neighbor’s blood” — there is no separate explicit obligation to save. And nevertheless this is counted as a prohibition, not as a positive commandment. So we see — and I could bring many more examples — that fundamentally the practical definition is not the correct definition, not in Jewish law in any case, okay? Basically this means less—
[Speaker E] To do.
[Rabbi Michael Abraham] In the question of the distinction between positive commandments and prohibitions, that is not what distinguishes them; that is not the criterion. But isn’t that surprising? Sorry?
[Speaker F] Isn’t that surprising? After all, the term “do” — yes — it’s right there.
[Rabbi Michael Abraham] If it weren’t surprising, I wouldn’t have needed this whole introduction, obviously; that’s my whole topic. But yes, of course it’s surprising. I’ll tell you more than that: it surprises leading Torah scholars as well. Even people who know the whole story — I didn’t find anyone who dealt with the question of what defines the difference between positive commandments and prohibitions, except for one article in Tarbiz by Aharon Shemesh, the Talmud scholar at Bar-Ilan University — that’s it. It’s unbelievable: the most basic concepts in the halakhic world, and there are no discussions of the definition of what it means for something to be a positive commandment as opposed to a prohibition, what distinguishes them. Look, for example — leave definitions aside for a moment, okay?
[Speaker F] Beyond counting them in certain fixed numbers, is there any other practical difference whether it’s a positive commandment or a prohibition?
[Rabbi Michael Abraham] That’s a good question, and it would require a long answer, so I won’t get into it here. All right? But it’s a good question. On the face of it there aren’t practical differences, but there are indirect practical differences. Down here I brought two examples. You see? Two formulations, say, of putting on tefillin. You could formulate it as “you are commanded to put on tefillin” or “there is an obligation to put on tefillin.” You could also formulate it as “you are forbidden to be without tefillin.” Now the first one, according to the non-practical definition — rather, according to the definition based on formulation — is a positive commandment, right? The second is a prohibition, but their content overlaps. Meaning, you are basically saying the same thing in two different formulations, and it receives a completely different halakhic status. There are many, many differences between positive commandments and prohibitions, many implications, and this is a very strange thing. It is very strange because even if the formulation is different, in the end what matters is the content. Meaning, if the content is the same content, then in what sense — what does it mean that one time it is a positive commandment and one time a prohibition? If I had written it once in Hebrew and once in English, would that mean something different? As long as the translation is reasonable, it means the same thing, just in two languages. Here too, these are two languages for saying the same thing. So how is it possible that two logically equivalent sentences lead to different implications at the normative level, at the halakhic level? Okay? After all, they are logically equivalent; it is like saying the same thing twice.
So here the point to notice is — perhaps even before that. The article by Aharon Shemesh that I mentioned earlier — may his memory be a blessing, he died relatively young — he really noticed this point. And in the way of Talmud scholars, he dealt with the archaeology of the passages, meaning the earlier strata and the later strata, something that in yeshivot people deal with less. And he discovered that in the earlier strata the definition really was the practical definition. Meaning, when you are required to do something, it is a positive commandment; when you are required to refrain, it is a prohibition. But in the later strata, gradually it undergoes a kind of metamorphosis, and it moves into the situation I have described to you here. I’m describing the situation in a, yes, diachronic way. What? The Talmud spans several generations, so in the earlier generations — yes, say the second or third century CE is early, the fifth century CE is later. Still, I do see, I—
[Speaker B] I don’t see this as logical equivalence, and I’m saying that from the direction of, for example, other normative matters, where I know that there is a difference, okay? For example, in the way people interpret what the government is allowed to do as opposed to what private individuals are allowed to do, meaning, in the—
As for the principle of legality, yes. When they tell you that you are forbidden to do something, then basically from that you say that everything else is allowed to me, and that brings with it, for our purposes, other interpretive implications between the two cases. And therefore I am not necessarily sure that they are logically equivalent in the example of phylacteries.
[Rabbi Michael Abraham] You are absolutely right not to be sure, and in another moment I’ll get to that, and it’s a very good comment. First of all, first of all, at the level of logical analysis, leave law aside, it simply is not equivalent. The two statements I marked here are not equivalent to one another. They would be equivalent if the command and negation were commutative. Right? Meaning, if I could say “a command not to” or “not a command to do something,” that would be equivalent, but it isn’t. Think, for example, if I say: you are not commanded not to—you are not commanded, sorry, you are…
[Speaker E] That’s not right.
[Rabbi Michael Abraham] …that you are commanded not to put on phylacteries. So what does that mean? That you are commanded to put on phylacteries? It could be that you are not commanded at all, right? Meaning, there is also a state of indifference between those two things. So the negative formulation allows for indifference. But if I tell you that you are commanded to be with phylacteries, there is no indifference; you must be with phylacteries. Right? Therefore the relation between these two operators, or these two logical actions, negation and command, is not commutative. Meaning, you may not switch them. “Commanded not to” or “not commanded to do so” is not the same thing. Okay? A question is possible?
[Speaker C] Yes. There’s something here I don’t understand. It’s true that “commanded not to” and “not commanded” are not equivalent, but ostensibly “commanded to do so” and “not permitted not to” should be equivalent. So if you are commanded to put on phylacteries, you are forbidden not to.
[Rabbi Michael Abraham] “Permitted” is a loaded expression. “Permitted” is a loaded expression. With “commanded,” that’s clear. With “permitted,” we need to understand what exactly that word means.
[Speaker C] Don’t you understand “permitted” as “not commanded not to”?
[Rabbi Michael Abraham] I’m not sure. We need to think about it; I’m not sure. Fine. But regarding “commanded,” I am sure. Meaning, with “commanded” it is not equivalent. “Permitted,” I need to think a bit about what the concept really means, and then accordingly. But either way, if it is the same thing as “commanded,” then yes, and if not, then it is something else, which is not what I am talking about.
[Speaker C] Okay? Fine, maybe at the end I’ll have more questions, thank you.
[Rabbi Michael Abraham] Okay. So there really is no logical equivalence here. So first of all, the difficulty as I presented it is not really there. Now, truly, what is the idea behind this? I think the definition is actually this: the question of what defines positive commandments as opposed to prohibitions depends on whether the Torah points to a desirable state or to an undesirable state. And if the Torah points to a desirable state in which you are required to be—desirable not in the sense of voluntary; desirable in the sense that you must be there, the desired state, yes? The state that the Torah wants—so when the Torah points to the desirable state in which it wants you to be, that is a positive commandment. When the Torah points to the state in which you must not be, a negative state, a state in which you are not wanted, that is a prohibition. Now, those states in themselves, positive or negative, can be states of action or states of omission. It really does not matter. And that is the definition of a positive commandment versus a prohibition. Meaning, when the Torah tells me, for example: you are commanded to put on phylacteries, it is essentially telling me: your being with phylacteries is the desired state; that is where you need to be, okay? In contrast, if it tells me: I do not want you to be without phylacteries—that is, I do not care if you are with phylacteries, but make sure not to be without them. Now, if you have some kind of zero state that is neither this nor that, I have no problem with that. It may be that there is no such zero state, and then de facto it comes out that in any case I am going to put on phylacteries, but even then I put on the phylacteries not in order to be with them, but in order not to be without them. Meaning, this is not something that has value in itself; I am merely fleeing a state that is undesirable, okay? Therefore in any case, whether there is an intermediate zero state or not, that is basically the meaning. And therefore, for example, when the Torah tells me to desist, we asked earlier: so is that a positive commandment or a prohibition? After all, all it is really telling me is not to do labor. Right, at the level of performance it is not doing labor, but when it tells me to desist, it is essentially saying: look, it is not that the state of labor is a negative state; rather, the state of cessation is the positive state. So if you do labor, I have no principled problem with that, except that you are not in the desired state of cessation. But that in itself does not bother me, says the Torah, yes, if you do labor. In contrast, if it tells me: there is a prohibition against doing labor, then it is saying: your doing labor is problematic in itself, not merely that you are not in a state of cessation. So that says something different, and it has all sorts of implications. For example, if I am under compulsion and I do not perform a commandment, okay? Then I am not guilty, but bottom line, I did not perform the commandment. But if I do not violate a prohibition under compulsion, then nothing happened; I did not commit the transgression, but I also did not fulfill any commandment. Meaning, there are states here— even if there is no zero state at the practical level—this has certain implications. Say I have a house; we are commanded to build a parapet on the house, “You shall make a parapet for your roof” (Deuteronomy 22:8). There is also the prohibition, “You shall not bring blood upon your house” (Deuteronomy 22:8); one may not leave a house with places where people can fall or something like that. This is basically saying the same thing: you need to put up a parapet so that people will not fall from the roof. What happens when I have no house at all? I have no house. Then clearly I did not fulfill the commandment to make a parapet for my roof. Nobody is going to come to me with complaints, but I did not fulfill the commandment. But on the other hand, I obviously did fulfill the prohibition, because I do not have a house without a parapet. Vacuously—I have no house at all. So vacuously I also fulfilled the prohibition, but that is only with regard to the prohibition. The positive commandment I did not fulfill, okay? So even though it seems that the practical content overlaps, it has all kinds of implications. Now for example, yes?
[Speaker C] Why, actually, not say that I also fulfill the positive commandment vacuously, because every house I have has a parapet vacuously, because I have no house?
[Rabbi Michael Abraham] No, you need to build a parapet, not that you need to have a house and that every house you have should have one. Say, if you bought a house and it has—if you bought a house and it has a parapet, you did not fulfill the commandment.
[Speaker C] Ah, I need to kind of—okay, yes.
[Rabbi Michael Abraham] The commandment is to build, yes, you need to see to it.
[Speaker C] But if I have no house at all, then can’t one say vacuously that I built a parapet for every house I have?
[Rabbi Michael Abraham] No, because you did not build. Vacuously, you have no house without a parapet—that is true—but I do not think one can say that vacuously you built one. But this is “built”—again, it is the question of how you relate to this action: can one perform an action vacuously, or only be in a state vacuously? Fine, good question, I don’t know, we need to think about it. Huh? Yes. No, vacuously is always something imaginary, yes? So the point is that what we are really saying here is that we divide states, from the standpoint of Jewish law, into positive states and negative states; in the middle there is some kind of zero state, say, some wall separating them. If I am commanded to be in the positive state, then I am forbidden to be either in the zero state or in the negative state, right? But even if I am in the zero state, it is not that I violated a prohibition; I just did not fulfill the positive thing that I was supposed to fulfill. In contrast, if I have a prohibition, then I am forbidden to be in the negative state. I am allowed to be, sorry, in the zero state, and of course also in the positive state, right? So here is the difference: whether I am allowed or forbidden to be in the zero state, okay? That is one of the things. Now in this context, when I spoke with Alon Harel, he gave me an example of this issue. He told me: there is Robert Nozick, a Jewish-American philosopher, a legal theorist—but not only a legal theorist; he also published Newcomb’s paradox and various other things—so among other things he asked: what is the difference between an inducement and extortion? An inducement is legally permitted and extortion is forbidden. Meaning, say I tell a person: look, if you do something, you’ll get 100 shekels. If you don’t do it, you won’t get it. Okay? I am trying to motivate him to do it. But “if you do it you’ll get it,” that is the carrot: if you do it you’ll get 100 shekels; if you don’t do it you won’t get it. I can motivate him by means of the stick. I can tell him, look, if you don’t do it I’ll take 100 shekels from you, and if you do do it, then I won’t take it. Now, in both cases, of course, the potential difference is 100 shekels, right? Meaning, the difference is 100 shekels. But inducement is permitted, and extortion is forbidden. Why? What is the difference? After all, overall you can always do it and I won’t take from you; everything is fine. I left you an option in which your rights are not harmed. So what—what? The answer is already there: you have to allow him not to comply as well. Or in other words, right—in other words, it seems to me that what this means is that when you offer someone a proposal, both alternatives have to be within the bounds of law. Meaning, not to harm his rights. Now, in inducement both alternatives are within the law: I can give him nothing, and I can give him 100 shekels. In extortion, only one of them falls within the law. When I do not take from him, that is fine. And if I do take from him, that is forbidden. Okay? But for our purposes, what interests us here is that if I relate to it only as a gap, as a difference in potential, as I said earlier, only as a gap, then there is no difference between them. The difference between them is created only because there is an objective zero state that is not relative. Everything above it is within my rights to do, and therefore if I choose two options above the line, that is fine. But if I choose two options of which at least one is below the line, that is not fine. Meaning, what stands in the subtext of the distinction between inducement and extortion is that there is a zero state that defines positive states above it and negative states below it. Harming rights is negative, or not harming rights is positive. Okay? And what this means, basically, is exactly parallel to what we see between positive commandments and prohibitions. Meaning, a positive commandment basically says: I am relating to positive states. The Torah points to a positive state. In a prohibition, the Torah points to a negative state. Okay? This means that there is some absolute line, irrespective of the Torah’s pointing, because in both cases the Torah points. There is a line prior to the Torah’s pointing, and it determines what is a positive state and what is a negative state. And now the Torah chooses: if it chooses to point to a positive state, that is a positive commandment; if it chooses to point to a negative state, that is a prohibition. But the line is a line that exists on the meta-level of Jewish law; it is not a result of the Torah’s commands, it is given. And one can expand on this in various contexts. But that is basically the parallel to Nozick’s distinction. Now, what does this actually mean?
[Speaker B] What this actually means, Rabbi, is that it somewhat reminds me of saving oneself with another person’s money, the same logic.
[Rabbi Michael Abraham] Right! That’s what I was hinting at. Rabbi Shimon Shkop there—exactly, exactly that. In any case, what this means basically is that the definition of positive versus negative commandment, the distinction between positive and negative commandment, is not a practical distinction, but a distinction based on some subtext or meta-halakhic framework of positive states and negative states. Yes—what harms my rights is a transgression, and someone who does not give me more than my rights—well, he did not perform a commandment, but he also did not commit a transgression; that is his right. Okay? So he is not righteous, but he is not wicked. Meaning, someone who is in a negative state is wicked; someone who is not in the positive state that the Torah wants is not righteous. But notice: both of these are defined as transgression in Jewish law. There is the transgression of neglecting a positive commandment—that is, not being righteous—and there is the transgression of being wicked. These are defined as two different categories of halakhic delinquency. Okay? So in practice—maybe I’ll go back to the world of law—what I wanted to say there to Alon Harel was: according to this definition, there are no positive commandments in law. There are only prohibitions. The duty to pay taxes or serve in the army—suppose I do it—nobody regards me as righteous. You did your basic duty. And conversely, if you do not pay taxes, you will be punished. You’ll go to jail, I don’t know what. Or if you do not serve in the army, assuming you are not wearing the right clothes, then you will be punished. Okay? So in fact, that is the indication. Say, in halakhic contexts, how do I know when this is a positive state and when it is a negative state? For positive commandments one receives reward—in the world to come or whatever, one receives reward. For nonperformance, if one violated a prohibition, one does not receive reward. Why not? Because if you are righteous, you deserve reward. If you are simply not wicked—well, why should we give you reward? That is the basic requirement, okay? In contrast, punishment is given only for prohibitions. Judicial punishment is given only for prohibitions; there is no punishment for neglecting a positive commandment. Why? Because you are not punished for not being righteous. You are okay, so you are not righteous. But if you are wicked—yes, if you are wicked, then you deserve punishment. Meaning, these are the implications of the distinction between positive states and negative states. When you look at it this way, Israeli law gives no prize to anyone for anything—not within the law. You might get to the president and receive the President’s citation for some wonderful civic deed—fine—but the law does not see you as righteous. That does not belong to the legal framework. Within the framework of law there are only wicked people and normative people. That is what there is; there are no righteous people. Therefore law, by its essence, speaks only in terms of prohibitions. Some of them are prohibitions that require you to act. Fine—but we said that the practical side is not relevant. We are speaking about the question: from my standpoint, not paying taxes is a negative state. Paying taxes is not a positive state; it is the ABC of not being wicked, okay? So that is why I think that according to this definition there are no positive commandments in law; there are only prohibitions. Yes? Yes.
[Speaker F] What you are basically saying is, if I understood you correctly, then the law says “pay taxes,” but what it is really saying is: you must not fail to pay taxes. Meaning, it is like a restriction; the restriction is what you keep.
[Rabbi Michael Abraham] Right. Like this sentence. Yes. Like the sentence I blackened here, you see? Exactly that. Instead of saying you are commanded to put on phylacteries, the law says you are forbidden to be without phylacteries. It’s the same—or when it says the upper one, it means the lower one; it is really saying the upper one.
[Speaker B] What is the connection, what is the connection between this and, for our purposes, love and fear of God? Love is certainly positive. Is fear positive, or is it a positive commandment or a prohibition?
[Rabbi Michael Abraham] You have excellent comments today, Erez. No, today too. Nachmanides on the Ten Commandments ties the difference between positive commandments and prohibitions to the difference between love and fear. But to explain that—it is not the commandment of loving God and fearing God; both of those are positive commandments—but rather the distinction between the inner motions of love and fear. But for that I need a separate class on how to define it. Reserve one. Reserve one. No—if you reserve all the things I need classes for, we won’t get very far. So therefore the claim, in the end, is that in the legal world, according to the non-practical definition, but according to what we may call the normative definition or however we want to call it, there are no positive commandments; there are only prohibitions. And now we are going to see some implications of this. So I now want to move to deontic logic and see what this says with regard to deontic logic. It has all sorts of interesting implications, I think. I’ll try to touch on a few of them, as many as I can. Logic, basically—when we look at language, we can see various types of sentences. There are sentences that are propositions, and the accepted definition of a proposition since Aristotle is a proposition that can be judged in terms of truth or falsity. A sentence that can be judged in terms of truth or falsity is a proposition, usually a factual proposition. Say if I say: it is dark outside now—that is a proposition; in this case a false proposition, but it is a proposition, okay? Or: it is light outside now—that too is a proposition; in this case a true proposition. Factual propositions are the simplest example of propositions. There are sentences that are not propositions. I ask you: what time is it? That is not a true sentence or a false sentence; it cannot be judged in terms of truth or falsity, but it is a sentence in language, okay? It is a sentence that is not a proposition, okay? There is, say, the question of truth and falsity; one can say that this is what logic deals with. That is not exactly right; science deals more with that. Logic deals with the relation between factual propositions and true and false propositions. But in general, say, science and logic deal with propositions—with propositions, factual propositions or propositions in general. Beyond that, there are propositions that some call prescriptive propositions as distinct from descriptive ones. There are descriptive propositions—say factual propositions, for example. Prescriptive propositions are propositions that do not describe something, but rather belong to the normative world. For example, one is forbidden to do something, or one must do something else, okay? These are propositions that are, one might say, in a certain sense loaded; they are not neutral. A factual proposition is neutral. “It is light now,” “it is dark now”—okay, what is there is there. A prescriptive proposition is a proposition whose role is to motivate you to do something or prevent you from doing something, okay? It is a proposition that carries some kind of charge in the sense of motivating action or inaction, okay? So basically the third type of propositions is propositions—let’s now call them norm propositions, okay? Propositions of obligation, prohibition, and permission, for the sake of the discussion. It is with propositions of that type that deontic logic deals. And deontic logic basically handles these operators that speak about obligation, prohibition, and permission—basically those three, let’s say, okay? Obligation, prohibition, and permission; the relations among them; what they maintain; and how exactly one handles this issue. To explain this a bit more, I may want to give you just a little of the notation, just so that you can get the idea. Do you see the tables here?
[Speaker F] Can I ask you a question? Yes. The moment it is normative, then is it like methodology? Meaning, it is prescriptive. If you are doing research, you must—if you want it to be scientific—there is a certain norm? This is how you do it, this is how you don’t do it, you know…
[Rabbi Michael Abraham] More than that: also a moral norm, a halakhic norm, and a legal norm, yes.
[Speaker F] It’s not what happens in practice, but what the norm is, yes.
[Rabbi Michael Abraham] Right, right. It is not descriptive; it determines what is proper and improper, or something like that. Now, say for example, if you say under Israeli law, according to Israeli law it is forbidden to steal—that is descriptive; it is not prescriptive. I am describing what is written in the statute book. When I say stealing is forbidden, that is a prescriptive proposition, okay? Because, say in the simple sense, if I want to test the truth or falsity of a proposition, I need to compare it to the state of affairs in the world that it describes. If there is correspondence, it is true; if there is no correspondence, it is false, okay? But with a prescriptive proposition I have nothing to compare it to. But with the proposition that under Israeli law it is forbidden to steal, I do have something to compare it to: I open the statute book and see, okay? So that means this is a proposition that in its essence has nothing to be compared to. And therefore…
[Speaker F] So what is the meaning—what is the meaning of inference in such a space? Yes? What is, as it were, the meaning of inference? So what—what—what is the pattern of inference?
[Rabbi Michael Abraham] Yes, before inference—what is the meaning, are there correct and incorrect sentences here, or true and false ones? Inference is already the next stage, meaning how you get from one true sentence to another true sentence, but in the first place, what does a true sentence mean in such a thing?
[Speaker F] So there isn’t truth here—there isn’t truth here because it is prescriptive.
[Rabbi Michael Abraham] No, if there is no truth here, then ostensibly there is no inference here either. There is some kind of truth here—call it truth or don’t, it doesn’t matter—but the proper and the improper. Meaning, tell me: when I say it is obligatory to murder, that is a false sentence. It is not false in the factual sense, but it is improper; it does not fit the standards of morality or something like that, okay? Fine, but this gets us into very large philosophical disputes—how objective morality is, moral realism, and all sorts of things like that. I don’t want to get into that. So there is here—look at the tables—in these two tables, you have the three basic operators at the top. Obligation, yes, that is O. O of p means it is obligatory that p. P of p means it is permitted that p. And F of p means it is forbidden, yes, forbidden. Those are the three operators. Now, the relations among them—look how many relations there are among them: O of p is equivalent to F of not-p. If I say that it is obligatory to do p, that means it is forbidden not to do p, or to do not-p, yes? Say, if I say there is an obligation not to steal—or, forbidden to steal—right? So when I want to move from O to F, I need to change the negation sign inside the argument, okay? Or permitted—permitted p—what does that mean? That there is no obligation to do not-p, right? There is no obligation to do not-p—what does that mean? That it is permitted to do p, okay? Because you have no obligation to do not-p, so you are also permitted to do p, okay? That is the second equivalence. The third equivalence is that it is obligatory to do p implies that it is permitted to do p. The reverse is not true, right? If it is permitted to do p, that does not mean that it is obligatory to do p. I am allowed to read a book; I am not obligated to read a book. If I am obligated to read a book, then obviously it is also permitted to me, okay? So there is here a relation of implication. These are basic relations between the deontic operators.
[Speaker D] Isn’t one missing here? Where?
[Rabbi Michael Abraham] You can apply more negations here, of course.
[Speaker D] No, because because permitted and… maybe I’m getting mixed up in the terminology, but permitted and… permitted and forbidden are—that is, just as there is obligation there is, as it were, exemption…
[Rabbi Michael Abraham] So I’m saying: substitute A into B. You see that in B on the right side it says: no obligation to do not-p, right? Now convert the obligation to do not-p, according to A, into a prohibition to do p, and substitute it in place—you’ll get what you want. That is the… I gave here the three basic relations, but obviously you can generate more relations from them.
[Speaker I] So the fourth one basically follows from…
[Rabbi Michael Abraham] Yes, you can derive them. So these are the basic relations. Now, it is customary in this world of deontic logic to give this meaning by means of wo
possible worlds; this is called a modal interpretation. What does that mean? Well, it really starts with modal logic. Modal logic deals with what is necessary or possible, the relations between necessity and… There are truths and falsehoods; that is ordinary logic. Modal logic talks about it being necessary that P, or possible that P. And there too, by the way, there are relations that are quite similar to what we have here; it is not accidental that they give it a similar interpretation. There are relations there, yes: if it is not possible that not-P, then it is necessary that P, and so on. Now, there it is customary to give the modal operators an interpretation in terms of possible worlds. What does that mean? When I say, for example, that P is necessary, what I really mean is that in every possible world I can imagine, P is true, P holds. Okay? What is the advantage of this interpretation? Instead of dealing with modal operators, I move to simple logic, just with quantifiers. That is, instead of dealing with the logic of necessity and possibility, I deal with ordinary logic of truth and falsity, but with quantification over all possible worlds. What is true in all possible worlds means that it is necessary in our world, within the framework of one world. So the price is that, instead of speaking about necessity and possibility, I stay with ordinary logic, without necessity and possibility, but with quantification over possible worlds. That is the trick of modal logic. There are disputes about that too; it also leads to problems, but that is not important right now. As far as I understand, this is the accepted interpretation in modal logic. A similar move is made in deontic logic as well. In deontic logic too, in order to avoid the ambiguity in these operators of P, F, and O, what people do is give them an interpretation—but this time in terms of normatively or deontically perfect worlds. Okay? What I am really saying is this: suppose I am in a given world, a certain W1. I quantify over all the worlds equivalent to it that are normatively perfect. Now, if I say that one ought to do P in our world, what that really means is that in all normatively perfect worlds, people do P. They do it—not that they ought to do it; there is no more “ought.” I got rid of “ought” and “not ought” and moved to true and false. Exactly the same idea. Okay? Now, the modal interpretation of deontic logic allows me to find all kinds of relations between modal operators and tautologies and things of that sort. In a moment I will show you some examples. Yes, you can test inferences, prove relations, and so on by means of the modal interpretation. These relations too, by the way, that we see here, can also be checked using the modal interpretation, right? For example, this equivalence between it being obligatory that P and it being forbidden that not-P. Okay? Check all the normatively perfect worlds: if it is obligatory that P, then P holds in all perfect worlds, so that means that not-P does not hold in any of them; therefore not-P is forbidden. Okay? So these relations too can be derived from the modal interpretation. Now, there are several problems with the modal interpretation, and here it is much worse than in logic
[Speaker F] modal logic; there too there are problems.
[Rabbi Michael Abraham] What? It means that there are worlds in which it holds. There is at least one world in which it
[Speaker F] holds, yes.
[Rabbi Michael Abraham] So that means the existential quantifier really parallels permission, and the universal quantifier is either prohibition or obligation. In any case, now, some of the problems with modal logic—and again, all these problems, all the problems I know, I am not an expert in this field, all the problems I know in modal logic are problems in deontic logic, sorry, that stem from the modal interpretation. And that is a very important point. Okay? I will give examples. For instance, modal conflicts, right? Suppose stealing is forbidden, but I need to steal in order to save a life. Now, whatever your view is—whether it is permitted, forbidden, obligatory—you can argue about it, but how do I test it according to the modal interpretation? After all, in a perfect world people do not steal, right? Stealing is forbidden. So if stealing is forbidden, then in all worlds there are no thieves, right? So what does that mean? In such a perfect world, if someone is in mortal danger, do people steal there or not? It cannot be that they steal there, because in a perfect world people do not steal, regardless of the situation. Okay? You cannot represent conflicts in this modal interpretation, right? Or injuring someone in order to heal him, performing surgery—it hurts him, and causing pain is forbidden, so in every perfect world it is forbidden to cause pain; but on the other hand, in every perfect world one must do everything possible to heal someone. So how do I describe that within the framework of possible worlds? What happens in those worlds? One of them comes out imperfect in some respect. In other words, there is something here that is hard to handle in the modal interpretation.
[Speaker F] There is something called defeasibility, meaning a logic where you are allowed to say, uh, unless, you know.
[Rabbi Michael Abraham] Okay, the question is how you insert that “unless” into this formalization.
[Speaker F] Yes, yes.
[Rabbi Michael Abraham] So, okay, here is another example. It could of course hold vacuously: in all perfect worlds there are no sick people, right? Like doctors always say: the hospital could be perfect, if only the patients would stop interfering—or in the university, if only the students would stop interfering with the lecturers, and so on. So yes, it can be perfect vacuously, but it cannot deal with real situations. There is also contrary-to-duty, right? CTD. These are situations where, if you robbed someone, you must return the stolen item, okay? But in a perfect world there are no robbers; people do not rob.
[Speaker C] May I ask a small question? Yes. Just to ask whether you are going to talk about Kratzer semantics or not, because it is very relevant here.
[Rabbi Michael Abraham] Ah, I do not even remember what that is, even though I saw it once. So maybe I will talk about it without knowing that that is what it is; I do not know.
[Speaker C] No, I will postpone that to the end too. Huh?
[Rabbi Michael Abraham] Ah, okay.
[Speaker C] I will postpone that to the end.
[Rabbi Michael Abraham] Okay, so, uh… the obligation to return a theft means that someone stole something, and now the question is—uh—so he is obliged to return it. How do you describe that in terms of perfect worlds, in a modal interpretation? So in all the worlds in which there is a thief, he also returns the stolen item. But there are no perfect worlds in which there is a thief. So how are you going to describe that in a modal way? Okay? There are, for example, proposals—okay, wait, before the proposals, look for example—
[Speaker H] Couldn’t one simply say that this applies to something that is actually the empty set?
[Rabbi Michael Abraham] Right, as I said, it can be perfect vacuously. You assume that in all perfect worlds there are no sick people, or no thieves, fine—but then the obligation to return has no meaning, because it holds only vacuously. Yes. Uh… so there are proposals to formalize this, right? Maybe it is related to what Daniel said earlier. Look at what I am blackening here, right? Like conditional probability. What I am doing is defining an obligation given Q. That is, it is a perfect world except that Q occurred in it—someone stole. Now, in a perfect world, everyone who stole must return. So it is true that you can formalize such statements this way, but it does not really help us deal with them logically, because when you now think through exactly what the perfect worlds are, when you want to draw inferences, you constantly have to remember that it is not really a perfect world, because after all, stealing happens there. So from the standpoint of theft, a perfect world is a world without thefts; from the standpoint of restitution, the perfect worlds are worlds in which thefts occur. So how am I supposed to handle these two sets of worlds and try to derive conclusions from them? Okay? So it is a little hard to use this proposal in order to solve problems. Look, for example, at conditional obligation, okay? For example: whoever wants to eat meat must slaughter the animal properly according to Jewish law, okay? And you can also just not eat meat—that is your right. But if you eat meat, you have to slaughter it, okay? Now the question is how to formalize this. So the first proposal—and this is debated among deontic logicians—there is a proposal, the simplest proposal, which is this. Okay? That it is obligatory that if P then Q; meaning, if you want to eat, then slaughter. Okay? And that is obligatory. But that raises all kinds of problems. Why? Let us look at it through the modal interpretation. According to the modal interpretation, it means you can infer the conclusion that if it is obligatory that P, then it is obligatory that Q. Right? Meaning, let us formulate it this way: if this is given, and now add this assumption as a second assumption—just the antecedent, right? Just this. Second assumption. Then this is the conclusion of the argument, right? If those two are assumptions, then this is the conclusion of the argument. Okay? How do I see that? Very simply. If it is obligatory that P, then in all perfect worlds P holds, right? Now according to the upper statement, in every world where P holds, Q must also hold. So that means that in all perfect worlds Q also holds. So that means O of Q. In other words, I can distribute that O, right? What do you call that? Associative? I do not know what to call it, right? That O of P implies O of Q. Okay? No, not commutative—commutative means interchangeable. When you open parentheses. Distributive. Distributive, yes, exactly. Distributive.
[Speaker F] But I think that does not express what we wanted to say, right? Because suddenly slaughtering has become obligatory. No, of course not.
[Rabbi Michael Abraham] Of course not. Which is why—again, without going on too long—it is quite clear that the more correct formalization is this one. Okay. Okay? If you want to eat, that is not obligatory or not obligatory; if you want to eat, then slaughtering is obligatory. Meaning, in all perfect worlds in which P holds—and P does not hold in all of them, but if P does hold—then in all those worlds Q also holds, okay? And that is the more correct formalization. So this, for example, is a use of the modal interpretation, right, of perfect worlds to find the correct formalization, okay? Of course I check it against my intuitions, but it gives me the correct formalization. Now here, for example, there is a collection of paradoxes in deontic logic. For example, Ross’s paradox. Right? Ross’s paradox says that if P is obligatory, then P or Q is obligatory. That is easy to prove in the modal interpretation, right?
[Speaker C] Sorry, one small question? Yes. In the previous formalization you wrote P arrow OQ; wouldn’t the way to interpret that be not that if P is true then Q is true in all perfect worlds?
[Rabbi Michael Abraham] No, P holds. “True” is a bit of a problem here. P holds in all perfect worlds. Because it is not exactly true; rather, it is an event that happens.
[Speaker C] Yes, but if it holds in all perfect worlds, then it is true in all perfect worlds that P, so shouldn’t you write OP here? No, no.
[Rabbi Michael Abraham] In all perfect worlds in which P holds—not in all of them does it hold, but among the perfect worlds, in those worlds where P holds, Q also always holds.
[Speaker C] So is that not simply O of P implies Q?
[Rabbi Michael Abraham] No. It is P implies O of Q. Fine,
[Speaker C] later.
[Rabbi Michael Abraham] Fine. If you want to eat meat, then slaughtering is obligatory. P is the desire to eat meat, and Q is the obligation to slaughter.
[Speaker C] I mean, okay, it is not quite the conventional way people usually use these symbols, but okay, I will not insist. Why?
[Rabbi Michael Abraham] I think it is. What, you mean the deontic symbols?
[Speaker C] Yes, I mean, from the standpoint of what you wrote here in deontic logic, it means that if P is true in the actual world, then in all perfect worlds Q is also true. That is the meaning…
[Rabbi Michael Abraham] Ah, sorry, I should have wrapped all of this in another O. You are right.
[Speaker C] That could, yes, okay.
[Rabbi Michael Abraham] If you wrapped the whole thing in O, maybe that would solve… right, you are correct. It is a different notation, you are right, but I should have wrapped the whole thing inside O. Now, for example, Ross’s paradox says this: if P is obligatory, then P or Q is obligatory. Right? That is easy to prove, because it is a simple implication in logic, right? And it holds in every world, so it also holds in all worlds. Now you understand that this means that if there is an obligation not to steal—or yes, to murder. Meaning, if there is an obligation not to steal, then there is also an obligation not to steal or to murder. But the obligation not to steal or to murder can be fulfilled either by not stealing or by murdering. So that means there is actually a positive value to murder in that world. Okay? So this is another problem in deontic logic. There are also various other paradoxes, it does not matter, there is Chisholm and others of that kind, but let us leave that for now. I want to move on. So basically, all these maneuvers and these problems—or rather, I presented very few, but there are many of the same kind—are really problems that arise, it seems to me at least, from the modal interpretation. In other words, in the modal interpretation one can prove that these things hold, and it does not fit with our accepted ethics, okay? So somehow it does not match the accepted semantics that we give to ethical principles. Now let us go back to Jewish law, okay? We return to Jewish law, and now look: can I write this equivalence in Jewish law, in light of the introduction I gave above? Look at this equivalence, for example. This one. Okay? If there is a positive commandment that P, then there is a prohibition of not-P. There is a prohibition on not-P. Never—not just not always. If there are two commandments, then yes, but it is not that one is derived from the other. If there is a commandment to rest and a prohibition against doing labor, then you have a positive commandment and a prohibition, but it is not that one is derived from the other. That is, it is not enough to state one and derive the other from it, okay? But this equivalence simply never holds—not just that sometimes it does not hold; it does not hold, period, okay? In Jewish law. Now why not? Because in Jewish law the concept “forbidden” has a double meaning: forbidden can mean a negative prohibition, and it can also mean failure to fulfill a positive commandment; that too is a kind of prohibition. The more correct relation here should be: it is not true that there is permission for not-P, okay? It is not true that not-P is permitted. But I cannot say here that there is an obligation concerning not-P. This is exactly the gap between positive states and negative states; one has to understand that there is not, and cannot be, any logical relation between what takes place above the zero line and what takes place below the zero line. No logical relation can take me from above to below. You can say there may be a commandment; it is not true that O of not-P is like O of P, or permission of P, or whatever, okay? But you cannot turn it into the plane of the F’s. The F’s and the O’s do not talk to each other. If F means a negative commandment and O means a positive commandment, right? If I give them that interpretation. So that means that in Jewish law something happens that deontic logic cannot really handle. On the other hand, it is clear that on the practical plane of Jewish law, there this does hold. Meaning, if I have an obligation to put on tefillin, then I am forbidden not to put on tefillin. It is just that this “forbidden” is not a negative commandment but failure to fulfill a positive commandment. But the relations, in their logical sense, exist in Jewish law too. Obviously—they are logical relations; they exist everywhere, okay? So what one has to notice here is that when we deal with Jewish law, with the deontic logic of Jewish law, we actually need to deal with two systems of deontic operators. One deontic operator deals with commandments and transgressions, okay? What commandments there are and what transgressions there are. The second system of deontic operators deals with what I am required to do. On the plane of what I am required to do, then even if someone tells me, “You are forbidden to be without tefillin,” it means I am required to put on tefillin in order to avoid that state. And if I have a commandment to put on tefillin, I am required to put on tefillin. Okay? So when I move to the practical layer, the deontic relations do hold, but they do not hold between the norms themselves. Fine? They do not hold among the positive commandments and the negative commandments. Therefore a full description of Jewish law must contain two systems of deontic operators. Yes, in practical Jewish law we have—for example this notation, do you remember this notation? An obligation to do not-P. According to Jewish law, what is that? It is a positive commandment. It is a positive commandment to refrain, or not to do something, but it is still a positive commandment. Right? In deontic logic that is a prohibition. It is a prohibition to do A. Obligation not-A means prohibition to do A. Okay? In Jewish law there are actually four states, not two: O of A and O of… and F of A. In Jewish law there are F of A, F of not-A, O of A, and O of not-A. Fine? There are four states, or four deontic states, or let us call them deontic states, say. Fine? So there are not the relations I mentioned earlier either. And that means that when—if I want to know, if I say there is an obligation to do A, then it is true that there is a prohibition against being in a state of not-A. There is no negative commandment, no formal prohibition, but there is a prohibition. On the behavioral plane the deontic relations do hold, but not on the normative plane. So I really need to prepare two systems of deontic operators, right? One of them deals with the practical plane, and there the ordinary relations hold; meaning that there will also be no difference between F and O, because O of A is the same thing as… not F of not-A—right? That is what… it is the same thing. No, sorry, it is F of not-A, without the “not.” So there it does hold, and therefore one of them is actually redundant. That is, I can use only the O’s because I express the F’s through the O’s, on the practical plane. But on the normative plane, no. On the normative plane I cannot move between O and F; both of them have to be present. In other words, the normative system is richer than the practical system, more independent, with more components than the practical system. Look at an example: “One who plows a single furrow… and is liable for it on account of eight prohibitions.” Meaning, you do one act, A, and you violate eight negative prohibitions. Right, like that old comedy sketch: driving on the sidewalk against traffic without a license and crashing into the kiosk, running a red light, right? One who plows with an ox and a donkey—it is forbidden to plow with an ox and a donkey together, okay? And they are consecrated; they are sacred property, right, and it is forbidden to work with consecrated animals. And mixed seeds in a vineyard: when he plows, there are seeds there that are forbidden mixtures that he is plowing. And in the seventh year. And on a festival in the seventh year, right? And besides that, he is also a priest who has also taken upon himself Nazirite status and is standing in a place of impurity, an impure area, where both a priest and a Nazirite are forbidden to be. In short, he violates eight prohibitions in that one act. You understand that what is happening here is that it is not enough to say that this act is forbidden. So what if it is forbidden? Forbidden in what respect? It may be forbidden because of eight prohibitions, or two prohibitions, or seventeen prohibitions. It may be forbidden simply because of failure to fulfill a positive commandment; there may be no prohibition at all, only neglect of a positive commandment. In other words, the deontic repertoire is too poor. It is not enough to tell me that something is permitted or forbidden. You have to tell me which prohibition I violated, or whether I violated a prohibition at all, and list them all. Therefore, as you can understand, a full picture of halakhic deontic logic, besides the two systems of deontic operators, also has an index. That is, every O-operator has an index i. Okay? And i runs from 1 to 613, the 613 commandments. Meaning, this commandment, that commandment—because if we are talking only about positive commandments, then it only goes up to 248. And the negative commandments are 365, okay? But there is an index, and so in fact I have not only two independent operators and two systems of operators, but for every kind of such operator there is an index that ranges over hundreds of commandments. And only that is a full description of deontic logic in the halakhic context. By the way, in my opinion, in the ethical context too. And standard deontic logic in the ethical context—precisely because it does not make these distinctions—that is what gets it into all the paradoxes I described before, in my opinion. And we showed this in a book we wrote about it. In my opinion, this solves all the paradoxes I know; I do not know, maybe there are others. So therefore, just think for example—let me give you an example, an amusing example, maybe a bit blunt, but still an amusing one. There is a man named Yaron Yadan. He used to be some Haredi head of a kollel, and he left everything and now works on attacking the halakhic system. By the way, some of his claims are valid, in my opinion. But never mind. One of the things he especially likes is the following criticism. And later I saw—there is that podcast “Meeting at the Professors’,” do you know it? It started with… what was his name, he passed away recently, Agassi. It started in Agassi’s house, but now it continues, never mind. So there too someone came and gave a lecture in which he basically copied everything from Yaron Yadan, some Aizikov fellow, never mind. His criticism is this: he brings this Maimonides from the laws of forbidden sexual relations, and he says as follows: “A man’s wife is permitted to him. Therefore, whatever a man wishes to do with his wife, he may do: he may have intercourse whenever he wishes”—I warned you, right? I gave a warning that this is blunt—“and he may kiss any limb he wishes, and have intercourse with her in the usual manner or in an unusual manner,” and so on, “provided that he does not emit…” In short, he does whatever he wants, right? Now he says: what do you mean? What is this, that the woman is some object and he decides whatever he wants to do with her? What kind of immoral system could write such a thing? Now, there are problems in Jewish law regarding morality; I do not deny that. This is not one of them. Why not? His misunderstanding actually stems from a problem in deontic logic. Why? And I said that one of Maimonides’ rules is that he is precise in his wording, and he is also precise about where he places each law. And you already have to pay close attention: this law appears in a collection of laws called the laws of forbidden sexual relations. The laws of forbidden sexual relations are laws that deal with the question of which sexual acts are permitted, from the standpoint of the Holy One, blessed be He. It has nothing to do with the question—nothing to do with the question—of whether you are behaving properly toward your wife or improperly toward your wife; the question is what is permitted to do. Say, for example, two spouses—that is, a married man and a married woman, not to each other, right? A married woman, they commit adultery together, and both of them agree, and their spouses also agree—this is open marriage, okay? Everything is fine, everything is allowed, okay? Now, no, that is not really polyamory, that is open marriage. So then, so then, so then, fine, there is no problem with anyone; there is no moral problem here, right? But Jewish law forbids it. Meaning, the halakhic prohibition is not a prohibition—it is not necessarily a prohibitionYour attitude toward your colleague isn’t the point here in this act; rather, there are things that the Torah is not willing for you to do. What Maimonides writes in the laws of forbidden sexual relations is that there are no limitations from the Torah’s standpoint. He doesn’t say a word about the question of what your proper relationship to your wife should be. What does one have to do with the other? These are two different things. That’s discussed in the laws of marriage, not in the laws of forbidden sexual relations. What does that actually mean? It means that the very same sexual act, of one sort or another, can receive O1 of A, but also F13 of A, of that same A, at the same time. There is such a positive commandment, or in this case a permission, not a positive commandment, and together with that there is a prohibition from another aspect. Say, with regard to your wife it is completely forbidden. Yet the Holy One, blessed be He, does not impose limitations on it from His standpoint. But obviously you are forbidden to do it, because there is a proper attitude toward… that is, toward your partner, okay? So here, for example, in this case it is even written explicitly in Maimonides in the laws of character traits: “Even though a man’s wife is always permitted to him, the two of them should not both be drunk, lazy, or angry, nor either one of them; and she should not be asleep; and he should not force her when she does not want it, but only with the consent of both of them and with their joy.” All right? In other words, here it’s already written explicitly in Maimonides, so I don’t even need to do interpretive gymnastics. But I… so you understand that the mistake here comes from a mistake in deontic logic. Because when I tell you that something is permitted, you have to ask me: permitted from what perspective? Permitted in terms of my problems with the Holy One, blessed be He, but forbidden from the standpoint of my wife’s rights. Those are two completely different things. So with regard to that same act itself, there can be O1 of A and F612 of that very same A. There is a prohibition on it from the standpoint of 612, and a permission or a commandment or whatever from the standpoint of 1.
Now, that’s still an easy case, where one side permits and the other side prohibits. There are situations in which one side obligates and the other side prohibits, and that is much worse. For example, look at this. Now, the subscript of T is Talmudic, that is, normative, and D is deontic, the practical one, okay? So now look: what does this logical expression actually describe? It basically says this: regarding act A, there is a normative prohibition i, and a normative obligation j, with respect to that same act. For example, if someone eats matzah from the new grain, after… grain that grew this year, one may not eat the new grain until the day after Passover, when they bring the omer offering; until then it is forbidden to eat the new grain. But I have a commandment to eat matzah on Passover eve, and that is still before the time when it is permitted to eat flour from the new grain. So what happens now when I eat that matzah, baked from flour of the new grain? From the standpoint of the commandment of matzah, I performed a commandment; I have O… I mean OJ of A on the T plane, that’s what I’m talking about now, right? And I have FI of A, because I have a prohibition against eating from the new grain. Do you understand? I and J are independent indexes. The prohibitions of new grain appear elsewhere in Maimonides, in other topics; this is from the standpoint of the prohibition of new grain, and this is from the standpoint of the commandment to eat matzah. Therefore these are I and J, completely independent indexes. So here there is a commandment of one kind regarding the same act, and a prohibition of another kind regarding that very same act.
Now the question is what do we do in such a situation? And what happens in such a situation is: there are override rules in Jewish law. And the override rules basically tell us—we mark this in our logic like this, you see? Now this expression helps me illustrate everything I’ve said until now. Because it basically means: I have a situation in which, regarding act A, I have prohibition I and obligation J—or really, a prohibition of a negative commandment I and an obligation of a positive commandment J, okay? The result is: the rule is that a positive commandment overrides a prohibition. What does that mean? Eat the matzah, even though there is a prohibition here against eating from the new grain. But this is already on the D plane, not on the T plane. Because on the D plane they tell you what to do in practice. They don’t tell you that the positive commandment disappeared or that the negative commandment disappeared—no, both are here. On the normative plane this is an unresolved tangle. That is, there is… well, it’s not really a tangle, because it comes from two different aspects, so there is no logical contradiction here. The indexes help me show that there is no logical contradiction here. This is from the standpoint of I, and this is from the standpoint of J. If it were OI and FI simultaneously, there would be some kind of problem here. But no, it’s OI and FJ, okay? So therefore there is no logical contradiction here, but there is a conflict, not a contradiction. And the whole idea in a conflict is that its resolution is not carried out on the T plane, but on the D plane. All right?
Think, for example, if I want to wound a person in order to operate on him, in order to heal him. So on the normative plane I have a prohibition against wounding him, but I also have an obligation to heal him. That is all on the T plane, the normative one. Now I ask: okay, there’s a clash now—what do I do? The decision is not on the normative plane; the decision is on the practical plane, of what to do. And it says: act, heal him—that is, perform the surgery. On the practical plane I ask not what obligations are imposed on me, but what I need to do. And on the practical plane, we said, those are the regular deontic operators. That is the O sub D, yes? Those are the regular deontic operators. There there is only O; F is simply an expression of O, yes, there is no F there. In the normative plane there are both F and O, and they are independent; you can’t translate them into one another. Okay? So here’s an example.
[Speaker K] So the normative plane is not complete enough? What? That is, the normative plane…
[Rabbi Michael Abraham] The opposite, the opposite—too complete. It’s too complete. It’s so broad that it contains even contradictions—apparent contradictions; it’s not a contradiction—it contains conflicts whose resolution is carried out on the practical plane. Why? Because the resolution will not bring me to a situation in which there is no prohibition. Of course—the prohibition remains even when I decided to violate it. But on the practical plane, the instruction is: violate the prohibition in order to fulfill the obligation. Therefore I think that the halakhic deontic repertoire is much richer—at least than what I know from deontic logic—and when you adopt it, the paradoxes disappear. All of them disappear. That means you now have to talk about perfect worlds from the standpoint of commandment F13, or from the standpoint of transgression F13, or commandment O2. Okay? If you want it to be perfect from both standpoints, then write that—but it may be that it cannot be perfect from both standpoints, in which case you won’t have such a world. But what I’m doing here is opening possibilities to split the set of perfect worlds with many more indexes, and that allows me to do all kinds of business. We built here all the possible kinds of clash—there is a book we wrote on this topic—all the possible kinds of clash, what? All the possible kinds of clash. We try to see: if there are two positive commandments and one prohibition, or two prohibitions and one positive commandment, triplets and doublets and things like that, and we try to see what kinds of clashes there are and how we construct the system of rules, and whether one can derive certain rules from other rules that are given—and we can derive them. I didn’t bring here the…
[Speaker F] Can you bring into it models like after the fact and ideally, or rabbinic and Torah-level?
[Rabbi Michael Abraham] Right, exactly—you’re anticipating me for a second, that’s my next sentence. Here you see this table that I skipped. So here, if you notice, it somehow jumped because of the right-to-left formatting. Look, for example, here—do you see the double negation here? Yes. It should have been on the left, right? So this double negation basically means there is no prohibition, no negative commandment, on A—you see? F of not A. That is, no—sorry. F of not A means there is a prohibition on not A, okay? There is a prohibition on not A, but there is no obligation to do A—yet it is desirable to do A. Double negation—this is called intuitionistic logic. Intuitionistic logic basically introduces intermediate levels. There is pious conduct; there are things it is proper to do, but it’s not just obligation and permission. Again, this is an expansion of deontic logic beyond obligation and permission. This is another expansion that exists, and in the halakhic world there is a whole set of such categories: pious conduct, beyond the letter of the law, “so that you may walk in the way of good people,” the trait of Sodom. These are all kinds of things where, from the standpoint of Jewish law, there is no absolute prohibition or absolute obligation, but Jewish law views what you are doing favorably or unfavorably. And those too can be brought into these tables of override and these rules.
Now, okay, I actually did this pretty quickly, so I think I won’t go into more here. I didn’t think I’d get even this far. That’s it. Basically what I want to say is that if we want to return to the regular deontic plane, then I think that if there we make distinctions—and don’t say this is morally permitted and this is morally forbidden, but rather this is morally permitted from the standpoint of helping another person, while it is morally forbidden from the standpoint of, I don’t know, harming the state, or something like that, just to produce different clauses—or theft, for example, is one specific prohibition, but returning stolen property is a positive commandment that is not the opposite of the prohibition of theft—then I can create perfect worlds and fight above them in such a way that all these conditional probabilities, or these conditionals that exist in the deontic operators, yes? It is perfect on the assumption that a theft occurred. Remember those notations? I can now restrict this to a subset of the perfect worlds, worlds that are perfect with respect to returning stolen property, but not perfect with respect to the fact that theft occurs in them. And I can discuss that too. Okay? So these indexes, and also the move to the practical plane, I think that also solves some of the problems. Because when you move to the practical plane, you are basically saying: on the normative plane the contradiction remains as it is—there is an obligation on me to do A, and also a prohibition on me to do A—and by the way that is not a contradiction. The fact that there is an obligation to do A and a prohibition to do A is not a contradiction, contrary to what deontic logic thinks. Deontic logic sees that as a contradiction because deontic logic deals with the plane of what I need to do. So if there is an obligation, then I must do it, and if there is a prohibition, then I must not do it. But in halakhic logic it is not like that. The transition from the normative dimension to the practical dimension is not automatic. The fact that there is a positive commandment does not mean that this is what must be done. Check whether there are additional parameters speaking here; whether there is a prohibition; what else exists from another standpoint regarding the same act. And only after you survey the whole layer, the whole normative sphere, can you make decisions in the practical sphere. Okay? And therefore a great many—in fact all—the contradictions that I know of, at least, are resolved if we adopt a richer deontic logic. Okay, I did this relatively quickly, even shorter than I planned. That’s it.
[Speaker F] Is there also a way here to translate this into worlds, to attach semantics? That is, if say you have a definition of a norm, a world of norms, yes.
[Rabbi Michael Abraham] Yes, I think so, but you need a set of worlds, and the set of worlds has all kinds of indexes. That is, there is no such thing as a perfect world, full stop. It’s not just a perfect world. It is a world that is perfect with respect to these norms and those norms. That is exactly the point. In the moral world, in the practical world, either I need to do it or I don’t. There is no room there for indexes; in the practical world there are no indexes. Not only are O and F dependent on each other so that you don’t need two operators, there are also no indexes. Because if it is obligatory to do it, then certainly it is not forbidden to do it—in the practical world. But in the normative world everything is open; there are no contradictions at all. The only contradiction is both O1 of A and not true that O1 of A—that is a contradiction, even in the normative world, but that, yes.
[Speaker D] It may be worth mentioning, in the practical plane—but the non-practical one here—that this topic of deontic logic is one of the research topics of our team, even though it is a topic we still haven’t reached.
[Rabbi Michael Abraham] Of which team, which team? What?
[Speaker D] Whose? Mine, Moshe’s, Dror’s, Mike’s. And the intention really is to generalize, and I think the intro you gave here explains, say—I didn’t think this would be the form, the semantic separation—but it just clarifies that this issue of doing something like this, which is tied both to worlds of, say, AI governance, and to worlds of philosophy, and to worlds of Jewish law, is very, very, very, very complicated to do in a way that…
[Rabbi Michael Abraham] Yes, but I think it’s worth thinking about these splits also in contexts where they are not natural. Say, in governance worlds, for example. There, seemingly, it is only a practical world: either you want it to happen or you don’t. But when you want to make a decision whether it should happen or not, it may be that you need to leave standing both the O that it should happen and the F that it should happen. That is, and then the decision has to be made now on the practical plane: what do we do when I have this combination?
[Speaker D] Yes, what I’m trying—and again, it seems to me this doesn’t go beyond the scope of the lecture—is basically my understanding: what is the purpose of deontic logic? At the end of the day, you do want to arrive—and this is somewhat connected to what Daniel or maybe Amit, I don’t remember which of them, asked regarding inference rules—in these worlds, the question is whether by means of deontic logic you are not supposed to strive toward… it’s not truth, not truths, we’re not talking here about truths, but toward… as it were, a perfect world from its standpoint. Does something hold here—some kind of normative fact that you would always want to have a Boolean value, that… either it does happen, and if so all these things…
[Rabbi Michael Abraham] That is behind it, even though people try to deny it, it is here too. When you talk about perfect worlds, you have to decide what is a perfect world and what is not, and there there are judgments. You cannot ignore the judgments. That is, if you decide that a world in which people steal is not perfect, then basically you have said that theft is bad. You are not saying it explicitly, but you are building it into the definition of what perfect worlds are.
[Speaker D] Yes, so from that point of view I go along with you—then it really does make this logic much more complicated when you make the split, because you really do have to, according to the indexes exactly,
[Rabbi Michael Abraham] define what is perfect.
[Speaker D] know how to say what is overcoming what; you really have to do weighting among all of this and say what overrides what.
[Rabbi Michael Abraham] We made a table. In the book we have a large table covering all the twelve categories that are here: when they clash with each other, what happens; and then two clash with one, and two clash with two, and…
[Speaker I] Nice, cool—another topic.
[Speaker F] What you said about governance is indeed very interesting. So in effect, policy considerations—an organization’s policy—that too, as I understand it, the inference is basically what decision I may take or what decision I must take.
[Rabbi Michael Abraham] Correct. What I want to say is that when you set the organization’s policy, the organization’s policy includes two things: first, what carries a prohibition and what carries a positive obligation; and second, what happens when there is a clash. Then what is our policy—who overrides whom?
[Speaker F] Who overrides whom, yes. But I think it’s dynamic; I don’t think you can make it static.
[Rabbi Michael Abraham] Okay, so that can be.
[Speaker D] So there is—again, this is out of scope here—a language called Cedar, which Amazon invented. It’s a language that is really very technical and mechanical, and my sense—I haven’t gone deeply into it; I’ll look at it again after this lecture—my sense is that there is no conflict resolution there at that fine-grained a level. Rather, they simply define only what is forbidden and what is permitted, and once there are conflicts, my impression is that the answer is “don’t know”; that is, I don’t have what to…
[Rabbi Michael Abraham] They made life easy for themselves,
[Speaker L] for themselves.
[Speaker D] Yes, yes, they made life easy for themselves, in quotation marks. But I’m not sure; I need to look. But there are indeed attempts to mechanize this in governance worlds in a much more simplistic way.
[Speaker L] Amit, did you want to ask something?
[Speaker C] Yes. Basically I mainly wanted to say: it seems to me there is quite a lot to say about the semantics and how to understand the operators, but specifically what I mentioned, Kratzer semantics, is a semantics specifically intended to talk about what are called comparative modalities—that is, all sorts of concepts like a better possibility, or an act better than another one, and so on. And it seems to me that most of what you’re trying to achieve, Miki, can simply be achieved through that semantics. So maybe it’s worth looking at the matter that way. Broadly speaking it is built like this: besides the set of possible worlds, one introduces a kind of ordering relation—formally, call it a pre-order—that ranks worlds according to degree of ideality. Then most of what you’re saying can, in my opinion, simply be formalized in that way.
[Rabbi Michael Abraham] It connects somewhat to what I said at the end about intuitionistic logic—that is, what is proper to do even though it is not obligatory, or what is proper not to do even though there is no prohibition.
[Speaker C] The semantics itself is entirely within classical logic; one can also do Kratzer semantics within intuitionistic logic, but I’m not even sure you need to go that far.
[Rabbi Michael Abraham] Okay. Do you have a follow-
[Speaker L] up? You—okay, send it, send it. Thank you very much. Thank you very much on Slack. Okay.
[Speaker C] All right, Rabbi, thank you very much.
[Rabbi Michael Abraham] Thank you.
[Speaker L] Thanks again, and have a good week. Thank you very much. Thank you, friends. Thank you. Next week, next week everyone, everyone joins the
[Speaker G] uh
[Speaker L] glove method.