Topics in Talmudic Logic, Lecture 10
This transcript was produced automatically using artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.
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Table of Contents
- General overview.
- The goal of the lecture and the mathematical assumption
- The cases in Kiddushin 7a: the law of the guarantor, the law of the Canaanite slave, the law of both
- Analogies in damages: one who throws a vessel, one who sets a dog on someone, and the ownerless ox
- A visual representation of kiddushin as arrows and presentation of the four cases
- The dispute between Rashi and the Ritva about the law of the Canaanite slave and the meaning of agency
- “Here is a maneh, and I will become betrothed to you” and the Talmud’s explanation through the laws of acquisition
- A group-theoretic model: primary cases, derivatives, closure, and non-commutativity
- Extensions to additional compositions, four factors, and monetary law
- The concluding claim about the Talmud’s awareness of the structure
Summary
General overview.
The text presents an example of conceptual construction in the topic / passage in Kiddushin 7a, where one posits a qualitative mathematical structure that can be proved to be a group, and from that derive conclusions that resolve difficulties in the Talmud. It describes how moving from the simple model of kiddushin, in which the husband gives money to the woman and she becomes betrothed to him, leads to more complex cases such as the law of the guarantor, the law of the Canaanite slave, the law of both, and even the case of “here is a maneh, and I will become betrothed to you,” while arguing that the Talmud itself is reflective and aware of the compositions it is performing. It develops a representation of the cases as arrows of money and kiddushin, shows how compositions generate “derivatives” from “primary cases,” and emphasizes that the Talmud rejects or limits certain cases for technical reasons in the laws of acquisition, not because of any fundamental contradiction to the verse “when a man takes a woman.”
The goal of the lecture and the mathematical assumption
The speaker presents another example of conceptual construction with a mathematical structure that can be proved to be a group, from which one can derive conclusions and even resolve difficulties in the Talmud. He says he will touch on the formal parts only in a qualitative way, in order to show the form of the thinking. He defines the starting point in kiddushin as the simple case in which the husband gives a perutah to the woman and she becomes betrothed, and adds the institution of agency in kiddushin, as is familiar from the beginning of chapter two.
The cases in Kiddushin 7a: the law of the guarantor, the law of the Canaanite slave, the law of both
The text presents Rava’s statement: “Give a maneh to so-and-so and I will be betrothed to you” as a case in which the woman redirects the destination of the payment, and it is called “betrothed by the law of a guarantor.” It explains the analogy to the law of a guarantor in a loan, where the guarantor obligates himself even though no benefit reaches him, and it describes the idea that reliance on the guarantor is itself a benefit that creates firm intent, while noting that the commentators discuss the relation between the passages and the fact that in kiddushin the language of the Talmud sounds as though it works even “despite the fact that no benefit reached her.” It presents “Here is a maneh, and be betrothed to so-and-so” as a case in which the recipient of the money remains the woman but the person to whom she becomes betrothed changes, and this is called “betrothed by the law of the Canaanite slave,” named for the redemption of a slave in which a third party gives money to the master and the slave acquires himself even though he has not lost anything at all.
The text presents “Give a maneh to so-and-so and I will become betrothed to him” as a case in which neither did the husband give money nor did the woman receive money, and nevertheless she is “betrothed by the law of both.” It defines this as a combination of guarantor and Canaanite slave. It emphasizes that the Talmud itself uses the language of composition (“the law of both”) and not a move of common denominator, and shows the structure of the argument: an attempt to derive it from guarantor is rejected because there at least the man betrothing loses money, an attempt to derive it from the Canaanite slave is rejected because there at least the acquirer is the one transferring, and then they return to guarantor as proof even though there is no common denominator here but rather a combination of two unique features. It portrays this as a process of abstraction in which one gives up the woman’s receipt once and the husband’s giving once, until it seems that nothing remains of the act of kiddushin except consent, and it compares this to other examples of exemption / liability created by the combination of causes, such as one who throws a vessel from a roof and another breaks it a moment before it lands.
Analogies in damages: one who throws a vessel, one who sets a dog on someone, and the ownerless ox
The text brings the example of one who throws a vessel from a roof and another comes and breaks it with a stick, to show the possibility that both might be exempt because “he broke a broken vessel,” while on the other hand the throwing only created the potential for breaking. It also brings at length the topic / passage of one who sets a dog on someone, where there is reason to exempt the instigator because the dog is not his property, and to exempt the dog’s owner because he did not set it on anyone, and it describes that “quite a few later authorities (Acharonim)” write that even if the owner himself set his own dog on someone, he is exempt according to the side that exempts. It explains this through the laws of a harmless goring ox and the ownerless ox, where “the liability is on the ox” and payment comes from its body, and therefore when the incitement removes responsibility from the animal there is no liability on the animal and therefore nothing is taken from the owner’s property either. It presents this as relevant to the investigation of the later authorities as to whether liability comes from negligent guarding or from “the very fact that my property caused damage.”
A visual representation of kiddushin as arrows and presentation of the four cases
The text moves to working with diagrams in which the solid arrow represents money and the dashed arrow represents kiddushin, and it defines the goal of the diagrams as making it possible “to keep your head straight.” It draws ordinary kiddushin, the law of guarantor in which the money goes to a third party and the kiddushin remains with the husband, the law of the Canaanite slave in which the money is given to the woman but the kiddushin goes to another man, and the law of both in which the money and the kiddushin split so that neither does the husband give nor does the woman receive. It adds a fourth case of “Here is a maneh, and I will become betrothed to you,” and presents it as a case that appears to be rejected in the conclusion in the case of an important man, but in the plain sense of the topic / passage appears as a direct continuation of the whole set of compositions.
The dispute between Rashi and the Ritva about the law of the Canaanite slave and the meaning of agency
The text presents a dispute between Rashi and the Ritva over whether, in the law of the Canaanite slave, so-and-so must be the agent of someone else, and explains that even if there is agency here, this still is not a “regular law of agency,” because the perutah belongs to the giver and not to the principal. It connects this to the question of what is novel in the law of guarantor when one understands the mechanism as benefit, and brings the difficulty of the Kovetz Shiurim regarding how to quantify the benefit in the case of giving a perutah to a third party on the basis of the woman’s words, to the point of concern that this benefit may be worth less than a perutah. It suggests that the novelty may be that giving to a third party is considered giving by force of the woman’s instruction, and not as ordinary betrothal through benefit.
“Here is a maneh, and I will become betrothed to you” and the Talmud’s explanation through the laws of acquisition
The text describes how Rava asks, “Here is a maneh, and I will become betrothed to you — what is the law?” as a simple possibility within the framework of these compositions, and it brings Mar Zutra in the name of Rav Pappa answering, “She is betrothed.” It emphasizes that the difficulty raised by Rav Ashi is not because of the reversal of direction in kiddushin as such, but because of a rule in acquisitions: it turns out that property that has responsibility attached to it is acquired together with property that does not have responsibility attached to it, “but we learned the opposite.” Therefore there is a technical blockage from the laws of land acquisition because “a person is compared to land.” It argues that from here it follows that the Talmud assumes that the kiddushin mechanism as such is valid, and the rejection does not stem from some essential requirement that specifically the man give to the woman, but from the topic / passage of acquisition through land and the comparison of a person to land that appears elsewhere too.
A group-theoretic model: primary cases, derivatives, closure, and non-commutativity
The text defines three “primary cases” with a source: ordinary kiddushin from “when a man takes a woman,” the law of guarantor from guarantorship in loans, and the law of the Canaanite slave from the redemption of a slave, and describes how from these primary cases “derivatives” are created through compositions. It argues that this is precisely the concept of a group: there is a base and there are operations that generate additional elements while preserving closure, and the Talmud assumes that everything built from these elements is a valid act within the “group of kiddushin operations.” It formulates operators A and B as actions that move the head of the payment arrow or its tail, and shows that the law of both is obtained through a serial composition of the operations, while emphasizing that the operators are not commutative and therefore the group is not abelian.
Extensions to additional compositions, four factors, and monetary law
The text argues that the structure generates additional configurations such as ABA, and that from this perspective the Talmud does not view “the woman gives money” as an independent invalidating act, but as shorthand for a series of legitimate transformations that in one stroke yield a result that looks reversed. It presents the possibility of structures with four factors that cannot be mapped onto the three-factor cases, and notes that he found in Tosafot Rid a possibility for a situation in which the father of two sons gives a perutah to the father of two daughters and both sons become betrothed to the two daughters with one perutah, with disputes among medieval authorities (Rishonim) as to whether the fathers are agents or not. It notes that the Talmud says “and similarly regarding monetary law,” and demonstrates how in monetary cases one can build chains and compositions with many factors in which giving money or transferring land is done by the law of guarantor and Canaanite slave and serves both as payment and as kiddushin money, so that one can create very complex structures that are determined by breaking them down into compositions from the basic operations.
The concluding claim about the Talmud’s awareness of the structure
The text concludes that the model is not an external “overlay,” because the Talmud itself uses explicit composition such as “the law of both” and continues to examine additional compositions in a way that assumes closure of the system. It argues that the mathematical way of thinking is evident in the fact that the Talmud assumes that what is built from the building blocks is valid, and only afterward looks for specific reasons not to apply it, such as limitations in land acquisitions. It ends by saying that the Talmud “is performing a group operation” even if it does not call it by that name.
Full Transcript
[Rabbi Michael Abraham] Okay, so today I want to deal with another example of conceptual construction. There’s some kind of mathematical structure here that I’ll touch on at a very qualitative level and not in an overly formal way, but in principle you can prove that this is a group and derive various conclusions from it, and it even resolves quite a few difficulties in the Talmud — the assumption that what we have here is a group. So I’ll comment a bit on the formal parts, but I mainly want to show the style of thinking that we saw in the previous examples too. In the case of kiddushin, basically, there’s the standard situation where the husband gives a perutah to the woman and the woman becomes betrothed. You can also do kiddushin through an agent — that’s at the beginning of chapter two of Kiddushin. The husband appoints someone else as an agent to give the perutah to the woman and betroth her, or the woman can have an agent to receive it, and then you can give the perutah to him on her behalf and she becomes betrothed when he receives it. Meaning, he acts in her name just like in the ordinary laws of agency. But in the Talmud in Kiddushin 7 there are another three, four, and later maybe even a few more cases where things start getting a little tangled. The law of the guarantor, the law of the Canaanite slave, the law of both — and there the simple structure we’re used to, I give money and then she becomes betrothed to me, starts to get complicated. I can give money to that guy and then she becomes betrothed to him, I give money to her and then she becomes betrothed to him, she gives money to me and therefore he becomes betrothed to her, or all kinds of tricks of that type. And they derive it from various places, but in the Talmud you can see — I think in a relatively unusual way — that the Talmud here is, I think, even aware of the mathematical nature of the operations it’s doing. It’s not just a description after the fact: the Talmud does what it does with the plain common sense of the Amoraim or the people dealing with it, and then you come along with your own tools and try to formalize it. But here it seems to me that you can actually see reflexivity, or a conscious look at what they’re doing, like I’ll try to show now. So maybe I’ll start with the Talmud itself. In the Talmud in Kiddushin 7a — the details aren’t important, so I didn’t photograph the whole topic / passage for you, because in the end we’re going to work with diagrams; otherwise you just can’t keep your head straight in this thing. It’s been empirically proven that there’s no magnet here. So let’s start with the Talmud. The Talmud says — Rava said — end of 6b and then I move to 7a. Rava said: “Give a maneh to so-and-so and I will be betrothed to you” — she is betrothed by the law of a guarantor. Meaning, the woman says — let’s say Rachel, and there are Reuven and Shimon. So Rachel says to Reuven: give a maneh to Shimon, and by that I’ll become betrothed to you. Or in other words, instead of you giving the maneh to me and I become betrothed to you, give the maneh to him and I become betrothed to you. We’ve shifted, redirected, the addressee of the payment. That is basically the law of a guarantor. Where does this strange invention come from? So the Talmud says: is it not the case with a guarantor that even though no benefit reaches him, he still obligates himself? So too this woman, even though no benefit reaches her, obligates and transfers herself. Meaning, what is the law of a guarantor? The law of a guarantor is the parallel in Bava Batra, but for our purposes it’s when someone serves as a guarantor on a loan. A guarantor on a loan is part of the transaction. That’s why, for example, the Talmud in Makkot 7 talks about Il’a and Tuvya, who were relatives of the guarantor, and they’re considered related witnesses. Related, and in principle disqualified from testimony. Why? The borrower and lender aren’t related to them. Because the guarantor is part of the deal; the guarantor is part of the deal too. Meaning, when the lender gives money to the borrower, several things are created. First, the borrower’s debt to the lender is created. Second, the guarantorship is created. That is, there’s a third party who is now undertaking to be a guarantor, so if the borrower has no money, they’ll take the money from him. How does he obligate himself? The borrower obligates himself because he received money, so he takes on the obligation to return it, to repay the debt. Okay — how does the guarantor obligate himself? The guarantor didn’t take money, didn’t receive money, didn’t perform any formal act of acquisition. What exactly is the act that made the contract with him? What created the firm intent here? So he says: a guarantor works because they relied on him. That’s what seems to come out in the Talmud there. I’m not going into it now — the medieval authorities (Rishonim) and later authorities (Acharonim) discuss to what extent that’s really so — but that’s the plain sense of the Talmud in Bava Batra, the parallel Talmudic text: when they relied on the guarantor. After all, when Reuven lent money to Shimon and let’s say Levi was the guarantor, then Reuven was willing to give money to Shimon because he relied on Levi, that if Shimon gave him trouble, Levi would pay him. That itself counts as benefit. Reuven says to Levi: look, I rely on you, you’re a serious person, an honest person, I can rely on your word. That benefit is a benefit he received, and that sealed the contract with him. Meaning, that’s what created his obligation as guarantor. Okay. Now you can discuss exactly what that benefit is — is it a money acquisition? Meaning, he received that benefit, so it’s like something of monetary value or something like that? Doesn’t matter, I’m not going into the details now, but that’s basically what the Talmud is saying. It’s as if he received something from me, just as the borrower received money — he received benefit. The borrower’s obligation to repay was created by his receiving money; the guarantor’s obligation to repay if the borrower has no money was created by his receiving from me that benefit. The Talmud says the same thing here in the law of guarantor. The woman says: “Give a maneh to so-and-so and I will be betrothed to you.” Right? Now he’s willing to give a maneh to so-and-so because he relies on her, right? He’s basically giving it in her name. So what happened is that she received something from me — namely, that I rely on her, that benefit. She’s basically in the exact position of a guarantor here. Not a guarantor in the sense of repaying a debt, because this isn’t a loan. That’s not what she’s saying. But the mechanism is the same mechanism. He was willing to spend money based on her word. The fact that she told him was enough for him to give money to so-and-so, to throw the money into the sea. Meaning, she saw that someone gave money based on her commitment. She received some kind of benefit here, and through that benefit she becomes betrothed. Okay? By the law of guarantor. Even though the wording of the Talmud here says: even though no benefit reached him, he obligates himself. The Talmud says no benefit reached him. Not that the benefit is the fact that they relied on him. So again, that’s a complication I’m not getting into here; the commentators discuss it. That’s case number one. Case number two: “Here is a maneh, and be betrothed to so-and-so.” Okay? Meaning, now I give the woman money, but she becomes betrothed to someone else. I’m not changing the recipient of the money; I’m changing the one effecting the betrothal. And the one receiving the money is, this time, the woman — not someone else as in the law of guarantor. But the one she becomes betrothed to is not me. Okay? This is called the law of the Canaanite slave. Why is it called the law of the Canaanite slave? Because with a Canaanite slave too, when I redeem him from his master, I give money to the master, and as a result the slave acquires himself from the master. Even though the slave did not give the money to the master — I gave the money to the master. But the one who got the exchange for that money is not me; it’s someone else. In that case, the slave. Okay? So that’s exactly the situation here. Meaning, the woman — the recipient, yes, not the husband the giver — I say, “Here is a maneh, take the maneh, but the exchange for this maneh, the kiddushin, you won’t give to me, you’ll give to him.” Exactly like the Canaanite slave: when I redeem the Canaanite slave from his master, I give money to the master; don’t give the exchange to me, give the exchange to the slave. The exchange is to set him free, yes, to transfer him to himself.
[Speaker B] It seems to me that you said no benefit came to her hand, so then what did come to her hand? There is benefit — meaning they have to translate that benefit.
[Rabbi Michael Abraham] No, no, no benefit reached her.
[Speaker B] The plain sense of the Talmud: nothing. What benefit?
[Rabbi Michael Abraham] The fact is that from what I explained based on the Talmud in Bava Batra, it comes out that some benefit did reach her — namely, that they relied on her. Right. In the wording of the Talmud here, it says that even though no benefit reached her, nevertheless she becomes betrothed.
[Speaker B] Maybe the benefit has to be something physical.
[Rabbi Michael Abraham] Maybe. Or maybe it simply isn’t called benefit in that sense. It doesn’t matter — you can explain the relation between the passages in different ways. But the plain sense of the passage here is that it’s not because some benefit reached her; rather, despite the fact that no benefit reached her, nevertheless she becomes divorced — she becomes betrothed. It’s enough that benefit reached someone else. So how did that happen? Right, “Here is a maneh and be betrothed to so-and-so” — she is betrothed by the law of the Canaanite slave. Is it not the case with a Canaanite slave that even though he loses nothing at all, he acquires himself? So too this man, even though he loses nothing at all, acquires this woman. Right — the second one, the one to whom she becomes betrothed, loses nothing at all. I gave her the money, and she becomes betrothed to him. Third case. “Give a maneh to so-and-so and I will become betrothed to him.” Now things have really gotten tangled. Meaning, the woman says to Reuven: give a maneh to Shimon, and by that I will become betrothed to him — to Shimon. Right? Give a maneh to so-and-so and I will become betrothed to him. The Talmud says: she is betrothed by the law of both. A combination of the Canaanite slave and the guarantor. These two laws together. A composition of those two laws together. Already in itself it’s clear that the Talmud here is aware of some sort of mathematical operation, some kind of composition of those two things. For our purposes, this is basically conceptual construction. We take the law of guarantor and the law of the Canaanite slave, and from the fusion of the two together, taking a certain component from here and a certain component from there, we create a third operation, one that has no direct source. We have a source for the Canaanite slave, because that’s simply how a Canaanite slave is redeemed. We have a source for the law of guarantor, because there is such a thing as guarantorship for loans, and from there we derive the law of guarantor. But this concept itself doesn’t exist. We build it by composing or fusing two concepts that we already know. These are two primary cases, and a derivative that is created as a result of conceptual construction from the two of them. Okay? That’s exactly what this is. Now I’ll show it even more. Again — “Give a maneh to so-and-so and I will become betrothed to him” — she is betrothed by the law of both. How does this work? Because what’s happening — look at the absurdity here. “Give a maneh to so-and-so and I will become betrothed to him.” Notice: none of the ordinary elements of kiddushin are taking place here. Meaning, the husband did not give money, and the woman did not receive money. So literally nothing remains of kiddushin except maybe the word kiddushin. Other than that, nothing of kiddushin happened here. Do you understand — we keep moving farther and farther away from the original kiddushin. In the original kiddushin, the husband gives money and the woman becomes betrothed, right? The woman receives the money and as a result becomes betrothed to the giver of the money. Right? The law of guarantor basically tells me: “Give a maneh to so-and-so and I will become betrothed to you.” The husband gives the money, and she becomes betrothed to the one who gave the money. The husband gave money, but the woman didn’t receive it. That’s the first change. The law of the Canaanite slave: the woman received, but not from the husband. The husband did not give money, but the woman did receive — that’s the law of the Canaanite slave.
[Speaker B] And “both” — that’s when the husband didn’t…
[Rabbi Michael Abraham] …give, and the woman also didn’t receive. So what’s left? Maybe next time two telephone poles will be betrothed to each other, because apparently you can strip this whole thing down completely and be left with nothing. She agreed to accept him? Yes, without that it won’t work. But that’s all — only consent remains here. The act of kiddushin, apparently, has nothing left of it. The act of kiddushin is that I give money and she receives it — what else is there? Now that’s missing and that’s missing too — nothing remains. So this is really a very strange process of abstraction.
[Speaker D] Maybe you could say that in these two cases there is something in place of it. Like here, in the loan case, there’s the benefit standing in place of the gift, the money.
[Rabbi Michael Abraham] That’s the question. In the Talmud it says there is no benefit, that’s why I said it beforehand. The Talmud says that even though she did not receive benefit, it still works. They learn from there that you don’t need benefit to be received. I said that in Bava Batra it does sound like yes — “through that benefit he obligates himself” — and the later authorities discuss the relation between the passages. Now look also at how it’s worded. Again, I’ll read it once more — listen carefully to the way I’m reading this. “Give a maneh to so-and-so and I will become betrothed to him” — she is betrothed by the law of both. Now the explanation. Is it not the case with a guarantor that even though no benefit reaches him, he obligates himself? So too this woman, even though no benefit reaches her, transfers herself. Right? So from the law of guarantor you can understand that even though the woman did not receive benefit, that’s okay — we learn that from the law of guarantor. The Talmud says: how is that comparable? In the case of guarantor, the one acquiring her loses money. In the law of guarantor, true, she didn’t receive, but at least the husband gave. Something from the kiddushin was there. Here the husband also doesn’t give; it’s not only that she doesn’t receive. So you can’t learn it from guarantor. This man acquires this woman and loses nothing at all. The Talmud says: the Canaanite slave will prove it, because with a Canaanite slave we see that even though he loses nothing at all, nevertheless he acquires. The Talmud says: what do you mean? A slave — the slave loses no money and acquires himself. The Talmud says: how is that comparable? There, the one who transfers is the one who acquires; here, this woman is transferring herself and she acquires nothing at all. The guarantor will prove it, for even though no benefit reaches him, he obligates himself. The Talmud says: after all, here the woman did not receive money, so the Canaanite slave should prove it. But with the Canaanite slave the husband gave money; here the husband doesn’t give — the guarantor will prove it. It doesn’t say here: no, and then the law returns, no common denominator of the two. There is no common denominator here. This is exactly classic conceptual construction. Right? There are no shared sides here. On the contrary, there are different sides. With guarantor, the husband gives and the woman doesn’t receive. With the Canaanite slave, the woman receives and the husband doesn’t give. The combination of the two joins the two unique sides; it doesn’t expose by elimination the shared element, but takes a case where the husband doesn’t give and the woman doesn’t receive — we’re left with nothing, and nevertheless it’s okay. Like with the help of the wind, if you remember from Sabbath or from damages, what we saw in previous lectures — this is really classic conceptual construction. Conceptual construction that takes the unique element in the first source, the other unique element in the second source, connects them together, and basically creates something new — and not even by adding, but by subtracting. Meaning, an element that should have been a problem, you see there that it isn’t a problem; an element that here should have been a problem, also isn’t a problem; remove them both, you’re left with nothing, but everything is fine because neither of them is an obstacle. Right, like I once mentioned with the passage in Bava Kamma about someone who throws a vessel from a roof. You know that one? Someone throws a vessel from a roof and another person comes and strikes it with a stick — meaning, before the vessel shatters, someone else comes and breaks it. So the Talmud there raises the possibility that perhaps both of them would be exempt. Why would both be exempt? There’s such a possibility — there’s a dispute there. Why would both be exempt? The one who broke it right before it broke anyway, because “he broke a broken vessel,” and the one above — well, he didn’t actually break the vessel; the one below broke it. He only created the potential for breakage. So how does that exempt both of them? If you go by the original act, then the one above is liable and the second is exempt. Okay. Now the later authorities discuss there what happens if the same person who threw the vessel from above runs down quickly and breaks it before it reaches the ground. So there’s a possibility there in the later authorities that he would be exempt. Because what difference does it make if those two people are the same person? On the face of it, it makes a huge difference. Why do you exempt the first one? Because the second one isn’t him; he did something. Why do you exempt the second? Because the first one wasn’t him; he also contributed. But here the first and the second are the same person, so he did everything. What, was there some other person who did something that I didn’t do? No, no, the later authorities discuss this. Why exempt the second if he did…? Because “he broke a broken vessel” — he broke a vessel that was already broken. If he broke a broken vessel, then the one above is responsible. Right, but he also didn’t really break the vessel; he only created the potential for breakage. And in order to impose liability, apparently you have to really break it. I’m saying, there’s a dispute in the Talmud; there are different aspects here, but at the conceptual level there is also a side that exempts both.
[Speaker B] Is it broken or not?
[Rabbi Michael Abraham] No — broken in the sense that when you broke it, you didn’t do an act sufficient to make you liable. But it’s not broken enough to see the one who threw it as already liable. To make the one above liable, you need to wait until the vessel actually breaks below, and only then can you really make him liable for throwing the vessel. But as long as that didn’t happen, the fact that you created potential breakage isn’t enough to make me liable.
[Speaker C] Then you can’t say he broke a broken vessel?
[Rabbi Michael Abraham] No, he broke a vessel that had the potential to break, and such a thing isn’t considered an act of damage sufficient for liability. It’s not binary. It’s not either broken or not broken.
[Speaker D] I don’t know if it’s related, but is this like the case of two people who did labor that doesn’t require two people?
[Rabbi Michael Abraham] It may be related to that too. No, there it’s one who cannot and one who cannot, whereas here it’s one who can and one who…
[Speaker D] …can, and each one could do both, at the Torah-level / of biblical origin.
[Rabbi Michael Abraham] Here it’s one who can and one who can, but it really is… okay. But there’s also the case of setting a dog on someone. You know that? There it’s even more common in the later authorities. Here it’s an anecdote. There it appears in many later authorities — the Chazon Ish, Pnei Yehoshua, Ayelet HaShachar — all of them on setting a dog on someone. If I take your dog and urge it on, and tell it: go bite, I don’t know, so-and-so’s chicken — then there is also a side, a dispute in the Talmud, that I’m exempt. Why? I’m exempt because the dog isn’t mine. It’s your property, and its guarding is your responsibility, so you’re liable for payment. If it isn’t your property, you’re not liable for payment. So make the dog’s owner liable. You can’t make the owner liable — he didn’t incite it, he didn’t incite it. You can’t make him liable, right? Like Hershele with the rolls, if I mentioned that, I think. You know the story about Hershele? Hershele goes into a deli and asks for rolls. Fine, they give him rolls. He sits down at the table, suddenly changes his mind, returns the rolls, says bring me doughnuts. Fine, he takes the doughnuts, eats them, and leaves. “What about the doughnuts?” “I gave you the doughnuts in exchange for the rolls.” “And you didn’t pay for the rolls?” “I didn’t eat the rolls.” This whole story of setting the dog on someone is basically something pretty similar. Meaning, you set the dog on him — you can’t make the dog’s owner liable, because he didn’t incite it. One who guarded properly is exempt, right? Somebody else caused the problem. On the other hand, the one who incited it isn’t the dog’s owner. You’re only liable when your property caused damage. If it isn’t your property, then you’re exempt. Now what happens if someone incites his own dog? So several later authorities write that he is exempt.
[Speaker B] Because of the fact that…
[Rabbi Michael Abraham] According to the side that exempts — there’s a dispute in the Talmud — according to the side that exempts both the dog owner and the one who incites,
[Speaker B] according to…
[Rabbi Michael Abraham] …that side, even if the dog owner himself is the one who incites it, he is exempt.
[Speaker B] Okay, that’s absurd, really absurd.
[Rabbi Michael Abraham] Absurd, but that’s what they write. The Chazon Ish too, and Pnei Yehoshua, and Ayelet HaShachar, and others too. Others write it. Actually I have a good explanation for that. For that I do have a good explanation. And unlike the case of throwing the vessel from the roof — there it really isn’t, it’s an anecdote, some pilpul maybe — it’s not really that serious later authorities are discussing it there. But on setting a dog on someone, yes. Okay, I’ll tell you — this really isn’t related to us — but I’ll say it briefly. The Talmud says that with an ownerless ox, a wild ox, that causes damage, in the case of goring damages, where payment is made from the body itself of the damaging ox — an ox that caused damage — right, in its first, second, or third goring, while it is still harmless, then payment comes from its body. What happens if the ox is ownerless? An ownerless wild ox, okay? It gores someone; it’s a harmless ox. I don’t know whether there can even be an ox that isn’t harmless if it’s ownerless — who gives testimony on it? But no matter, let’s say it’s harmless. Okay? So it says there that half its body belongs to the injured party. What’s the practical implication? If afterward someone takes control of it — after the ox gores someone, someone finds the ox, it’s ownerless, and takes it — then the injured party can come and claim half the ox. It belongs to him. That’s a bit strange. After all, payment for damages is imposed on the owner who didn’t guard it. There is no owner here. Who is liable? The ox has to pay damages? Who was liable at the stage when the ox was ownerless?
[Speaker D] But that’s the persistence of ownership over something that was already designated partially; it already caused damage.
[Rabbi Michael Abraham] Be careful, because it’s forewarned. Okay. So if it gores next time, it may already be considered forewarned. Fine, that I’m willing to accept. But why did the injured party acquire anything? What did the injured party acquire? Against whom is his claim? What do you want? It’s an ownerless ox; I took it. What do you want now, to make me pay for something this ox did before I even had to guard it? It wasn’t my property. How are you taking half my ox? You see that the liability — at least in the case of a harmless goring ox, and there’s a question whether this is true elsewhere as well, but at least there — the liability is on the ox. The animal that caused the damage has to pay. It has to pay from its body, of course, in the case of a harmless ox. If it has owners, then it depends. If the owner guarded it properly, then true, the animal owes payment, but we don’t want to harm the owner; he’s not at fault. We won’t take it. But if he didn’t guard it properly, then we’ll take what is owed to us from the animal. Ah, that harms you? Too bad — you didn’t guard it properly. But notice, the liable party here is the animal, not the person. Okay. Now, I incite my dog. Okay? If I incited my dog, and the dog bit, and this is a harmless ox case, right? This is goring-type damage — the dog that bit. Is that harmless? I mean, with a dog that bit…
[Speaker D] Isn’t it always forewarned because it’s, like, an aggressive creature? Suddenly? Not suddenly. Nowadays no, right?
[Rabbi Michael Abraham] With wild creatures it says — the question is whether a lion is forewarned from the outset, a snake, it has no domestication — that’s another discussion. A dog, no. A dog can be harmless or forewarned. “A certain dog that ate sheep, a cat that ate sheep” — there in Bava Kamma 15b there are discussions about whether we judge this nowadays; it’s a fine. It’s a harmless ox case. No, it’s a harmless ox case. Yes yes, otherwise it wouldn’t be a fine. In any event… If I incited it, you can’t impose liability on the dog. It’s not at fault; I incited it. Right? I’m at fault. Yes. But in the case of a harmless ox, the liability isn’t on me; the liability is on the animal. So you can’t impose liability on the animal; consequently they also won’t take from my property, because all they ever take from me is simply half of my animal. If it’s an ox belonging to someone else, then when I incited the ox, why don’t they make the ox’s owner liable? Because the ox isn’t at fault. Because in any case the liability isn’t on him; the liability is on the ox. Why not make the ox liable? Because the ox isn’t at fault. Why not? Because I incited it. Consequently they don’t make the ox liable, and therefore its owner also doesn’t actually pay, because they don’t take half his ox. Now if that ox is mine, it’s the same thing, because in order to make me liable they don’t make me liable for the incitement. They make the dog liable for the damage, but once the dog is liable, they take it, and it comes out that they’ve taken my money. But if I incited it, then basically the question is whether the dog is liable. The dog is not liable — I incited it. So there is no liability on the dog. If there’s no liability on the dog, then they won’t take it, and then I won’t be harmed either, right? And therefore, therefore, therefore I’m exempt in such a case. That’s the argument. Fine, you can show this in other places too. The whole investigation of the later authorities — right — regarding damaging property, is it because of negligence in guarding, or because of the very fact that my property caused damage? Now according to this, at least in the case of a harmless goring ox — I’m saying there’s room to hesitate here — but at least there, what does it mean? That it’s because of the very fact that my property caused damage, not because of negligence in guarding. That isn’t even the question. My property itself is liable, not me. It is liable. My not guarding it is only a condition, because otherwise they won’t take it. Why harm me? I was fine. If I wasn’t fine, then they’ll take it even though it harms me, because I was in the wrong. It’s not that I pay because I didn’t guard properly. It pays. Only if I didn’t guard it properly, then they’re not concerned that harming me is unfair, because I wasn’t okay, so they don’t take my interests into account. That’s all. And they take it — it owes payment.
[Speaker B] So why raise dogs at all, then?
[Rabbi Michael Abraham] Another reason, yes. Anyway, for our purposes, let’s get back to the slave, to the law of guarantor, the law of the Canaanite slave. Okay, I’ll spare you all the learned analytical explanations about this, and let’s get to work. This is ordinary kiddushin. The husband gives money — let’s say black is the money and green is the exchange. The woman basically becomes betrothed to the husband. Okay? That’s ordinary kiddushin. What happens in the law of guarantor? “Here is a maneh and be betrothed to so-and-so.” So here we have — okay, like this. So-and-so gives money to the woman, “here is a maneh” — well, here it doesn’t matter, I’m calling him so-and-so — and the woman becomes betrothed to him. It says, “Here is a maneh and be betrothed to so-and-so,” but I want everyone to stay consistent: so-and-so is the husband and the woman is the woman, the husband — okay, I called him so-and-so.
[Speaker F] Fine. That’s “here is” — so-and-so gives to someone else and the woman becomes betrothed to him? No, that’s the last one. This is…
[Rabbi Michael Abraham] …the law of guarantor.
[Speaker F] Okay.
[Speaker B] Maybe just write next to it exactly — this is…
[Rabbi Michael Abraham] …ordinary, this is guarantor, and now there’s the law of the Canaanite slave. The law of the Canaanite slave — wait, maybe I got mixed up here for a second. No, that’s just kiddushin through an agent, my mistake. The woman goes to someone else, and that someone else gives to so-and-so.
[Speaker B] Someone else gives to so-and-so.
[Rabbi Michael Abraham] “Give a maneh to so-and-so.” Right? “Give a maneh to so-and-so and I will become betrothed to you.” “Give a maneh to so-and-so and I will become betrothed to you.” Fine. So the green is the kiddushin relation and this is the giving of the money. That’s the law of guarantor. Now the Canaanite slave. The law of the Canaanite slave is… “Give a maneh to so-and-so and I will become betrothed to him.” Wait, no — “Here is a maneh, and be betrothed to someone else.” Okay? “Here is a maneh” — so-and-so gives — “and be betrothed to someone else.” Okay? That’s the law of the Canaanite slave.
[Speaker B] You won’t really see the green that well…
[Rabbi Michael Abraham] I think.
[Speaker B] The green — wait, let’s try a little test. The question is whether on camera…
[Rabbi Michael Abraham] …they’ll see a difference between red…
[Speaker B] …and black.
[Rabbi Michael Abraham] You know what, then maybe I’ll do it like in the original. I’ll just make it a dashed line. Black dashed. Okay. What was it here? “And be betrothed to someone else”?
[Speaker F] Woman to someone else here, in return.
[Rabbi Michael Abraham] Okay? So the dashed line is the kiddushin and the solid line is the money.
[Speaker F] Right. Makes it Instagram.
[Rabbi Michael Abraham] Okay. Just money. Okay. And we said I already did the law of the Canaanite slave. Now the law of both. “Give a maneh to so-and-so and I will become betrothed to him.” So-and-so and the woman to so-and-so. Right, but here I just marked it differently; I want to stay consistent with the diagrams. So I do it like this. Someone else is the one effecting the betrothal. The giver of the money is so-and-so. Fine? Just so that the woman is always the wife of someone else. Here really it doesn’t matter — so-and-so and someone else don’t matter here, you can keep calling them the husband and the woman. Okay? So basically the woman is always betrothed to someone else, and the only question is where the money goes from and to. Where the money is.
[Speaker B] That’s all that’s left to check.
[Rabbi Michael Abraham] Okay. Now another interesting point. In the topic / passage there is a fourth case. Right. A fourth case in the topic / passage. Let’s see, I’ll do it here. It’s apparently — and afterward I’ll argue that it’s not only apparently — “Here is a maneh, and I will become betrothed to you.”
[Speaker D] That also doesn’t count, right?
[Rabbi Michael Abraham] The Talmud brings it, but in the end it says that this is only in the case of an important person; in the end it rejects that. Apparently it rejects it—we’ll talk about that. Fine. That’s called an important person. Later on the Talmud says: what if she says, “Take a maneh and I will become betrothed to you.” And then the Talmud says this can’t be, and then it says no, this applies only to an important person. But at first, at least before we said that this was an important person, the assumption was that maybe this could actually work with any person. Afterward they rejected it for various reasons, which we’ll discuss. Okay, so those are basically the cases. All right? So you have this case, and this case, like this. All right? Those are the four or five cases. Now basically the claim is the following claim.
[Speaker B] First of all, let’s finish the case. What? Of an anonymous woman.
[Rabbi Michael Abraham] That’s two. Fine. Now the point is, there are all kinds of disputes among the medieval authorities (Rishonim) about how exactly this whole thing works. I don’t want to get into too many details here, but the question is how these mechanisms work. The one dispute that may be more relevant for us, and that I’ll focus on, is the dispute in the law of a Canaanite slave. In the law of a Canaanite slave there’s a disagreement between Rashi and the Ritva over whether so-and-so has to be the agent of so-and-so.
[Speaker C] What do you mean? Immersion in water?
[Rabbi Michael Abraham] What do I mean? In the law of a Canaanite slave there’s a dispute over whether so-and-so has to be the agent of so-and-so or not. You see, if so-and-so is the agent of so-and-so, then so-and-so gives the woman a perutah and through that she becomes betrothed to so-and-so. Now, if that so-and-so appointed him as an agent, then you understand that this is the ordinary case of agency, right? Yes. So the Ritva claims—I don’t remember anymore who says what—there’s Rashi and the Ritva and they disagree; one of them claims that there needs to be an appointment of agency here. I think the Ritva says this. That the anonymous Canaanite, the slave, does not need to be the agent of so-and-so. It could be that in principle it should work under the law of acquisition on another’s behalf. But acquisition on another’s behalf is based on agency.
[Speaker D] In any case he can’t, so to speak, betroth her in his name without his knowledge.
[Rabbi Michael Abraham] No, you can’t force something on someone.
[Speaker D] So what’s the practical difference?
[Rabbi Michael Abraham] So here, of course, the question is what the novelty is. Fine, if he’s an agent then it’s obvious—it’s just ordinary betrothal through agency. That’s not true, because the perutah is a perutah belonging to so-and-so. In normal agency I give the agent the money and he performs the physical act of handing it over, but here we’re talking about a perutah that belongs to so-and-so himself. This is not the ordinary law of agency. The Ritva’s claim is that the law of a Canaanite slave is in any case a separate law. It’s just that the Ritva claims it won’t work unless there is an appointment of agency here. According to Rashi it would work even without appointing an agent. But in any case ordinary agency is not enough to explain the law of a Canaanite slave. There is a special novelty here in the law of a Canaanite slave. That is true in any case. By the way, here too, if I remind you, in the law of a guarantor, if we really say that the woman becomes betrothed to so-and-so because she received benefit from the fact that he gave money based on her statement, because he relied on her, then once again this is just ordinary betrothal through benefit. So what’s the novelty? There you have to say either that if we say there is benefit at all—or that there’s a contradiction between the passages and here they really do not assume there is benefit—or that if we say there is benefit, then the novelty is that something like this counts as benefit. But really, once you’ve made the novelty that something like this counts as benefit, then it’s just ordinary betrothal through benefit. And we know that the Talmud in tractate Kiddushin brings several cases in which I betroth a woman by some act that gives her benefit: “Dance before me,” or “on condition that I speak on your behalf to the authorities.” I do all kinds of acts that are worth money to the woman or that give her benefit. In such a case it’s clear that this is just ordinary betrothal by money.
[Speaker C] So what do you need…
[Rabbi Michael Abraham] So what is the novelty in the law of a guarantor assuming there is benefit? If there is no benefit, then it’s certainly a novelty. But if there is benefit, as in the Talmudic passage in Bava Batra, then what is the novelty in the law of a guarantor? The novelty is that this kind of thing is called benefit. If only because the other kinds of benefit can be translated into money. Say that if I dance before her—people pay millions to see me dance. So if I tell the woman that I’ll dance before her, then I’ve given her the value of the ticket, right? Which is millions, as I said. I could betroth all the women in the world with that dance. But if it’s… or “on condition that I speak on your behalf to the authorities,” then she’ll gain something from that, it has monetary value. Here, the fact that you give someone money on the basis of my statement—even if we define that as benefit—I very much doubt how far such a benefit can be quantified in money. I’ll say more than that: the Kovetz Shiurim even asks—say he gives… after all, simply speaking, the Talmud says that she is betrothed. There’s no limitation on the amount. A perutah. Simply speaking it’s a perutah, right? Now if he gave so-and-so a perutah based on my words, what is the value of the benefit that I received? What is this? If he gave a perutah based on my words, did I receive the full benefit of the perutah? In other words, there’s some kind of perpetuum mobile here, something that creates value out of nothing. We had one perutah and produced from it benefit worth two perutot. That person got… the full benefit of a perutah, and the woman also got benefit worth a perutah. Not reasonable. Therefore, says the Kovetz Shiurim, apparently there is a problem here, because she actually received less than the value of a perutah. This is another argument, by the way, in favor of the claim that in our passage they are not assuming at all that the woman receives benefit. It may be that benefit that cannot be quantified in money, for purposes of betrothal, is not called benefit. But even so, from the law of a guarantor we learn that such a thing is possible. It’s possible because the giving by so-and-so to so-and-so is considered as giving to the woman since she instructed it. Not the benefit that he acted on her word, but the gift itself—instead of giving it to the woman, as we see here, you can redirect it to so-and-so. That too is fine. That’s what we actually learn from the law of a guarantor. Okay? Think that even here there was room to hesitate. What?
[Speaker B] What’s different about all this? So-and-so gets the perutah, so why the woman? The woman—it’s considered that she received it.
[Rabbi Michael Abraham] What did she receive? A perutah. That perutah was received by so-and-so in her place—what difference does it make? But that is the perutah that was given for betrothal.
[Speaker B] No, but she didn’t receive it. She says instead of giving…
[Rabbi Michael Abraham] “To me, give it to him”—what difference does it make? She got benefit, she got something. Now I’ll put it to you in the simplest way. If I formulate it like this, then again it becomes non-novel, but here’s an example: suppose the woman says to you, “Give me a perutah,” all right? And I want to give it to Avishai. Avishai, excuse me. I want to give it to Avishai. Okay? That’s fine, there’s no problem at all: I receive the perutah, I’m betrothed, and now I give it to him. Now wait. And now the lien of Rabbi Natan. If you give it to me and I transfer it to him, then just give it directly to him, what difference does it make? Now, once you gave on the basis of what I said, it could be that halakhically this is considered giving to me that then passes to him. All in all, we just shortened the route, but basically that’s what happened here. So then once again the question returns: what is the novelty at all? Therefore that probably is not the right conception of what happens there. I’m only saying that it isn’t illogical. In other words, there is something to it, you can definitely understand it. But that’s what is learned from the law of a guarantor.
[Speaker B] Maybe you can aggregate this benefit into more than a perutah? What? Maybe you can aggregate this benefit into more than a perutah, and then you have half a perutah…
[Rabbi Michael Abraham] Here and a perutah there.
[Speaker B] What do you mean aggregate the benefit? Yes, but there is benefit; the value of the benefit you said she got is worth more than a perutah, at least to her.
[Rabbi Michael Abraham] How can that be? What, all that happened because they relied on her was that they spent a perutah based on her word, so why is that worth more than a perutah?
[Speaker B] Yes, because she—the fact that you did what she asked is worth to her, in terms of benefit, more than a perutah.
[Speaker D] Yes, but that’s a subjective claim.
[Rabbi Michael Abraham] But if I did something banal, nothing special—I gave a perutah—it’s hard to believe that the benefit she derived is worth more than a perutah. Why would she get more benefit? If I gave you a perutah, then there’s no greater appreciation toward you than giving you a perutah based on her command. You yourself actually received a perutah from me. That isn’t a greater benefit than someone on whose word I was willing to spend a perutah. That claim doesn’t sound plausible to me. Okay?
[Speaker B] There are other things that matter to me here in the Torah. What?
[Rabbi Michael Abraham] That she gets benefit because giving to an important person is benefit. I’ll get to that in a moment, in just a second. For now I’m speaking here not about an important person. That’s just the name of the mechanism, but I’m not treating it as a case of an important person. In a moment I’ll explain why. All right? Okay. So now look, in the Talmud itself, in the Talmud itself it says: Rava raised a question. We’ve finished the law of “both of them”; I’m continuing to read without interruption, it’s a continuation of the passage. Rava raised a question: “Take a maneh and I will become betrothed to you.” In this case. All right? “Take a maneh and I will become betrothed to you”—what is the law? At this point it’s clear that he is not speaking about an important person. It’s a continuation of all the earlier cases. He is simply saying: okay, you brought me all the tricks, we moved the arrows from every direction to every direction. This one you still haven’t answered me about—what about this? In other words, Rava at least considers it as a possibility that this betrothal would work even not in the case of an important person.
[Speaker B] What does “take” mean?
[Rabbi Michael Abraham] What? Huh? Take. I give you a perutah, and through this I become betrothed to you.
[Speaker B] Meaning she betrothed him?
[Rabbi Michael Abraham] Yes, the exact opposite of everything you could imagine. Okay? First of all, because “when a man takes a woman” means this is not betrothal at all—she is taking herself to him, not he taking her. This goes against all the rules of betrothal, and Rava asks it innocently as though there were no problem at all. Now more than that: after he asks this question, how does the Talmud answer him? Look, the Talmud says: Mar Zutra said in the name of Rav Pappa: she is betrothed. Yes, excellent, what’s the problem? What’s bad about it? How would you have understood that until now? Why in the world should she be betrothed? What does that have to do with everything that came before?
[Speaker D] If we think of it like the previous example, then it’s like she gave in order that he should give—exactly, exactly like that.
[Rabbi Michael Abraham] Basically the Talmud sees this as a composition of the previous mechanisms. Take another conceptual building block, take one, build it into the second—in a moment I’ll show you how to do it, okay?—and you’ll arrive at this mechanism. I can build it out of those. It’s like the law of “both of them,” and I built the law of “both of them” from those two; I can build this one from those two as well. In a moment I’ll show you how I do that, okay? So since that’s the case, basically what’s the problem? If every composition is possible, then this is possible too. That’s exactly the idea of a group. Every element that results from these operations belongs to the group. That’s the assumption. And therefore now you need specific explanations for why not. So about this the Talmud says: Rav Ashi said to Mar Zutra, “If so, then movable property would be acquired together with real property; but we learned the opposite: movable property is acquired together with real property by money, document, and possession.” In other words, the woman gives money and she herself is acquired by the one who receives the money—so what comes out? That the other person is acquiring property that has responsibility attached to it, namely the woman, like land—for a person is compared to land—together with property that does not have responsibility attached to it, namely the money. But that can’t be, because usually one acquires movable property incidentally through real property. That’s your problem with this act? It’s just a technical problem in the definition of acquisition of land. Do you understand that this is only a technical problem? So in principle, if I could acquire the woman and incidentally the money, everything would be fine. The whole problem is only that I’m acquiring the woman incidentally through the money. The Talmud has no problem whatsoever with the fact that the direction of both is from the same direction—from the woman to the husband. That doesn’t bother the Talmud at all. The whole problem is only that in the laws of land acquisition such a thing is not supposed to work, and a person is compared to land. Very strange. In other words, you see that even in the conclusion, the Talmud assumes that in principle such a thing should work. Only because a person is compared to land and there’s a problem in the laws of land, then no. Therefore I claim that this case is not a case of an important person; it is valid betrothal. The problem is only in practice—it won’t happen because there is a problem with land acquisition. But in principle, in terms of the law of a guarantor, the law of a Canaanite slave, the law of “both of them,” and all that, this too is a mechanism of valid betrothal.
[Speaker E] Is this also a conceptual building block? Yes, exactly.
[Rabbi Michael Abraham] In other words, the Talmud assumes that every… right, exactly like that. It’s simply a construction out of the two previous ones. Therefore I told you that here my feeling is that the Talmud is not merely doing something that afterward I can come and build some mathematical model for; you can see the mathematical thinking in the Talmud itself. The Talmud itself takes something that on its face has no logic at all, it goes against all the rules of betrothal, but it is clear to the Talmud that if you can build it from the fundamental building blocks, then it is valid. Because one plus one is two; that is, everything stays inside the group. If you manage, from the basis, to produce some additional element by composing two elements, then this new thing also belongs to the group, the group of acts of betrothal. Okay? So I’ll show you even more complex extensions. In any case, what I want to claim now is the following claim. Well, look: this is the ordinary law of betrothal. “When a man takes a woman”—that’s the ordinary case, and for that there is a clear verse. This too has a source, the law of guarantorship in a loan; the Talmud somehow compares it, but it has a direct source. This one is learned from the law of a guarantor in a loan. This too has a source, the redemption of a Canaanite slave. All right? That’s it. Basically, in the language of the previous classes, these are the primary categories.
[Speaker B] Right?
[Rabbi Michael Abraham] Three primary categories, four mothers, right? Here there are three primary categories.
[Speaker B] Okay, building blocks.
[Rabbi Michael Abraham] And now we can make derivatives. Derivatives can resemble one of the primary categories, they can resemble two, or maybe resemble all three. Every composition you make among the primary categories will produce some derivative. Those with some background in mathematics—this is really the concept of a group. In other words, you have some basis, and by means of some operation among the elements of the basis you can produce additional elements within the group. And this group is closed, meaning the operations won’t take the elements outside the group. Apply the operation to each of the elements, and you’ll get something else—or the same element—within the group, but an element that belongs to the group. It will never go out. What I’m claiming, in mathematical language, is that the Talmud assumes that the acts of betrothal form a group. That is what the Talmud assumes. That’s really exactly what it assumes. It isn’t some clever thought afterward where I come with modern concepts; the Talmud assumes this, it just doesn’t call it that because the concept was not familiar to it. That is exactly what it assumes. It assumes there is an inverse element, it assumes closure, it assumes—you can prove that this is a group and the Talmud assumes it completely. Completely, in all the definitions. Now look: when I want to show how the law of “both of them” comes out, before I said it in words, the conceptual construction that doesn’t end with a common denominator, what I called in the Talmud. Now I’m saying it formally. What do I do? Suppose I call the law of guarantor A, or operator A, and this is operator B. So I begin with an act of betrothal like this: if this is so-and-so, this is so-and-so, and this is the woman. Now an ordinary act of betrothal is that so-and-so gives money and receives a woman. Right. So what do I do to obtain the law of guarantor? The operation A is the first element. This is the first element—for those who know Dirac notation, this is the standard one. All right. Now I say: how do I get the law of guarantor? I apply operator A to this element, to this element. The notation doesn’t matter, for those who don’t know it, it doesn’t matter; I call it guarantor. That’s how it’s denoted in Hilbert spaces. The point is that what you’re doing, visually speaking, is taking the head of the arrow and moving it to another party. That is the operation, basically. If you have a legitimate operation, you can take the head of the solid arrow and move it to another target. In other words, this means that the recipient of the money does not have to be the recipient of the original act. You can change the recipient, right? That’s the law of guarantor. Therefore, when I now take this thing and move it here, that is operation A. What I get is this situation. This situation is denoted by state A, the state of the law of guarantor. Operation B basically takes the ordinary state—I apply B to it. Notice what B is: B is the Canaanite slave. B is basically taking the tail of the solid arrow and moving it, taking it out from one person—in other words moving it to another person. Not the woman, not so-and-so, excuse me, but another so-and-so. Right. Earlier the guarantor acted on the head of the arrow; the law of a Canaanite slave acts on the tail of the arrow. So if you now take the tail from here to here, all in all you get the law of a Canaanite slave. In other words, operation B gives me the state of a Canaanite slave. Now it’s very easy to see how I get the law of “both of them.” In a completely visual way—it’s a mathematical operation. What do I do? Let’s assume I take the ordinary state; it’s drawn here. All right. I apply operation A to it. What is operation A?
[Speaker B] The head of the arrow goes up.
[Rabbi Michael Abraham] Right. Now to the result I apply operation B. This operation is basically guarantor, right? And I do B on the law of guarantor. Now what is B? What is operation B? Operation B is taking the tail and shifting it, right? Am I right? No, no, sorry, wait. Again. The law… wait, that is right, we’ll see in a second. We have an arrow here like this, right? Now A tells me yes, it goes here. And B tells me yes, it’s like this. That is BA. And what is AB? It is basically A acting on the law of a Canaanite slave. Right? So basically the law of a Canaanite slave is this, and A is moving the arrow. Right? Moving the head of the arrow. Right? The law of “both of them” is basically AB.
[Speaker F] Yes. Agreed? You moved the woman here.
[Rabbi Michael Abraham] No, he did the law of “both of them.” I didn’t understand.
[Speaker F] Is the transition from the line to the arrow? That’s the body of the betrothal. Where?
[Rabbi Michael Abraham] In AB, and then AB on the ordinary case, on the ordinary state of ordinary betrothal. This is the ordinary state. Yes, now I’m here. Now if we apply AB we get the law of “both of them.” If we get BA we get this law. It’s different. “Take a maneh and become betrothed to me for so-and-so.” Right? In other words, in principle I could have another law here from the composition. If I assume that this is a full, closed group—that is, that all operations that are compositions of the basic operations are legal—then in principle I could talk about this as well. There’s one trick here that isn’t entirely simple: I’m moving the tail from the husband to the woman, not from one husband to another husband. I’m moving it between two different figures. But we know that, for example, here I’m moving the money from the woman to the husband, so you can also move between a woman and a husband; it doesn’t have to preserve moving from husband to husband or from woman to another woman.
[Speaker B] Right? This is the general structure of the conceptual construction—that the woman does not receive and the husband does not give. Okay. Here too the husband does not give, yes, you can see it.
[Rabbi Michael Abraham] Right. No, that’s why I say: but now I’m no longer talking about it generally, that the woman does not receive and the husband does not give; rather, I’m giving it a precise mathematical pattern. And once there is such a mathematical pattern, suddenly you discover that there are two situations in which the woman does not receive and the husband does not give, not just one. What the Talmud calls the law of “both of them” is the state AB, but there is also the state BA. The state BA is another state, this state. Okay?
[Speaker B] How did you arrive at the law of “both of them”? You said how to do it? Again? The law of “both of them,” how…
[Rabbi Michael Abraham] The law of “both of them” is BA. I’ll start again from the state—I’m just doing it completely formally, there’s nothing to remember here. Look, this is ordinary betrothal. Okay? Now if I do A first, that means I move the arrow—wait, A…
[Speaker D] It takes the money from so-and-so to so-and-so. Yes.
[Rabbi Michael Abraham] A goes like this, right? A goes like this. And then I apply B to it.
[Speaker B] B is moving the…
[Rabbi Michael Abraham] No, that’s not the law of “both of them.” So that’s AB, not BA. That’s AB. Let’s try. B is moving the tail, yes, B is moving the tail. The operations are not commutative, these operators are not commutative. Yes, like this. Right? Then you move the head, and you come down here—that is the law of “both of them.” So AB is not equal to BA, in short. The operators are not interchangeable; the order in which you apply them matters. Okay? In other words, the group is what’s called non-abelian. An abelian group is one where the operations are commutative, where the order of application doesn’t matter. But this is entirely a group. Now if I really assume this, then one of the necessary implications is that the operation I described before as BA, not AB—which was basically this thing—should also be legal. If I’m right that the Talmud assumes the group is a full group, then this is legal. Why? We need to understand: I’m not checking this as “how can it be that the woman gives money to him and becomes betrothed to that one.” As far as I’m concerned, that’s not what happened here. What happened here is that first of all, basically so-and-so gave money to the woman in the name of so-and-so, and afterward they basically said to the woman, “Take the money in my place,” as they say in the law of a Canaanite slave. In other words, in practice what we… it’s like what I said earlier, the lien of Rabbi Natan. I don’t see this act as a basic act; I see it as the sum of these two acts. After all, each of these does not interfere with the effectiveness of the betrothal, so if I do them one after another then certainly—you agree? So what difference does it make if I do them simultaneously? So doing them simultaneously gives me this result, but I’m not checking in the end who gave money here and who received. If I can break it down into two acts, each of which is a legitimate act of betrothal, then why should doing both one after the other not be legitimate? Everything is fine; at no stage did I do something that interferes with the effectiveness of the betrothal. This kind of superposition. Exactly! Now I join the two—I look at this operation, let’s call it C, as an operation that is AB, and A and B separately do not interfere with the effectiveness of the betrothal. Think about the conceptual construction. What I’m basically… this is exactly conceptual construction. I say: in winnowing we see that the wind does not interfere with liability on the Sabbath, right? Even though wind is involved. So I say: then in throwing too it will be like that. Right? Here too I say: the fact that the woman does not receive does not bother me; it’s considered as if the woman received, right? And it also doesn’t bother me that the husband does not give, right? So if I now combine the two together—that is exactly the conceptual framework of the Avnei Miluim that gives me this. And therefore the Talmud ignores it completely. Now you understand why the Talmud here raises the possibility that maybe it works, and as I said earlier it also concludes that it works. The whole problem is only the ordinary laws of acquisition of land. And in principle the Talmud remains with the view that it works. Even in the initial assumption, Rav Pappa in the name of Rav Zutra says as law that it works. The Talmud afterward says, wait, there’s a problem with movable property being acquired with property that has responsibility attached? Fine, so the Talmud says it’s only an important person. But first of all there is an amoraic opinion that it really works. Rava’s initial assumption too—he asked it as though it were obvious: why not? In other words, he did not look at this at all as a case where the woman gives money and the husband receives betrothal. He does not see it that way at all. It’s merely a composition. How do I build it? Do you understand that I can build it easily? Take this, all right? And now apply A to it again. Maybe like this, or the reverse. Wait, does that make AB? No, sorry. Like this. All right, let’s see.
[Speaker B] We start…
[Rabbi Michael Abraham] We start with this. Okay, this is ordinary betrothal. Now we apply A. What is A? A is to move the arrow here. Right? That’s A. On the result we apply B. B is to move the tail. Right? Like this. Okay? And on the result we move A. To move A is again the head. I have simply reversed the direction of the arrow by combining the basic operations. Okay? So ABA is another result beyond AB and beyond BA. It’s the only remaining possibility, by the way. Apparently there isn’t any more. Okay? And basically I arrived at this. Therefore the Talmud says: why shouldn’t this work? When you don’t look at it through the lens of a group built from basic operations, you say, what do you mean? The Torah said, “When a man takes a woman”—give her a perutah and she becomes betrothed to you. How did we arrive at turning the whole passage upside down? In other words, the woman gives me a perutah, and in fact even if the woman merely speaks that ruins the betrothal. The husband has to speak, he has to take the woman. Because “when a woman is taken to a man” is problematic, or “when she takes herself to a man.” She would be taking herself. If she takes herself to a man, that invalidates the betrothal. And that’s just in speech. So when you give the money, there’s nothing to discuss at all. And the Talmud says: what are you talking about? This should work. Because the Talmud does not see this at all as money that the woman gives. That is simply not true. It is money that the husband gives that underwent one transformation here, another here, and another here. But that doesn’t matter. It remains inside. I only did it in one stroke instead of in three stages. But if we had done all these stages one after another, each individually, none of them would have interfered with the effectiveness of the betrothal, right? I did all three together—what difference does it make? The fact that the final result came out problematic doesn’t matter. Because, you know, it’s like what I said about combining the law of a Canaanite slave and guarantor. After all, once I waive the requirement that the woman receive, and the second time I waive the requirement that the husband give, so what remains, for heaven’s sake? The Torah law is that the husband gives the woman a perutah and she is betrothed. That is the law. Now suddenly we waive the requirement that the woman receive. Then we waive the requirement that the husband give. It’s like “the one who throws from the top of the roof.” In other words, in the end nothing is fulfilled and yet everything is fine—or there everything is fulfilled and still he is exempt. There is betrothal. Yes. Why? Because we do not see it that way. We do not look at it as a case where the woman gave money at all. The husband gave money to the woman. Only afterward she gave it to someone else, and that someone else gave it back to the husband. That’s all. Therefore we did it in one stroke. Like I told you before with that perspective, we’re just looking at it like the lien of Rabbi Natan. Instead of doing it in three stages, we do it in one stage. But if we had done it in three stages, none of them would have interfered with the effectiveness of the betrothal. So if I do the three all at once, that also doesn’t interfere. That is what the Talmud is basically claiming. Without this sort of mathematical perspective, I think you simply can’t understand what the Talmud is saying here. It is just completely incomprehensible.
[Speaker D] And yet I’m still taking advantage of the fact that there is another logic, so as not to reach that conclusion.
[Rabbi Michael Abraham] No, that’s because of the laws of land acquisition, and it doesn’t say that this contradicts the requirement of betrothal. But what I would have expected is for it to say: wait, in betrothal the husband has to give to the woman. “When she takes herself to a man” is not betrothal. But that doesn’t bother the Talmud at all. It doesn’t even raise it.
[Speaker D] Right. But this analogy is what makes possible the sort of contradiction in not accepting the conclusion, as it reaches it. It reaches some conclusion and then contradicts it.
[Rabbi Michael Abraham] Not everyone accepts the conclusion in the end, but I’m saying they don’t accept it for a side reason. In other words, on the principled level, in terms of the laws of betrothal, it was fine. Why was it completely fine? After all, in the laws of betrothal the husband has to give a perutah to the woman, and what happens here is the opposite.
[Speaker D] I’m just trying to see it as part of the system, and then it goes here.
[Rabbi Michael Abraham] But it isn’t part of that system, because it’s not from the laws of betrothal; it’s from the laws of land acquisition in general. It has nothing to do with betrothal.
[Speaker D] But this analogy—where is it from?
[Rabbi Michael Abraham] Meaning, the analogy of what?
[Speaker D] Of land to a woman?
[Rabbi Michael Abraham] Just that a person is compared to land. It’s true of a slave too, not only of a woman. It isn’t specific to betrothal. A person in general is compared to land. There are several places where this appears; in the Talmud in tractate Kiddushin, page 6, you can see it, one page earlier. There are other places too. The claim is that everyone knows slaves are compared to land, but the medieval and later authorities say that in fact human beings are compared to land. Usually when you acquire a person, you acquire a slave. So there you see it, but the comparison is not between a slave and land, but between a person and land, a free person and land. Now, one of the questions we can ask ourselves, yes.
[Speaker C] So the group is basically these three vertices, and that’s the basis.
[Rabbi Michael Abraham] That’s the basis. These elements are composite elements. You apply the basic operations of the group to the elements; whatever is generated is part of the group, because a group has to be closed. Okay? And the assumption is that anything you can generate within the group will be a valid act of betrothal. That’s the point. This is the group of acts of betrothal. Therefore the Talmud assumes that if I succeed in generating some act, however absurd it may be, if I can generate it from these three basic elements, then it is a valid act.
[Speaker B] But that’s a manipulation, because right now you’ve basically turned the Torah law into… you’ve turned it on its head.
[Rabbi Michael Abraham] I haven’t turned it—that’s exactly the point. I’m abstracting, not turning it over. This is the law, because I performed betrothal here. In this case the husband gave money to the woman. You may not see it, but he gave money to the woman. It’s just that afterward other things happened. Afterward the money passed to someone else, and that someone else gave money to someone else, and suddenly we arrived at this. But within it there was also a stage where the husband gave money to the woman.
[Speaker B] So what you’re saying is that if you create a group with many more things that you can do all these operations in…
[Rabbi Michael Abraham] No, that I’m not sure about. If the group is broader, then first you need to justify the basic elements. If your basic elements can be reached legitimately and you want to attach them, they of course will no longer be the basis. Will you attach them to the basic elements and now generate a larger group? No problem.
[Speaker C] As long as I can carry out all these operations?
[Rabbi Michael Abraham] No, I’m saying again: if you make a group on a broader basis, then what justifies adding two more elements to the basis? Where do you get them from? Who says they are legal? If you didn’t build them from these operations…
[Speaker C] It went through more people.
[Rabbi Michael Abraham] Right, so you need to build them out of these operations; otherwise they themselves won’t be legitimate. You can’t build something else on their basis. But if you built them on the basis of these, then they don’t belong to the basis. Then they are elements already built by the basis. They are not independent of the basis; the basis built them. Therefore the basis remains this. There isn’t any more than this. The interesting question is—look, I’ll give you an example, maybe just a note. Now the interesting question—I mentioned that in the law of a Canaanite slave there is a dispute between the Ritva and Rashi whether agency is needed. What do you say? In the law of “both of them,” is agency needed? And between whom and whom? Who has to be the agent of whom? So without getting into that whole tangle, this is exactly the passage we dealt with in “fire and a stack” in tractate Bava Kamma.
[Speaker D] Or in cases of “the wind assisted him.”
[Rabbi Michael Abraham] I said that in a conceptual construction, if one is basic and the other merely removes an obstacle, then the characteristics of the basic primary category will also appear in the derivative. Okay? If it’s a common denominator, then it doesn’t have to be so. But if it’s a conceptual construction, then not only does it not have to be so, rather the characteristics of both will be there. But if it’s a conceptual construction, then there is room to hesitate depending on whether it is symmetric or not symmetric; we already discussed that. And now it will depend on the question whether in the law of “both of them” agency is really required or not required. And what comes out here is absolutely crazy, because what comes out is that so-and-so has to be the agent of so-and-so to give money to so-and-so himself. In other words, so-and-so has to appoint so-and-so to be his own agent to give money to himself. You understand that this is completely abstract. In other words, it is perfectly clear that this does not come from legal thinking; it comes from mathematical thinking. In legal thinking you don’t see such a thing; people would simply laugh at you if you said such a thing. In mathematical thinking it is demanded. In mathematics it comes out immediately. Now I’ll give you another example. These are all the possibilities; it can be shown that these are all the possibilities. All the elements of the group are only these, as far as I remember; maybe there is one more, but as far as I remember it’s only these. There aren’t any more. There is an inverse element here, by the way: if you apply A to A itself you get back the original state. If you apply B to B itself you get back the original state. Even though A and B themselves are not commutative. Therefore it’s clear that ABA will yield an additional element. It doesn’t bring you back to the same place. And BAB as well, but it will be identical to something else. In any case, that’s the number of elements; there are no more than that. But now the question is what happens if there are four people? It starts to get… what about something like this? This is so-and-so one, so-and-so two, this is so-and-so, and this is the woman.
[Speaker D] How can you get this?
[Rabbi Michael Abraham] Here—you can set it up. We have four characters like this, and now you can start talking among them. In fact this is the only option that exists in this situation. Any other option of arrows that you make will be one of those elements; one person will simply remain superfluous. Right. Even, for example, if you put the dotted arrow here, then remove this and it’s basically a three-person state. Put the solid arrow here or here, and you’ll always get one of the states of the three factors.
[Speaker F] Can you add another arrow of giving money?
[Rabbi Michael Abraham] No, for now I’m saying there is an arrow of giving money and an arrow of betrothal. In a moment I’ll say something more about that too. Okay, so this is the only state that does not map onto three-person states. Okay, now it turns out that I found such a situation in Tosafot Rid: what happens when a father—and this depends on many positions among the medieval authorities, you need to work it out, but in principle I can show that in Tosafot Rid there is a view that something like this would also work. So-and-so one gives money to so-and-so two, and the woman is betrothed to so-and-so. And by the way I can of course build this thing from the basic elements. You can build it from there, it’s not a problem. Move this element here, then move that here, and you understand that you get the law we had before.
[Speaker B] How does that come out? The father gives to the father of…
[Rabbi Michael Abraham] This is a father of two sons. There is a discussion there in the Talmud: a father of two sons gives a perutah to the father of two daughters, and the two sons are betrothed to the two daughters with one perutah. Not with two—with one perutah. And now there is a question, a dispute among the medieval authorities, whether the fathers on both sides even need to be agents of the children or not. Now if you do the calculation—and again, you have to get into various medieval authorities, so I won’t do that—but there are positions where there is no escape from assuming it. Because if they are agents, then there’s no problem: you’re an agent and I give a perutah in your name; that’s just ordinary betrothal. But if it doesn’t work under the law of agency and instead we do: I give money to the father—say the two daughters are adults, the two daughters are adults and the two sons are adults, and I am not an agent. If there is such a situation, for example, then this is exactly this situation. In other words, one father gives money to the second father, and the daughter is betrothed to the son, or the daughters are betrothed to the sons. Even two. And there in that case it’s not certain that you need…
[Speaker B] Even two—two against one, each one half a…
[Rabbi Michael Abraham] Right, the Talmud discusses it there and the medieval authorities disagree on the matter. So this is a state that I can show of four connected to each other. Now there are even more complex states, and with this I’ll finish, but there are even more complex states. The Talmud says: and so too with regard to monetary law. There is some dispute whether we actually rule this way in monetary law or not, because Maimonides omitted it. But look, in monetary law wonderful things can come out. What do I mean? For example, if I now do—let me give you another example so you can get a taste, “Taste and see that the Lord is good.” For anyone who thinks Carlebach prayers are enjoyable—I don’t know what’s enjoyable about that. You see the group of betrothal; do you have something more enjoyable than that? The group of betrothal and the dog—like a thriller. Ah, there, I see. Yes yes, it’s not a whole book, it’s the last part of the book. I’ll draw the picture for you and then I’ll explain it. So-and-so one and so-and-so two. Was the whole previous board documented?
[Speaker B] The previous one that you did?
[Rabbi Michael Abraham] What I did before. Didn’t I erase something, which one?
[Speaker B] No, it wasn’t documented. No, I didn’t actually photograph it. There was some example you gave there—I didn’t understand that it was…
[Rabbi Michael Abraham] Here is so-and-so number three, and this is so-and-so, and this is a woman. And “among all these I did not find a woman,” so here, we found one. Okay, now look: that one gives that one money, and it looks like this works for monetary matters too. Okay, so so-and-so transfers a field to so-and-so number two; so-and-so number one transfers a field to so-and-so number two by means of so-and-so number two giving money to so-and-so number three. In other words, this is the law of a guarantor applied to monetary matters. Okay, now this land is the money of betrothal for the woman. And we transfer the land by the law of a guarantor, and that creates—I’ll make this double, because this is betrothal and this is the land—it creates the woman’s betrothal to so-and-so. You see? Now we already have five factors. Of course, now you can put together as many as you want. Because in betrothal it ends with four, but in monetary law you can make whatever combination you want; you can build completely crazy structures here. It can be that one transfers land to a second person by the law of the Canaanite slave, and that land is payment for another object that passes by the law of a guarantor to someone else, and by combining the two this results in betrothal for that woman—and make it as large as you like, as complex as you like. In other words, you can combine whatever you want. And in principle, if I’m right that this is a group, then all these things are legally valid. You can do anything. Anything that I can show can be built out of these basic operations takes effect. We don’t need to think about each case separately—that’s the advantage of mathematics. We don’t need to stop and ask a halakhic decisor: tell me, what happens if so-and-so number one gives money to so-and-so number two, and then so-and-so number two gives money to so-and-so number three, okay? And the land of so-and-so number one is given to so-and-so number two as the woman’s betrothal to so-and-so. There’s no way to think about this in legal forms—you can’t really analyze it on the legal level. But if I look at it mathematically, there’s no problem. I can build it as a set of operations. After all, first I decoded these four here, and I already proved that they’re valid. Now this giving here—I replace it with the law of the Canaanite slave. All I’m saying is this. I’m completely allowed to do that, because a transfer can be done by means of the Canaanite slave or by the law of a guarantor, right? So I can replace every arrow like this with a transfer of the Canaanite slave type, and everything is fine. So I’ve proved that this thing is also an element in the group—or in other words, that these are valid betrothals. And so on, at any level of complexity whatsoever.
[Speaker B] From the standpoint of Jewish law—wait—what even brings this into the context of betrothal at all? He has to say it to her, and she has to agree.
[Rabbi Michael Abraham] Yes, of course. He has to say, “Behold, you are betrothed to me with this land that so-and-so number two acquired from so-and-so number one by giving money to so-and-so number three.” I don’t know whether he has to say the “by giving money” part, but he has to say “with this land.” The land has to be transferred by his saying to him—
[Speaker B] The sequence of acquisitions.
[Rabbi Michael Abraham] If they’re sharp enough, they’ll come out married at the end.
[Speaker B] I don’t know how this suddenly got to a Canaanite slave.
[Rabbi Michael Abraham] Yes. No, I think it’s nice.
[Speaker B] In terms of acquisitions, in terms of the laws of acquisition?
[Rabbi Michael Abraham] Both acquisitions and betrothal, yes, yes. The Talmud says, “and likewise regarding monetary matters.” This works for acquisitions too. On the contrary, in betrothal it’s a bigger novelty; originally this comes from acquisitions. The Canaanite slave and the guarantor are acquisitional mechanisms.
[Speaker B] Go to the rabbinate and tell him something like this—he’ll throw you out immediately.
[Rabbi Michael Abraham] If that were the only thing he heard from me, he’d be delighted. Usually he throws me out for things that are more fundamental. Fine. Okay, I just want to mention again that basically what we see here is that this is not some model that I come and impose on the Talmud. You can see that the Talmud itself was aware of this mathematical structure. Otherwise it couldn’t have said this. This wasn’t done accidentally. It’s clear that when the Talmud brings these strange cases, it simply saw that they were combinations of the simple cases. It says, “the law of both of them”—this isn’t something you have to guess. The Talmud itself says: I performed a group operation here. Okay. Good.