חדש באתר: עוזר בינה מלאכותית המבוסס על כתביו ושיעוריו של הרב מיכאל אברהם

Paradoxes and Contradictions in Halakha, Lesson 7, Part A

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This is an English translation (via GPT-5.4). Read the original Hebrew version.

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

🔗 Link to the transcript on Sofer.AI

Table of Contents

  • [0:00] Conflicts and loops in the Talmudic text
  • [1:28] Rabbi Shimon Shkop’s solution to the loop
  • [2:29] The halakhic principle of consistency
  • [4:19] The liar paradox and logical connection
  • [10:23] Drinking wine and a condition — is it permitted?
  • [12:08] Turning permitted intercourse into forbidden intercourse
  • [21:39] Conditional divorce and halakhic implications
  • [23:48] Conclusion: invalid marriage and consistency
  • [25:07] The condition of the bill of divorce and its connection to betrothal
  • [26:53] Violating the condition of the bill of divorce and retroactive betrothal
  • [30:42] The liar paradox and Rabbi Shimon’s solution
  • [31:47] The ad hoc principle in solving logical paradoxes
  • [33:41] Differences between law and logic — summary

Summary

General Overview

The text develops Rabbi Shimon Shkop’s solution to the paradoxical loop created by a conditional bill of divorce, and explains that the solution rests on the principle of consistency: a halakhic effect which, if it were to take effect, would uproot itself, does not take effect at all. Alongside this, it is argued that the solution works only because we are dealing with a legal world and not pure logic, and that in the world of logic, paradoxes like the liar paradox cannot be solved in the same way.

The loop in a conditional bill of divorce

In the case of a man who divorces his wife on condition that she not marry a certain man, if she marries that man a circle is created: the marriage cancels the divorce, so she is still a married woman, so the marriage does not take effect, so the divorce remains valid, and again she is married to him. Tosafot asks why the Talmudic text determines that the bill of divorce is invalid and the children are mamzerim, rather than the opposite — that the bill of divorce is valid and the children are legitimate.

Rabbi Shimon Shkop’s principle of consistency

Rabbi Shimon Shkop proposes that such legal effects do not take effect at all, because if they were to take effect they would be retroactively canceled because of the condition, and anything that has no possible way of taking effect does not take effect at all. According to this, a bill of divorce whose effect is consistent remains valid, while an effect that creates an internal contradiction does not even begin. This principle solves the loop by stopping it at the point where the legal effect was supposed to uproot itself.

Time, logic, and legal causation

The text emphasizes that the halakhic loop does not occur along a real time axis but within a single point in time, because the connections between the events are logical or legal rather than physical. The order looks as though it has sequential stages only because legal thought lays it out along an axis, but in fact everything happens simultaneously. Therefore Rabbi Shimon Shkop assumes, in addition to consistency, that one can also treat the logical order as though it were a sequential order.

Conditions, prohibitions, and consequences

The text distinguishes between what the husband can do and what he cannot do. The husband can make his divorce conditional, but he cannot impose prohibitions on the woman like a legislator; he only determines that the divorce will take effect if the condition is not violated. Therefore the question arises whether there is any prohibition at all against drinking wine or having intercourse in a way that retroactively creates mamzerut, and the text suggests that even if there is a prohibition, it may be a prohibition between one person and another rather than the prohibition of a married woman.

Restrictions, consecration, and konam

The text compares the topic to other cases in which a person creates a binding legal situation with his property or domain, such as consecration or konam. When a person consecrates an animal or prohibits his property to others, he himself creates a framework of prohibition, and one who intentionally violates it commits an offense. From this it is argued that the problem is not the very creation of a legal situation, but whether one can create a legal effect that cancels itself.

Paradoxes in logic versus law

The text argues that the liar paradox cannot be solved by Rabbi Shimon Shkop’s method, because there we are dealing not with legal effects but with truth values, and one cannot establish a legal rule that settles the paradox from within. It compares this to Russell’s theory of types, which restricts statements to referring only to levels below them in order to prevent paradoxes, but argues that this is not a real solution, only an ad hoc rule that prevents the formulation of the problem. By contrast, in the legal world one can add a new rule that limits the very application of the legal effect itself, and so one can solve a legal loop even if a purely logical loop cannot be solved.

Full Transcript

[Rabbi Michael Abraham] Today we’ll finish the issue of conflicts and loops. At the end of last time I started discussing loops, halakhic loops, and I want to continue that. So first of all I’ll briefly reconstruct what I said at the end of the previous lecture. The case in the Talmudic text in tractate Gittin — the Talmudic text there talks about someone who divorced his wife on condition that she not marry a certain man, and then she went and married that man. If you want to enrich the story, then in the middle she also married someone else and had children from him, and then that also brings mamzerut into the picture and all kinds of far-fetched little embellishments. In any case, she was divorced on condition that she not marry a certain man, and then she marries that man. The moment she marries that man, her divorce is invalidated. If her divorce is invalidated, then she is still married to the first husband. If she is married to the first husband, then the marriage to that other man doesn’t take effect because she is a married woman, and if it doesn’t take effect then she didn’t marry him, and if she didn’t marry him then the divorce is valid, and then she did marry him, and so on. Right? That’s basically some kind of loop. And that’s what Tosafot asks there on the Talmudic text: why does the Talmudic text say that this is an invalid bill of divorce and her children are mamzerim? One could just as well have said that the bill of divorce is valid and her children are legitimate. Meaning, it’s a loop — it depends where you stop the loop. So I brought Rabbi Shimon Shkop, who proposes a solution to this loop, and it’s basically some kind of general logic for dealing with loops. He wants to argue — maybe I’ll read his wording — “because these marriages cannot take effect, for if they were to take effect they would be retroactively nullified because of the condition, and anything whose taking effect has no possible reality does not take effect at all. Therefore the bill of divorce remains valid and the marriage is invalid.” Why do we say that the bill of divorce remains valid and the marriage is invalid? Because any legal effect such that, if we decide that it takes effect, that itself uproots the branch on which it sits — then that effect does not take hold. I said that in yeshiva language people are used to saying: any legal effect such that if it takes effect it does not take effect, then it does not take effect. Meaning, if deciding that it takes effect would itself uproot the branch on which it rests, then it does not take effect. You can’t impose such an effect, so we stop the circle — it simply doesn’t take effect. And then I said that this principle — let’s call it the principle of consistency — meaning that if I want to impose some legal effect, it has to be consistent; if it’s not consistent, it doesn’t take effect. This principle doesn’t stand on its own. You have to assume here another assumption, which Rabbi Shimon Shkop doesn’t say explicitly, but it has to be there in the background, because without it this doesn’t solve the problem. And that assumption is that I can see the different halakhic stages as sequential stages along some kind of time axis. In principle, in this case — let’s talk about the previous case, someone divorcing a woman on condition that she not marry a certain man — the moment she marries that man, the marriage to him takes effect, which means the divorce is invalidated; if the divorce is invalidated, that cancels her marriage because she is a married woman; if she isn’t married to him, then the divorce is valid, and so on. This whole circle does not happen along a time axis, meaning not that there is one stage and then after it comes the second stage as a result, and then the third and the fourth. All of it happens in one instant. Therefore it goes backward and forward equally, because it’s all in the same instant of time. When Rabbi Shimon Shkop wants to apply the principle of consistency here, he is really assuming an additional assumption: that I can go by the order in which the events occur, the logical or causal order in which the events occur, and treat that as though they are sequential events. As though one of them happens after the other. It doesn’t happen after the other; it happens because of the other — not after. That’s not the same thing. Because in the legal world there aren’t the rules, yes, of relativity, where if something is the cause of something else then it also has to precede it in time. There can’t be an influence faster than the speed of light, so basically logical priority or physical priority is also temporal priority. In the legal world that isn’t so, and in the logical world that isn’t so either. Think about the liar paradox: statement A says, statement B is true; statement B says, statement A is false. A version of the liar paradox. Now which statement is later and which is earlier? There is no later and no earlier here. It’s a logical relation between two statements; either one could have been the first, and if it’s true then the other isn’t true, and so on. Meaning it doesn’t matter at all which one I handle first, and therefore it’s a circle. There is no priority to one because it appears before the other. You can take whichever one you want as the first, and therefore when we talk about logical relations, in logical relations there is no temporal priority. I said this in one of the previous years when I talked about logical determinism. So I said that logical determinism suffers from this point. It thinks that a logical relation is really a causal relation, and therefore there also has to be some temporal priority and so on. But no — a logical relation is atemporal, meaning it has nothing to do with time at all. I can say that if there is rain then there are clouds. When I say such a thing, it sounds a little jarring to an ear sensitive to physics, because the clouds are the cause of the rain, not the rain the cause of the clouds. Only if…

[Speaker B] What do you mean only if? Only if there’s rain…

[Speaker C] If there’s rain… there’s rain only if there are clouds.

[Speaker B] I see.

[Rabbi Michael Abraham] If I see rain, I see clouds like that. No, no — not there’s rain only if. If there’s rain, there are clouds. It can be that there are clouds — leave aside the “only.” That’s another question, whether it’s only or not only, because I can also produce artificial rain without clouds. No, but if there is rain, there are clouds. Okay? What kind of claim is that? In physics you can’t make that claim. In physics the claim is the opposite. The clouds create rain — not all clouds, but rain clouds create rain. Okay? But in logic the situation is the opposite. You can’t say that if there are clouds then there is rain, because there are situations where there are clouds and no rain falls. It’s not true that if there are clouds then logically there also must be rain. What is true is that if there is rain then necessarily there are clouds. There is no rain without clouds. There are clouds without rain, but no rain without clouds. So the logical direction is actually the opposite of the direction of time, against the physical direction. The direction of causation is forward in time, and the logical direction in this case is backward in time. But there is no problem with that, because logic does not refer to the time axis. The logical order between things is not a temporal order between them. If it’s true, then it’s true. It doesn’t mean this one comes first and that one afterward. The “if… then…” can run from here to there or from there to here; logic is indifferent to time. Okay, so now here, when we talk about these relations, they are relations of causation — but not physical causation, rather logical or legal causation, if you like. Not physical. It doesn’t matter. But it isn’t something that necessarily has to unfold along a time axis, with the cause preceding the effect. Everything happens simultaneously. The moment there was no bill of divorce, then she is a married woman — not after there was no bill of divorce she is a married woman, but rather the absence of a bill of divorce means that she is a married woman — that she is in fact a married woman, sorry. Okay? There is a logical connection between those two things — again, legal, not exactly logical. “Logical” may not be the best example or term, but legal. But in the legal world there are no constraints of relativity saying that the cause has to precede the effect and that it can’t move too fast beyond the speed of light and all those sorts of things. In the legal world, the moment there is no bill of divorce, she is a married woman. It’s immediate. Meaning it’s not — there is no time gap between them. And therefore this whole circle that Tosafot is talking about and that the Talmudic text is talking about is a circle that happens within a single point in time. This circle takes place in our heads, not in the world. Or in our heads or in the legal mind — it doesn’t matter right now whether specifically ours — but within the world of legal thought. Within that world of legal thought there occurs a very large series of events, maybe even infinite if we keep the circle going all the time, and all this happens at a single point in time, because the relations between the events are logical relations and not physical relations, and because of that it takes no time; it’s the same point in time. Now Rabbi Shimon Shkop’s implicit assumption is that we can treat this as if it were physical causation. Meaning, that one thing really does happen after another — I don’t care how much after, but after. Meaning there is some kind of internal order here. All these events that happen within the same point in time really do have an order between them, some axis along which I arrange them one after another, where the “after” here is not temporal after but legal or logical after. Doesn’t matter, but there is still some sort of order, and I can discuss the things one after another. If I assume these two assumptions, then indeed one can solve the loop. One can stop the loop. And then it works like this — as I already said last time — it works like this. A person divorces the woman on condition that she not marry, right? Reuven divorces the woman on condition that she not marry Shimon or Levi — let’s take the richer case. Fine. So she is divorced, right? The divorce in itself is not an inconsistent legal effect. There is no problem of consistency here. It’s not that if there is divorce then there is no divorce. Fine, he divorces her — one is allowed to divorce, one is allowed to divorce conditionally. Everything is fine. He divorced her, so she is divorced. So she is not a married woman. Now she goes and marries Shimon. Everything is fine — she is unmarried, she can marry Shimon. They have children too — also fine, everything is fine, the children are fine, the marriage to Shimon is fine, everything is fine. Good. Now she leaves, Shimon divorces her, she leaves, and now she marries Levi. The same man whom the condition said she should not marry. Again, a condition is not a prohibition. It’s not that she is forbidden to marry Levi. She is allowed to. The husband cannot impose prohibitions on her; the Holy One, blessed be He, imposes prohibitions on us, not the husband. The husband can only say: I am not divorcing you if you marry Levi. It’s not forbidden for her to marry Levi; it only invalidates the divorce. Okay? Suppose a man divorced his wife on condition that she not drink wine for ten years. He can stipulate such a condition. Now if she went and married someone, had children, and now she wants to drink wine after five years, still within the ten-year period — she wants to drink wine. Is it forbidden for her? It’s permitted. What…

[Speaker B] Forbidden and permitted here aren’t like in civil law. You’re allowed to park here on the street, it just costs you 250 shekels.

[Rabbi Michael Abraham] Okay, but here that’s the question. It turns her acts of intercourse into forbidden intercourse and her children from the second husband into mamzerim. Okay? But on the other hand, who is the first husband that he can define prohibitions for his wife? He’s not the Holy One, blessed be He. All he can do is condition the actions that he himself performs with whatever condition he wants. Okay? He can’t say you’re forbidden to do such-and-such. Forbidden to you? Who are you to tell me what is forbidden and what is permitted? I decide for myself what I do, within the constraints, say, of the Torah. The Torah says what is forbidden and what is permitted, but a husband who makes a condition cannot impose prohibitions on the woman.

[Speaker D] It’s not him — it’s the prohibition of a married woman that will be created, the ordinary prohibition of a married woman. That will be created.

[Rabbi Michael Abraham] What — is it forbidden to create the prohibition of a married woman?

[Speaker D] Where is that written?

[Rabbi Michael Abraham] Maybe, but maybe not. Hm?

[Speaker D] And is Shimon liable to punishment?

[Rabbi Michael Abraham] No, punishment there certainly wouldn’t be, because they are under compulsion. He didn’t know she would later drink wine. If he has relations with her afterward, that’s another matter. It retroactively turns the acts of intercourse into forbidden intercourse and the children into mamzerim. Okay, nobody is going to be punished here. That’s not the point — punishment.

[Speaker C] Except for the mamzer children.

[Rabbi Michael Abraham] Yes, the mamzer children will be punished, because they become mamzerim and de facto they have many problematic restrictions on them. But not as a punishment; rather because they are mamzerim they cannot marry and so on. So what does this thing really mean? Is it forbidden for her to drink the wine and thereby turn the intercourse into forbidden intercourse and the children into mamzerim? Because unlike the husband, she has free choice. She can choose not to drink the wine. By drinking the wine, she turned the intercourse into forbidden intercourse. On the other hand, what is forbidden is to have forbidden intercourse, not to turn intercourse that already took place into forbidden intercourse. I don’t know of such a prohibition in Jewish law. So who says that this is forbidden? True, after she drank, the acts of intercourse became forbidden — fine. But is there a prohibition against making acts of intercourse forbidden? And what if I make somebody else’s acts of intercourse forbidden? You could also have such a situation by condition: you are divorced on condition that that other fellow not drink wine. Fine, and now he has to deliberate whether to drink wine or not, while the woman already has children and is married to someone else. Same question. What does that mean? Who is he to impose prohibitions on me? I want to drink wine, so what if he made conditions? He made conditions, so what? Of course he can determine when he divorced and when he didn’t divorce. There are limitations he places on the divorce.

[Speaker E] But who says that those acts of intercourse are considered forbidden and that the children are mamzerim — who says the acts of intercourse are considered forbidden?

[Rabbi Michael Abraham] Why not? What do you mean?

[Speaker E] After all, it turns out retroactively that she was a married woman. But how do you define forbidden? What do you mean by forbidden? It was then, and then it was permitted; now it’s something else.

[Rabbi Michael Abraham] No, now it becomes clear retroactively that already then it was forbidden.

[Speaker E] It becomes clear retroactively that the result of the intercourse caused something bad.

[Rabbi Michael Abraham] Not the result of the intercourse. No, no — the intercourse itself: she is a married woman who had relations with someone who was not her husband. Leave aside the mamzer children.

[Speaker E] Leave aside the children, but you can’t call it that the intercourse was forbidden. The intercourse then was permitted. What are you talking about?

[Rabbi Michael Abraham] The intercourse was forbidden; it’s just that the woman was under compulsion, or the husband was under compulsion — he didn’t know it was forbidden, because it only became clear through a future event. But now we know that already then she was a married woman. This is a condition phrased as “on condition that” — a condition that goes backward. Okay, she was a married woman, and now she had relations with someone who was not her husband — what do you mean? That’s the prohibition the Torah states, isn’t it? That’s certainly forbidden intercourse. The intercourse is definitely forbidden; it’s just that the intercourse already happened. The question is whether I am forbidden to drink wine, not whether I am forbidden to have intercourse. Drinking wine — it doesn’t say in the Torah that it’s forbidden to drink wine. Drinking the wine turns the intercourse into forbidden intercourse, but the question is not whether it is permitted to do the intercourse; the question is whether it is permitted to drink wine. So I’m only saying this to sharpen the point, because many times this is the topic of retroactive clarification — there is retroactive clarification. Right, same thing. Conditions or retroactive clarification — you can ask a thousand questions about it. So the claim is that when a person imposes a condition, he obviously cannot define for someone else that it’s forbidden for him to do something. He is not a legislator; he does not have authority to establish prohibitions. He can define: if I performed an act that is within my authority to perform, like divorce, I can qualify it and say I did it only if a certain condition will not be fulfilled, or will be fulfilled. No problem, I can do that. I could have chosen not to divorce; I can choose to divorce; I can also divorce conditionally, in a qualified way. No problem. I cannot establish prohibitions. It may be that there are prohibitions here between one person and another — not prohibitions of a married woman, but interpersonal prohibitions. When she drinks wine, that isn’t the prohibition of intercourse with a married woman — are we going to execute her because she drank wine? That’s absurd. But on the other hand, look — you harmed the children, you are turning them into mamzerim, you are ruining their lives. Fine, maybe an interpersonal prohibition, I suppose.

[Speaker C] So in the case of another person too, would that also be an interpersonal prohibition?

[Rabbi Michael Abraham] Yes, yes, apparently so. But it really does seem absurd. What, they make all kinds of deals between themselves, so what? What is that to me? What does that have to do with me? Right. Okay, good question. I don’t know. But there is definitely room to say that there is an interpersonal prohibition here. But when I asked earlier whether it is forbidden, I meant a prohibition of a married woman; I wasn’t talking about an interpersonal prohibition.

[Speaker C] And if a person wants to cause trouble for a bunch of people, then when he divorces his wife he…

[Rabbi Michael Abraham] …will make a complicated condition.

[Speaker C] For all of them, and then they have a problem, and then they want to preserve the interpersonal obligation?

[Rabbi Michael Abraham] Yes, right. There once was such a story, yes.

[Speaker E] How is this different from indirect causation, for example on the Sabbath? You do an act which in itself is permitted, and its result can cause something that is forbidden on the Sabbath.

[Rabbi Michael Abraham] Okay. No, but that doesn’t cause my action to have been a transgression; it causes a result such that, if I had done it directly, it would have been forbidden. On the Sabbath there is no prohibition that something become sorted out; there is a prohibition that I sort. So if I did it by indirect causation, I didn’t sort — what do you want from me? Indirect causation is not an act of sorting. But here the problem is the result. The result is that the act of intercourse was forbidden intercourse, that the children become mamzerim, and I caused that result. It’s not that I did it by indirect causation — I did do it by indirect causation, but the point is that here the result is the problem and not the action. By the way, that’s one of the reasons why, at least according to some views, indirect causation on the Sabbath is really permitted. On the Sabbath the point is that I have to desist, I am forbidden to perform actions on the Sabbath. If I do it by indirect causation, then that’s not the action the Torah prohibited, fine? Because the prohibition is really on the action. Where the prohibition is on the result — say, killing by indirect causation — that’s a very interesting question. The Talmudic text says that one is exempt. Aside from arrows and pebbles and all that — halakhically that isn’t called indirect causation — but never mind, other kinds of indirect causation, less direct kinds, then it would indeed be called indirect causation, even though the result is unequivocal, meaning the result is clear, it will happen.

[Speaker H] And is there no problem with the validity of the bill of divorce itself? What? The issue of complete severance. The moment he ties her up…

[Rabbi Michael Abraham] If it’s for a fixed period, then there is no problem of complete severance. Only when the condition restricts her forever is there a problem of complete severance. “On condition that you never drink wine” or “that you never go to your father’s house” — that’s not a valid bill of divorce. But here I said ten years, that she not drink wine. Now here too, “that you not marry a certain man” — there too it depends. Suppose I do it only for a fixed time, because if I do it forever then you’re right. If I do it forever, there is a problem of complete severance. But suppose even for a fixed time. That’s also better. Like someone who consecrates an animal.

[Speaker I] Someone who lies with it outside the Temple courtyard — no, someone who consecrates an animal, and someone who misuses it commits sacrilege and is liable to karet — what’s the difference? He created the prohibition himself.

[Rabbi Michael Abraham] No, one who commits sacrilege is not liable to karet, because sacrilege is unintentional; he is liable to a sacrifice.

[Speaker I] If he did the transgression intentionally?

[Rabbi Michael Abraham] Intentionally? Okay, so what is the problem? He knows it’s holy. So what if I created it? It’s my right to create it; it’s my property. There is no problem with that. I create a situation; if you know that this is the situation and you intentionally decide to violate it, then you’re the offender. A religious court determines that Passover falls on a certain date — they intercalate the year, sanctify the month, whatever it may be, doesn’t matter. Am I to blame because the religious court decided to establish Passover for now? It’s in their authority; they can determine that now is Passover, and from this point on we all have to fulfill the commandments of Passover today. So I too can determine — it’s within my authority to determine that my animal is consecrated, it is holy. It’s my animal; I’m allowed to determine that it is holy. Assuming it is now holy, then all the restrictions of sacrilege apply to it, and there is no problem with that. More than that: even without consecration, I can prohibit things to you by konam, things that are mine, not things that are yours. I can’t prohibit you by konam from using your own things, but things that are mine — no problem, that’s within my authority. Why not?

[Speaker D] But in the condition he made, he is playing with the prohibition of a married woman. He is saying, “I control it.”

[Rabbi Michael Abraham] But you don’t control the prohibition of a married woman; you control the process of divorce. The act is conditional.

[Speaker D] No, it’s…

[Rabbi Michael Abraham] The question is whether that also controls the prohibition of a married woman. That’s what I asked; I don’t know. You control the process of divorce; you can determine whether there was a divorce here or not, because the act of divorce is within your authority. But you cannot control whether it will be forbidden for her to drink wine — and especially what Shmuel said earlier, suppose with someone else: I make it conditional on someone else drinking wine. Then what? What, can you control his wine drinking? He does what he wants. What does he owe you? You decide on one side whether you divorced or didn’t divorce, whether it’s qualified, conditional, unqualified — do whatever you want. What do you want from me? I do what I want. In the simple way I see it, from my perspective there is no prohibition at all for this woman to drink wine, even though the children will become mamzerim and all the acts of intercourse will become forbidden intercourse. There is no prohibition against turning acts of intercourse into forbidden acts of intercourse. There is a prohibition against committing forbidden intercourse. Turning intercourse into forbidden intercourse — who said there is such a prohibition? There is a Talmudic text against me — I once saw it. What do I mean, against me? The Talmudic text does not rule this way in practice. But by reasoning, that’s what I would say. There is a dispute among Amoraim — doesn’t matter, in tractate Nedarim — and from there it emerges that there is a dispute among the Amoraim, and in my opinion it’s on this very point. And the halakhic decisors rule like the Amora who says not like me. Meaning, the Amora who says that it is indeed forbidden. Meaning, there is a prohibition against turning the intercourse into forbidden intercourse just as there is a prohibition against having forbidden intercourse, or against being involved in it. And is that on the same level? Yes, it’s a prohibition of forbidden intercourse, the same prohibition. It doesn’t — it has no other source, it is…

[Speaker E] A prohibition, a prohibition of forbidden intercourse.

[Rabbi Michael Abraham] And the prohibition is on her? And the prohibition is on her. What do you mean, on her?

[Speaker C] If a third person turns it too into forbidden intercourse, then on him too… I don’t know. It’s not written in the Talmudic text; I don’t know.

[Rabbi Michael Abraham] Good question. I also don’t know. It could be — there are possibilities in the Talmudic text, I don’t know. I haven’t found anyone who discusses it. But it seems clear to me that this is the dispute there in the Talmudic text. You asked earlier whether it’s the same level of prohibition. I’m not sure the Talmudic text means to say that it’s literally the prohibition of forbidden intercourse. It may be that the Talmudic text understands that if there is a prohibition of forbidden intercourse, there also has to be a prohibition against turning an existing act of intercourse into forbidden intercourse. But it isn’t exactly the prohibition of intercourse with a married woman, because it’s hard to assume — I don’t know, by logic — this is the same logic I had, it’s hard to assume that for drinking wine they would stone her for the prohibition of intercourse with a married woman.

[Speaker C] Stone her? Yes, with witnesses and warning.

[Rabbi Michael Abraham] They would not warn her now before drinking wine: if you drink wine, then your children will become mamzerim and the acts of intercourse will become forbidden. There is warning, there is everything.

[Speaker C] No, but the warning has to be about the intercourse. Why? Not about the act that causes the intercourse.

[Rabbi Michael Abraham] Why? Drinking wine.

[Speaker C] That’s the same reasoning…

[Rabbi Michael Abraham] …that I said earlier. So leave aside the warning. This has nothing to do with warning; rather, the intercourse was done permissibly. Now I drink wine and turn it into forbidden intercourse. So what do you want — how can you stone me for the intercourse? You’re stoning me for drinking wine, not for the intercourse. But drinking wine — what, is it forbidden to drink wine? Fine, okay, we won’t get into that here. In any case, for our purposes: what Rabbi Shimon Shkop is basically assuming, beyond the fact that he requires consistency from every halakhic act, is also that I can go by the order. And then what happens? Let’s begin following the order — I started and cut it off in the middle. So the husband divorced his wife on condition that she not marry Levi. No problem. That doesn’t contradict itself. That is a legal effect that takes effect, and its taking effect does not contradict its own existence. Right? So no problem; it doesn’t violate the principle of consistency. Then she marries Shimon. She is unmarried; she can marry Shimon. Then children are born; Shimon divorces her. All of that is perfectly fine acts, with no problem at all. And now she comes to marry Levi, to become betrothed to Levi. Okay? The moment she becomes betrothed to Levi, at that moment the divorce done earlier would be uprooted, and then it would turn out that the marriage to Levi also could not take effect because she is the first man’s married woman — Reuven’s.

[Speaker C] The whole loop happens at the point where she becomes betrothed to Levi.

[Rabbi Michael Abraham] Exactly — and you’re talking about the point only because you’re already assuming that not everything happens at the same point. That’s why you notice, that’s why I have to assume that each such thing supposedly happens at some different moment, and at each stage I reach a different stage in the process.

[Speaker C] Not all these things really happened each at a different stage.

[Rabbi Michael Abraham] They didn’t happen at different stages. Why? Everything happens now. At this precise instant the divorce is uprooted, and at this precise instant my betrothal suddenly gets canceled even though it was there from the start. Right.

[Speaker C] And what is this “at this instant”?

[Rabbi Michael Abraham] Right. And what does it mean, everything at this instant? He says yes, but at this instant a process really occurs that takes me backward along the sides of time — I make the whole circuit within one moment of time. And then what this means is that now I spread this circuit out along a straight line instead of a circle, and I say, okay, so what happens? I married Levi. That act itself triggered the whole mess. Here the mess was activated. The divorce didn’t activate any mess; if I hadn’t married Levi, nothing would have happened. Only the fact that I married Levi activated the mess and uproots the branch on which these very marriages rest. Right? At the end of the process — or not at the end but in the middle of it. And then of course it continues, but that’s what happens. So this is a legal effect such that if it takes effect, it does not take effect. It doesn’t satisfy the principle of consistency. Therefore you can’t impose such an effect. But notice the result: the result is that the bill of divorce remains valid and the marriage to Levi is invalid. Fine? That’s the point. The marriage to Levi is invalid even though the bill of divorce remains valid. That’s a little strange, no? After all, if the bill of divorce remains valid, then she is not Reuven’s wife, so she can marry Levi. What’s the problem? She isn’t Reuven’s wife. Right, so an inconsistent situation seems to come out here, as it were. But that’s the result. The divorce is valid because she didn’t marry Levi, and she didn’t violate the condition of the divorce, so why shouldn’t the divorce be valid? She cannot marry Levi because if that took effect it would uproot that legal effect, the branch on which that legal effect sits. A legal effect of that kind cannot be imposed — not because she is a married woman and therefore betrothal to Levi doesn’t take effect, but because of Rabbi Shimon Shkop’s principle of consistency. The principle of consistency says, irrespective now of whether she is a married woman or not, a legal effect such that if you try to impose it, it would uproot itself — such a legal effect Jewish law does not allow you to impose. So the reason she is not married to Levi is not that she is Reuven’s wife, that because she is a married woman Levi’s marriage cannot take effect in her, Levi’s betrothal cannot take effect in her. It’s not because of that. She is not married because this is a legal effect that cannot be imposed, because it is a legal effect such that if it were to take effect it would uproot itself. And there is a rule in Jewish law — not connected to the issue of a married woman at all — there is a rule in Jewish law that says: a legal effect such that if we impose it, it will uproot itself, does not take effect. This is where we stop the… and then something comes out that is, as it were, self-contradictory.

[Speaker C] We don’t stop it — we don’t start it at all. Yes, but why did the bill of divorce have to be a valid bill of divorce?

[Rabbi Michael Abraham] The bill of divorce is valid because the condition was not violated. The condition was that the bill of divorce would not be a valid bill of divorce if she married Levi.

[Speaker C] If Levi’s betrothal doesn’t take effect, then the bill of divorce is perfectly fine.

[Rabbi Michael Abraham] But Rabbi, he violated the condition. Levi’s betrothal doesn’t take effect… She didn’t marry Levi, there is no problem at all, the bill of divorce is perfectly fine. Levi’s betrothal doesn’t take effect. If you can invalidate the bill of divorce, you can do that only through the mechanism of a condition, but then you have to see whether the condition was violated or not. The mechanism of marriage to Levi failed not because of problems of condition, but because there is a rule in Jewish law that a legal effect which, if you impose it, uproots itself, cannot be imposed from the outset. From the outset, yes. Such a legal effect cannot be imposed.

[Speaker F] In this story, the role of Shimon and his children is just to create drama.

[Rabbi Michael Abraham] I said that, right — just to enrich the story. So that it’ll be more interesting. Right, yes, one could have gone straight to Levi. But now let’s continue discussing it, since you already mentioned Shimon and his children. So if the bill of divorce is valid…

[Speaker C] …then there’s no problem.

[Rabbi Michael Abraham] No problem, right. The marriage to Shimon was fine, the children are legitimate, and everything is fine. But the marriage to Levi doesn’t take effect.

[Speaker F] Yehudah, Issachar.

[Rabbi Michael Abraham] Yes, yes — only the marriage to Levi doesn’t take effect. What this really means, this woman — whoever she is — that’s a point I hadn’t thought through, by the way. According to this it follows that someone who makes this condition in the bill of divorce, according to Rabbi Shimon Shkop — according to Rabbi Shimon Shkop in Tosafot, if Rabbi Shimon Shkop is right, then it turns out that she will never be able to marry Levi. Right?

[Speaker C] Not forever — until the condition period ends, the duration of the condition.

[Rabbi Michael Abraham] Ah, as long as the condition is still in force, right.

[Speaker F] Maybe as long as her first husband is alive.

[Rabbi Michael Abraham] Hm? If her husband is alive… that’s a dispute.

[Speaker F] By definition she is a widow.

[Rabbi Michael Abraham] Ah, but this invalidates the betrothal retroactively. It would turn the children into mamzerim because it works retroactively. That’s the betrothal while her husband is alive. The bill of divorce while he is alive. It’s not the betrothal.

[Speaker C] It’s the bill of divorce. There is a dispute among the Sages if…

[Speaker F] The bill of divorce, not the betrothal. She can become a married woman if…

[Rabbi Michael Abraham] If it becomes retroactive, then it will turn out that then she was a married woman, not now. She did not fulfill the condition. So when she was married to Shimon — supposedly married — she was a married woman.

[Speaker F] But no, suppose for a moment we remove the…

[Rabbi Michael Abraham] No, but the discussion about Shimon and his children — that’s the discussion.

[Speaker C] No, but…

[Speaker F] Even if there is no Shimon, we said that even without Shimon she basically can’t marry. Right, okay.

[Rabbi Michael Abraham] Even if Reuven died.

[Speaker C] Okay, yes.

[Speaker F] Reuven died, so now there is…

[Rabbi Michael Abraham] No, if Reuven died there is no problem. She…

[Speaker F] …can.

[Speaker C] …marry Levi.

[Rabbi Michael Abraham] Why? Why not? Did she violate the condition? So what? Now she is a widow and not a divorcee. Fine, a widow is also allowed to marry.

[Speaker C] But he told her until… no, what does it mean she’s a widow and not a divorcee?

[Speaker F] Before too she was a divorcee.

[Rabbi Michael Abraham] No, before she was a divorcee and wanted to marry him as a divorcee, Levi. Now the husband died, so if she marries him she violated the condition and the divorce is invalid. Okay, invalid — but she is a widow. So she is married to the first husband and he died, so she is a widow. In the meantime she became a widow.

[Speaker C] She became…

[Rabbi Michael Abraham] …a widow, and as a widow it’s permitted. Meaning again, the condition was violated, the divorce was invalidated — that’s true. The divorce was invalidated, and in the meantime she became a widow. Right. So even if the divorce is invalidated, that means she isn’t a divorcee but a widow. But a widow is also allowed to marry.

[Speaker J] What happens if Reuven makes the condition: “Here is your bill of divorce on condition that you not have relations with Levi”? So then what’s the question?

[Rabbi Michael Abraham] If she had relations with Levi… then certainly the bill of divorce is invalid. What do you mean? She violated the condition. What’s the question?

[Speaker J] So if now she is Shimon’s wife, then the children are mamzerim.

[Rabbi Michael Abraham] Certainly. The children are mamzerim, and there is no problem… there is a problem, but not a logical problem. There is no logical problem here, no circle, because we don’t need to discuss the possibility that the marriage to Levi won’t take effect; we’re talking about a condition concerning intercourse, not betrothal.

[Speaker C] In the previous case there is a practical difference if Levi is a kohen.

[Rabbi Michael Abraham] Then the woman is either a divorcee or a widow. Exactly, right, of course. If he is a kohen she is forbidden… no, but betrothal still takes effect even between a kohen and a divorcee.

[Speaker C] Fine, in prohibitions of negative commandments betrothal still takes effect.

[Rabbi Michael Abraham] It takes effect, but… if it were something that also invalidated the betrothal, it would…

[Speaker C] It takes effect, but it’s forbidden.

[Rabbi Michael Abraham] Yes, it’s forbidden; the betrothal takes effect. And then it comes out that she violated a prohibition.

[Speaker C] The question is whether she violated a prohibition or not.

[Rabbi Michael Abraham] Exactly. No, the betrothal took effect. Since the betrothal took effect, then the divorce document is void. If the divorce document is void, then she’s a widow and not a divorcee.

[Speaker C] And then she didn’t—so then she didn’t violate any prohibition.

[Speaker F] What would happen if the condition were: “Here is your divorce document unless Rabbi Michael Abraham gives a lecture”?

[Rabbi Michael Abraham] So—what’s the question?

[Speaker F] If Rabbi Michael—

[Speaker C] Abraham gives a lecture?

[Rabbi Michael Abraham] Yes. No, that—we talked about that as a third party case. Ah, and she already got married and the children are mamzerim and all that—so that’s what we discussed earlier, a third party case, like making it conditional on someone not drinking wine. Same thing. The question is whether someone else is forbidden to drink wine. I asked that earlier; I said I don’t know. Maybe in the interpersonal sense he’s forbidden, but on the other hand the idea is a bit outrageous, that someone can dictate to me not to drink wine. What do I have to do with this? Why are you playing all these tricks? It’s your problem—what do you want from me? You can dictate it to ten people. Yes, you can say that the whole world may not drink wine.

[Speaker C] Right, from now on the whole world is forbidden to drink, if—

[Rabbi Michael Abraham] —if someone drinks wine that isn’t Carmel Mizrahi. I’m the owner of Carmel Mizrahi. If someone drinks wine that isn’t Carmel Mizrahi, then my wife is not divorced, that’s all—and her children are mamzerim. Now nobody will drink that wine anymore, so I’m set for life. So that really does sound absurd. I don’t know how to solve it, but morally it sounds absurd, it sounds absurd. In any case, what I want to sharpen here is that the solution Rabbi Shimon Shkop proposes requires not only the principle of consistency, but also laying out this whole wheel that happens entirely at one point in time across some kind of axis—you could call it an axis of legal causation, not a time axis, because it all happens at the same moment. But I relate to it as if these are successive events, and I follow the process step by step until it gets stuck. When does it get stuck? The moment I apply a legal effect whose application cancels itself. All right? And then everything is fine, because then you solve the problem. Now how did this miracle happen, that Rabbi Shimon Shkop managed to solve a paradox? A paradox, by definition, can’t be solved. How do you solve the liar paradox? It’s a paradox—you can’t solve it. How is it that we solve this paradox? Again, there’s some kind of principle here.

[Speaker C] What? There too there’s some similar principle. Where? In the liar paradox. What principle? That if it’s something that loops back onto itself, then he says that I’m actually canceling the— No, so what?

[Rabbi Michael Abraham] No, you can’t cancel it. If you canceled the earlier assumption, you canceled this statement too, and so on. So the first assumption—no, there’s no legal effect there. What does “legal effect” mean? The question is whether the statement is true or false. Statement A is: “Statement B is true.” Statement B is: “Statement A is false.” You can’t apply Rabbi Shimon Shkop’s principle there. Why? Because there we are not dealing with legal effects. You can’t decide that truth does not take effect; either it’s true or it isn’t true—that’s a fact. It’s not a question of what you determine. Here he can do it because he can determine legally that a legal effect that is inconsistent cannot be applied. A new meta-legal principle that he creates in order to solve this problem. That’s exactly how the miracle happens; that’s exactly how the miracle occurs. He adds another principle that goes beyond the pure logic of the problem. He brings into this problem an additional legal principle, and that can be done because we are dealing with law and not with logic. If we were dealing with pure logic, with true and false statements like the liar paradox, there would be no way to solve it using Rabbi Shimon Shkop’s techniques. It doesn’t help. Because there you can’t insert something ad hoc: a statement won’t be true if, when you declare it true, that will cancel its being true.

[Speaker C] Isn’t that similar to what Russell does in set theory?

[Rabbi Michael Abraham] Similar in what sense? Rabbi Shimon Shkop’s principle?

[Speaker C] This insertion of—

[Rabbi Michael Abraham] Why yes? In what way is it similar?

[Speaker C] When he did it, he inserted some rule there that doesn’t allow the paradox.

[Rabbi Michael Abraham] But that’s exactly why it isn’t a solution. No—type theory, not set theory. In set theory, what he did—there’s no problem at all, he didn’t insert any rule. He simply rebuilt set theory axiomatically. Not he rebuilt it—others did, never mind—but he knocked down the earlier version. But that’s regarding the paradox in set theory, of the set that does not contain itself as an element—sets that do not contain themselves as an element, exactly. But here you’re talking about type theory. Meaning, when there are self-reference paradoxes, he proposed in the introduction to Principia Mathematica a hierarchy among statements, such that every statement can refer only to statements lower than it in the hierarchy. Okay? It can’t refer to statements on its own level. That’s an ad hoc principle inserted into the problem and supposedly solves it. But that is exactly why I said it isn’t a solution. Because the paradox is a paradox in logic, not in law. You can insert whatever ad hoc thing you want; then you can define a language in which the paradox can’t be expressed, but that’s not a solution. It’s a Stalin-style solution to a paradox. Meaning, if you express a problem, they cut off your head and then there’s no problem. In other words, you’re not allowed to express the problem—that’s basically this kind of solution. So it solves nothing. Okay? That is exactly the point. It perhaps illustrates precisely the difference between law and logic. In logic you can’t insert ad hoc principles. What is true is true; what isn’t true isn’t true. It’s not that you can’t say, okay, let’s propose that if it’s true then it isn’t true, so it won’t be true. You can propose that forever; the question is whether it is true or not. It doesn’t depend on your definition. In the world of law, you can say: look, there is such a rule. After all, being able to apply legal effects is itself a legal innovation. The same system that innovated that legal effects can be applied also innovates that if that legal effect uproots itself, then it cannot be applied. All right? The same mouth that forbade is the mouth that permitted. Since there is some legal innovation here, that legal innovation can be qualified; it has a condition. We have now imposed a condition on the application of legal effects: only legal effects that are consistent can be applied. There’s no problem with that; that’s fine; it can solve problems—but only problems from real life, not problems in logic.

[Speaker F] So then it’s different from the square triangle discussed by… Russell?

[Rabbi Michael Abraham] Because a square triangle is a problem in logic. That’s exactly the point. In logic, if it’s a triangle, I can’t declare it to be a square.

[Speaker F] It becomes a constraint on language; language is not every—

[Rabbi Michael Abraham] No, that’s what I’m saying—it’s not language.

[Speaker F] A language where we know it has no meaning in the language.

[Rabbi Michael Abraham] Exactly. No—it has no meaning not in language, in the world! There is no such thing in the world as a circular triangle, not just that in language the term “circular triangle” has no meaning.

[Speaker F] Okay, but in language there are words that have no meaning—that does exist.

[Rabbi Michael Abraham] No problem. But he adds a problem to language, because the assumption of the analytic philosophers is that there are no real problems. If there is a problem, it is only a problem in language, so let’s choose another language in which the problem cannot be expressed. And I say that’s not true. There are problems that are real problems; language only reflects them, like the circular triangle. So then what are you telling me? You’re telling me: let’s define another language in which the problem cannot be expressed. So what have you said? That’s Stalin’s solution. You’re basically saying: I create a language in which it is forbidden to express the problem, impossible to express the problem, so everything is fine, there is no problem. But that’s not true—there is a problem in reality. If you created a language that cannot express the problem, then you simply created an impoverished language, that’s all. You haven’t solved any problem. It’s like saying: if there’s a lion threatening me, I’ll look away—I won’t look, I’ll look upward like an ostrich, and then there’s no problem. I’m not afraid because I don’t see the lion. He’ll devour me whether I’m afraid or not afraid. Okay? I can’t solve the problem by dealing with its representations. I have to solve it. It doesn’t help to deal with the representations, with the language that represents it. That’s assuming there really is a problem in the world. There are claims by analytic philosophers who say: there can’t be a problem in the world; the world has to be consistent. If something is inconsistent, that is only a bug in our thinking. Then they say: fine, so let’s propose another framework, another conceptual framework in which the problem doesn’t arise, and then that’s fine because the whole problem was only in our framework of thought. I think that hasn’t convinced me. I think there’s a real problem here. Russell’s language seems artificial to me. Why shouldn’t a statement be able to refer to statements on the same level as itself? There are, by the way, statements that refer to statements on their own level and do not lead to paradox—so why do you forbid those too? Just because it solves your problem.

[Speaker C] You forbid it because you need a rule.

[Rabbi Michael Abraham] Yes, exactly, because you need a rule. But then that shows that the rule is not correct; it’s just an ad hoc rule. Solving things ad hoc is not interesting; it’s not important either. Okay, so really, when we talk about these looped self-references on the logical level, you can’t solve them. Because in order to solve loops or paradoxes—I spoke about this last time—you have to step outside the system, like Gödel’s theorem. You have to step outside the system, look at the system from the outside, not from within that system of rules. That’s how Gödel’s theorem is proved: you go outside and think about the system; you don’t think within the system. And that statement has no proof within the system, from the rules of the system, but when I look at the system, I see that if I assume the opposite it leads me to a contradiction, and so I have a proof. All right? So here too, the same thing: when you solve paradoxes, it is always by stepping outside the system. Now when your system is the basic logic of truth and falsehood, there is no such thing as stepping outside the system.

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