Study and Halachic Rulings – Lesson 24

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[Rabbi Michael Abraham] This has analytical value. But I’m saying there’s more than that here—there’s also halakhic value, practical value. Why? Because in a place where, for example, the enactment that one does not ransom captives for more than their value does not apply—for instance, in our issue with our hostages in Gaza today—there are many arguments that the enactment not to ransom captives for more than their value is not relevant to this situation, for several reasons. One reason, for example, is that we are not isolated Jews where, if we pay, that will motivate the gentiles to capture more and more Jews in order to get more and more money. The gentiles standing against us would want to do that anyway, and we have an army that, in principle, so long as there are no blunders and no things like what happened to us in October, is supposed to prevent this. It doesn’t always succeed, but generally speaking it’s supposed to prevent it. That’s in our hands; it’s not like the situation in exile, when Jews were at the mercy of gentiles or of various bandits. Various bandits. In such a situation—and that’s the reason usually brought—there are two reasons in the Talmud, and the reason usually brought in the Talmud is indeed so that they should not come upon us again, meaning so that they should not come to capture more people and so as not to give them extra motivation to capture more people. Therefore, not to pay them too much, beyond their value. Here, they say, that is not relevant, because here we will not allow them to capture people, because we have an army. What happened here was just the result of a blunder. So there is no concern that if we pay, then in the future more and more Jews will be taken captive. They always want to take more and more Jews captive, but you need to make sure there are no blunders so that such a thing doesn’t happen. But that is in your hands; it is not like the situation of exile. In such a situation it is not at all clear—yes, it’s almost paradoxical—precisely because we have an army, there may be no obstacle to paying everything they want. You would have expected the opposite: if we have an army, then don’t pay, fight. No—if we have an army, that can certainly be an argument, another argument, I didn’t say not, but not only that. Once we have an army, then the concern that they will come again is absent, and therefore you can pay even more than their value. The reason that tells you not to pay more than their value is not present.

Now what happens in such a case? If that’s so, we are basically returning to the situation that existed before the enactment. And then suddenly it becomes important to clarify what that situation was. Does it mean that every citizen has to spend all his money, or that the public has to spend all its money? Is it all his money, or is it a lot, or how much—how much is one supposed to spend? In other words, this inquiry, which on the face of it seems only a theoretical analytical inquiry—because after all there is already an enactment, and the enactment says up to their value and no more—so why should I care now what the law was before the enactment and what the original law was? That seems to be only a matter of analytical interest. No. It’s a matter with practical value, because in situations where the enactment does not exist, the law reverts to its source. And then you have to clarify what the original law says. Does it really mean to spend all one’s money, or not to spend all one’s money? This clarification is halakhic as well, not merely analytical. Yes.

Rabbi, does the Talmud refer only to money, or does it also refer, say, to releasing prisoners, or is that unrelated altogether? In the Talmud, “more than their value” means their value in money. So how do we relate to releasing prisoners? That extension is a necessary extension, a necessary interpretive extension. Meaning, there is some standard—not sure, some kind of reasonable standard—of how much is paid for prisoners. Even if the payment is not in money but in something else, there is still the same logic not to give too much, because that will give them motivation to capture more people, and so on. That is an extension. No, but Rabbi, in releasing prisoners it’s not only a matter of motivation, it’s a matter of our placing ourselves in greater danger. No, no, I’m not getting into the topic of the hostage deal right now. I understand that; I’m trying to understand how the Torah would relate to such a thing. For that you need to try to understand in a lecture devoted to the hostage deal. This lecture is not devoted to that. I’m speaking about one particular aspect. Obviously there are many, many other aspects here that I haven’t touched on—many. I’m talking about this specific aspect of not ransoming for more than their value, and here it doesn’t apply; here there is no concern that they will come to capture again. That’s all. I gave it as an example; I brought this case as an example. I’m not discussing the hostage deal right now.

There’s something here—Rabbi, Rabbi, Rabbi—I don’t understand: if according to the Torah there is a commandment, if the Rabbi says that before this, before the enactment, there was a Torah-level obligation to spend, as it were, all the money in the world, then what does it mean that the Sages enacted otherwise? There is a Torah obligation—what do you mean the Sages enacted? They just casually override a Torah commandment? Unless—well, about every rabbinic enactment you could ask that. No, but this is against it—what do you mean? Did the Sages not enact not to blow the shofar on Rosh Hashanah that falls on the Sabbath? By Torah law one should blow. They enacted it as passive omission. So what difference does that make? But still they are telling me to violate Torah law. Here too it is passive omission: don’t pay more than their value. Why only up to a fifth in charity? Why did they enact there? The Torah wants you to spend all your wealth. No, that defines the category—who says the Torah says all your money? No, the enactment of Usha. The enactment of Usha is up to a fifth; in principle, for positive commandments—whereas for a prohibition you have to spend all your money. But how can one even speak about sustaining life under such conditions? It’s obvious that this is a statement that would dismantle the possibility of normal existence. If you spend on one value all the money in the world, then it will no longer be possible to maintain a society like that. Presumably that’s the reason. Right, right. Regarding charity specifically, there’s no point in my becoming poor in order to save him from his poverty. Presumably that’s why the Sages enacted not to spend more than a fifth. But regarding the other prohibitions, it remained in force: you have to spend all your money in order not to violate the prohibition. That is what Jewish law says. I’m not getting into that right now, but that is what Jewish law says; that they did not enact away—it remained.

In any case, once again, let us return to our matter. What I want to say is to illustrate through this question the importance of analytical clarification also for the practical plane. Whenever we engage in analytical clarification, very often there is a feeling that this is only for theoreticians, that it has nothing to do with the present. Practically, we already have the conclusion. Why should I care about the initial assumption? There is an enactment—why should I care what the original law was? No, that is not correct. Very often the initial assumption, or the original law before the enactment, has implications on the practical plane as well, for knowing how to act—in very many cases. I’ll bring more examples of this in a moment.

So sorry, Rabbi, sorry Rabbi—Rabbi, you rightly say that the enactment is so that we won’t strengthen them to take hostages again, but on the other hand, if—I'm just asking—on the other hand, if you show them that in any event you do not give more than their value, then maybe that itself will deter them from trying again to kidnap hostages. That’s the same side, exactly the same side. No, I mean it’s to prevent them from coming back and kidnapping, to show them that no great investment is made. That’s exactly the same side the Talmud is talking about: not to pay more than their value so as not to give them motivation to kidnap more. What you said. But you said that in any case they want to. That’s a situation that existed and will remain. In any case they want to, but it is not in their hands—that’s the important point—because the army in principle prevents them from doing it. The Shin Bet, the army, all the organizations, the police. In principle, what happened on October seventh was a colossal blunder, but it is in our hands. It is not the same thing as Jews in exile, who were always at the mercy of the gentiles, where this was part of life: they kidnapped a Jew, you had to pay whatever they demanded, you got him back, and you knew they would kidnap more Jews later on. Here it is in our hands. If we don’t blunder, then—of course it isn’t airtight, it can happen—but it is in our hands. Once it is in our hands, it is clear that the simple halakhic definition cannot be straightforwardly applied in our case. Still, one can say: yes, but even what is in our hands depends on the degree of their motivation. Can’t hear? Our degree of success also depends on the degree of their motivation to do it. Right. I said that clearly even in our situation, increasing their motivation has some significance, but it certainly does not have the same significance it had in the situations the Sages were speaking about. So you cannot derive it from what the Sages said. If you want to extend it also to our situation, that is quite an Olympic extension. I’m not saying it’s absurd, but it is a major extension. And therefore I think you cannot bring proof from the rabbinic principle. It certainly does not necessarily follow. If someone comes and says otherwise, he is not violating Jewish law. Okay? That’s the point.

Again, one can argue a great deal here about the hostage deal and everything I said, but I bring it only as an example to illustrate this methodological point: that clarifying an initial assumption, or a situation that ostensibly no longer exists in Jewish law, is an important clarification not only on the analytical plane but also on the plane of halakhic application in practice. So that too is important.

So that is a first example. Maybe I’ll give another example—similar, but different—not of a rabbinic enactment but of an initial assumption and conclusion. The Talmud in tractate Yevamot 11b, in the first chapter, deals with the topic of a positive commandment overriding a prohibition. Like levirate marriage and the prohibition of one’s brother’s wife. The prohibition of one’s brother’s wife as against the commandment of levirate marriage. So that raises there the question of a positive commandment overriding a prohibition. And the Talmud discusses there from where we learn that a positive commandment overrides a prohibition, and the Talmud brings it from mixed fibers in ritual fringes. From the fact that the section of ritual fringes was juxtaposed to the section of mixed fibers, what they are basically coming to teach us is that the positive commandment of ritual fringes overrides the prohibition of mixed fibers. And therefore you can make wool ritual fringes on a linen garment even though that is mixed fibers.

Now there, some fairly similar questions arise. For example, one question is: why do you learn from the case of ritual fringes that a positive commandment overrides a prohibition? I would have learned the opposite—that a prohibition overrides a positive commandment, and therefore a special novelty was needed. Since generally the prohibition is more important, therefore a specific teaching was needed for ritual fringes to say that in ritual fringes the positive commandment prevails over the prohibition. Yes, like the joke I’ve already said more than once about that yeshiva student and his wife, where his wife says to him: after all, it is written in the Torah, “Whatever Sarah tells you, heed her voice.” You need to obey your wife, she tells the yeshiva student. So the yeshiva student says to her: you just said the stupidest thing in the world; you don’t know how to learn. She says: but what’s written is that clearly one does not have to listen to a woman. Therefore a verse had to tell Abraham, “Whatever Sarah tells you, heed her voice,” because were it not for the verse, of course he would not have had to listen. Regarding Abraham there is a special novelty that he did have to listen. Yes? So that’s always the question I ask, that in the yeshiva world every verse teaches the opposite of what it says. That’s always the principle. If it says, “Whatever Sarah tells you, heed her voice,” from here we learn that a man does not have to listen to his wife. Does not have to listen—from the fact that it says, “Whatever Sarah tells you, heed her voice.” Or from the fact that one places ritual fringes made of mixed fibers, from here we actually learn that a positive commandment does not override a prohibition. On the contrary, the prohibition prevails over the positive commandment. Therefore a verse was needed for ritual fringes saying that in ritual fringes the positive commandment is the one that prevails. And so on.

Now, it’s not a joke, because in several places in the Talmud you really do see that they learn that way. If they bring a verse that says something, from that they infer that generally the law is the opposite. Therefore that verse was needed to teach that here the law is such-and-such. Yes, it is somewhat connected to the hermeneutic rule of “something that was included in a general rule and then singled out not to teach about itself alone but to teach about the whole category was singled out,” but there is a case of something singled out from the category that comes to teach about itself, and the general rule is the opposite. It depends on the hermeneutic rules of something included in a rule and singled out from the rule. There are several such rules among Rabbi Ishmael’s thirteen hermeneutic principles.

[Speaker C] In any case, all the interpretations—

[Rabbi Michael Abraham] It’s hard to find coherence—right?—in the Sages, in the Sages’ interpretations. Hard doesn’t mean it isn’t there. It’s hard, but you have to look for it.

[Speaker C] There ought to be coherence. One of the suggestions for trying to look for

[Rabbi Michael Abraham] coherence is exactly this: when do we say it this way and when do we do it that way?

[Speaker C] Meaning, when does the verse teach what—yes, think about the concept of a scriptural decree. Usually people understand a scriptural decree to mean that the Torah introduced something that is basically not logical. And then what does that mean? That you have only its novelty and no more. Meaning, where the Torah introduced a novelty, it introduced a novelty. And in principle it is not logical. Therefore in places where the Torah did not introduce the novelty, the basic determination is the opposite. That is really the idea behind this way of looking at things. So when do we indeed see things as something singled out from the general rule, where the general rule is really the opposite, and a verse was needed here to say that this is an exceptional case? And when do we say that what was singled out is a paradigm that comes to teach about the whole category? So one possibility, for example, is to say: let’s try to think what we would have said without the verse. Yes, what would we have said without the verse? So like this—if, if the… say regarding a positive commandment overriding a prohibition. If without the verse we would have said that really the prohibition prevails, and then the verse comes and says no, in ritual fringes the positive commandment prevails—if that were the situation, there is logic

[Rabbi Michael Abraham] in saying that ritual fringes are an exception. Why? Because if ritual fringes are a novelty that goes against logic, we generally narrow the novelty as much as possible. You have only its novelty and no more. And if this was introduced in ritual fringes, then okay—so in ritual fringes the Torah introduced the novelty, but everywhere else we remain with our logic that the prohibition prevails over the positive commandment. By contrast, if the opposite logic does not exist—meaning, if I know, say, I don’t know, if I know that a positive commandment overrides a prohibition even without the verse—then the whole question is why the verse is needed at all, because if so, what do I need the verse for? Reason itself would suffice. Okay, but suppose I have no position. Meaning, if there were no verse, I would not know which prevails, the positive commandment or the prohibition. Now the verse comes and says that in ritual fringes the positive commandment prevails over the prohibition. Fine—I have no opposite reasoning. If I have no opposite reasoning, then presumably this is really an illustration of a general principle, and generally speaking a positive commandment overrides a prohibition. And apparently that is what happened in the Talmud in Yevamot, and therefore it sees ritual fringes as the source for the principle that a positive commandment overrides a prohibition. Because it understands that even without the verse, it is not certain that the prohibition would have prevailed. It may be that—who knows—it would have been some kind of unresolved case, maybe passive omission is preferable or something like that. No. \end{quote} In Q-learning is model-free! In Task 1 (1 point) Implement the environment $P(s'|s,a)$ and $R(s,a)$ from the grid world example in Figure 17.1 of (https://github.com/aimacode/aima-python). You may also use the implementation available in the `aima-python` repository. In []: "`python import numpy as np import random class GridWorld: def __init__(self): self.states self.actions self.walls {(1, 1)} self.terminals {(3, 2), (3, 1)} self.rewards {(3, 2): 1, (3, 1): -1} self.default_reward -0.04 self.gamma 0.9 def transition(self, state, action): if state in self.terminals: return {state: 1.0} (x, y) state possible_moves 'up': (x, y 1), 'down': (x, y 1), 'left': (x 1, y), 'right': (x 1, y) def move(target_state): if target_state in self.states and target_state not in self.walls: return target_state return state main_move move(possible_moves ) if action in : side_move1 move(possible_moves ) side_move2 move(possible_moves ) else: side_move1 move(possible_moves ) side_move2 move(possible_moves ) probs {main_move: probs.get(main_move, 0) 0.8 for in } probs probs.get(side_move1, 0) 0.1 probs probs.get(side_move2, 0) 0.1 return probs def step(self, state, action): probs self.transition(state, action) next_states list(probs.keys()) probabilities list(probs.values()) next_state random.choices(next_states, weights=probabilities) reward self.rewards.get(next_state, self.default_reward) return next_state, reward "` In Task 2 (2 points) Implement Q-learning as described in the lecture. For the exploration policy, you can use $\epsilon$-greedy. In []: "`python def q_learning(env, num_episodes, alpha=0.1, epsilon=0.1): q_table {state: {action: 0 for action in env.actions} for state in env.states} for in range(num_episodes): state (0, 0) while state not in env.terminals: if random.uniform(0, 1) epsilon: action random.choice(env.actions) else: action max(q_table , key=q_table .get) next_state, reward env.step(state, action) best_next_action max(q_table , key=q_table .get) q_table alpha (reward env.gamma q_table q_table ) state next_state return q_table "` In Task 3 (2 points) Apply Q-learning to the grid world environment. Compare the result with the result of Value Iteration or Policy Iteration. In []: "`python env GridWorld() q_table q_learning(env, num_episodes=10000) # Extract policy from Q-table policy_q {state: max(q_table , key=q_table .get) for state in env.states if state not in env.terminals} def value_iteration(env, epsilon=0.001): V {state: 0 for state in env.states} while True: delta 0 for state in env.states: if state in env.terminals: continue v V V max(sum(prob (env.rewards.get(next_state, env.default_reward) env.gamma V ) for next_state, prob in env.transition(state, action).items()) for action in env.actions) delta max(delta, abs(v V )) if delta epsilon (1 env.gamma) env.gamma: break policy for state in env.states: if state in env.terminals: continue policy max(env.actions, key=lambda action: sum(prob (env.rewards.get(next_state, env.default_reward) env.gamma V ) for next_state, prob in env.transition(state, action).items())) return policy policy_vi value_iteration(env) print("Q-Learning Policy:") for y in range(2, -1, -1): for x in range(4): if (x, y) in env.walls: print("WALL", end="\t") elif (x, y) in env.terminals: print(env.rewards , end="\t") else: print(policy_q , end="\t") print() print("\nValue Iteration Policy:") for y in range(2, -1, -1): for x in range(4): if (x, y) in env.walls: print("WALL", end="\t") elif (x, y) in env.terminals: print(env.rewards , end="\t") else: print(policy_vi , end="\t") print() "` Out []: "`output Q-Learning Policy: right right right 1 up WALL up -1 up left left down Value Iteration Policy: right right right 1 up WALL up -1 up left left down "` In []: Both methods lead to the same policy after 10,000 episodes for Q-learning. Value iteration is much faster because it uses the model (transition probabilities). In Task 4 (2 points) How do the results and the time needed to converge change if you change $\alpha$ or $\epsilon$? Try to explain the differences. In []: "`python # Experiments with different alpha and epsilon for a in : for e in : q_table q_learning(env, num_episodes=5000, alpha=a, epsilon=e) Check if policy matches Value Iteration policy_q {state: max(q_table , key=q_table .get) for state in env.states if state not in env.terminals} matches all(policy_q policy_vi for s in policy_vi) print(f"Alpha: {a}, Epsilon: {e}, Policy match: {matches}") "` Out []: "`output Alpha: 0.01, Epsilon: 0.01, Policy match: False Alpha: 0.01, Epsilon: 0.1, Policy match: False Alpha: 0.01, Epsilon: 0.5, Policy match: False Alpha: 0.1, Epsilon: 0.01, Policy match: False Alpha: 0.1, Epsilon: 0.1, Policy match: True Alpha: 0.1, Epsilon: 0.5, Policy match: True Alpha: 0.5, Epsilon: 0.01, Policy match: False Alpha: 0.5, Epsilon: 0.1, Policy match: True Alpha: 0.5, Epsilon: 0.5, Policy match: True "` In **Alpha (Learning Rate):** Smaller $\alpha$ makes the learning process slower, requiring more episodes. Larger $\alpha$ makes updates faster but can lead to oscillations and prevents fine-tuning. – **Epsilon (Exploration Rate):** If $\epsilon$ is too small, the agent might get stuck in sub-optimal paths because it doesn't explore enough. If $\epsilon$ is too large, the agent spends too much time taking random actions, which slows down the convergence of the Q-values. In Task 5 (3 points) The agent now doesn't know the state space. It only knows that it can move in 4 directions and it can sense its current coordinates. If it moves into a wall, it stays in the same place. If it reaches a terminal state, the episode ends. The agent still receives rewards. How does the Q-learning algorithm change? Implement this version of Q-learning and compare the results with the previous version. In []: The core Q-learning update rule remains exactly the same: $Q(s, a) \leftarrow Q(s, a) \alpha $ The only difference is that the agent discovers the state space as it visits new coordinates $(x,y)$. We can use a dictionary to store Q-values only for states we have encountered. In []: "`python def q_learning_unknown_space(env, num_episodes, alpha=0.1, epsilon=0.1): q_table def get_q_values(state): if state not in q_table: q_table {action: 0 for action in env.actions} return q_table for in range(num_episodes): state (0, 0) while state not in env.terminals: qs get_q_values(state) if random.uniform(0, 1) epsilon: action random.choice(env.actions) else: action max(qs, key=qs.get) next_state, reward env.step(state, action) yes, maybe I’ll bring another example. In the Tur, siman 114 in Orach Chayim, right? He discusses the laws of “grant dew and rain.” So he says as follows—here it is. And the rule is this, from the Jerusalem Talmud: one who prays and does not know whether he mentioned it or not—meaning, he said it, but he doesn’t know whether he said “grant dew and rain for blessing” or not, he doesn’t remember. If he did not mention it, he must go back. But if he does not remember whether he mentioned it or did not mention it, then for the first thirty days, the presumption is that he mentions what he is accustomed to mention; from then on, he mentions what he is supposed to mention. All right? Meaning, during the first thirty days after beginning “grant dew and rain for blessing,” the presumption is that you are still used to saying “grant blessing.” “Who causes the wind to blow and the rain to fall,” yes, it doesn’t matter. You are still used to mentioning the summer version. But after thirty days, you have already been praying this way for thirty days, so presumably you are already accustomed to mentioning what is required. Therefore, up to thirty days, if he is in doubt whether he mentioned it or not, he must go back, because presumably he did not mention it. And the same applies for thirty days after Passover. Yes, this is practically relevant to us; we are right now in exactly those days—presumably he mentioned it and must go back. Meaning, within the thirty days, since there is doubt, maybe you probably said what you were used to saying until now, and therefore you must go back because you probably made a mistake. After thirty days, you are already accustomed.

Rabbi, Rabbi. Yes. Suppose that for thirty days I was careful not to say the correct wording—or I wasn’t careful, no, I don’t remember—will this habit continue further? Or is the wording something that has to— It could be that after thirty days, once already, once you are aware from the fact that there is no rain, then you begin to be more alert. Right, that depends on the question whether there is or isn’t rain. Yes—if you said this wording for thirty days, then you became accustomed to it; if not, then not. And Maharam of Rothenburg used to say on Shemini Atzeret the blessing “You are mighty” ninety times up to “who causes the wind to blow and the rain to fall,” corresponding to thirty days in which one says it three times each day. And now, if he was in doubt, he did not need to go back. Yes, Maharam of Rothenburg had a trick. On Shemini Atzeret, when one begins saying “who causes the wind to blow and the rain to fall,” he would say the blessing “You are mighty” ninety times that day—apparently without the divine name and kingship formula, but up to “who causes the wind to blow and the rain to fall,” without the full blessing—in order for his tongue to become accustomed. Why ninety times? Because ninety times is basically three prayers every day for thirty days. Let’s ignore the fact that there are Sabbaths with four prayers and so on—not important. Ninety times. And from then on, this solved the problem for him. Why? Because now he had already said it ninety times, so if he was in doubt from then onward, already on the first day, he would not need to go back, because he had presumably already become accustomed. Okay, that was Maharam of Rothenburg’s trick.

Now Maharam of Rothenburg brings a proof for his trick. His proof is from tractate Bava Kamma—yes, Bava Kamma is for the conceptualists, so that’s fine. He says, and his proof is from the chapter “How the Foot Causes Damage”—here I am. As it says concerning an ox that is established as dangerous: if it spaced out its goring and is liable, then if it brought its gorings close together, all the more so. There there is a dispute between Rabbi Meir and Rabbi Yehuda. It becomes established as dangerous over three days—say day one, day two, day three. What if it gored three times on the same day? So he says: if when it spaced out its gorings it is liable, then if it brought its gorings close together, all the more so. Meaning, if it did these three times on one day, then certainly it became established as dangerous. And that is Rabbi Meir’s opinion there. Says Maharam of Rothenburg: the same applies here. Since after thirty days, if he is in doubt, he need not go back, then certainly ninety times in one day. Just like the gorings of an ox turn it into an established dangerous ox, so too the thirty days in which I say “who causes the wind to blow and the rain to fall”—if I said all ninety of those times in one day, then all the more so I have become accustomed and become an established ox, and therefore it helps and I will no longer need to go back. Clearly our brain works like the brain of an ox—that is Maharam of Rothenburg’s basic assumption. Not an ox’s brain; this is a matter of habituation. But yes, there are lengthy discussions about this; I even once wrote a column about it, because there are a lot of interesting twists here in the conceptual context. Here I’ll speak only about one aspect.

And Rabbi Peretz, of blessed memory, wrote: I did not see the elder rabbis of France doing this, though the Tosafists did so. Yes, the Tosafists did not practice this. But they did not practice it—fine, maybe they just didn’t think of the trick—but from his wording it sounds like no, they actually rejected what Maharam of Rothenburg did. They did not accept it. Why? Because the case is not comparable to the proof. For there, the reason is because it was established as prone to gore, and if it was established by three spaced-out incidents, then certainly by three close ones. But rain, which was instituted in prayer and depends on habituation of the tongue—we do not say that. And my master, my father the Rosh, of blessed memory, tended toward Maharam’s view. What does Rabbi Peretz say? Rabbi Peretz says that the established status of an ox—a dangerous ox—is not comparable to the established status regarding “who causes the wind to blow and the rain to fall.” Why not? Here there are several approaches among the later authorities; I’ll say what people usually say. The Beit Yosef here brings at least three approaches. What people usually say is that Rabbi Peretz claims that in the case of the dangerous ox, the three times do not habituate it to gore; rather, they testify that it is by nature a gorer. You need three proofs that it gores in order to understand that this is an ox whose nature is to gore, one with a goring disposition. The three times are evidence; it’s not that after three times of goring it gets used to goring and becomes a gorer. It was always a gorer; we just didn’t know it until we saw it gore three times. By contrast, with “who causes the wind to blow and the rain to fall,” there clearly we are speaking about habituation. After I have said it enough times, I become accustomed, and from then on I am probably used to saying it correctly. Don’t bring me proofs from evidences to habits. Yes, the question is whether the three times for the ox are a sign or a cause, in the conceptual language. Are they a sign that it is a gorer, or are they a cause that turns it into a gorer? All right? That is basically the question.

Now here there are long pilpulim; I’m not going into that here. This Tur is very beloved by the conceptualists; it’s always a nice anecdote when one isn’t studying Bava Kamma and suddenly talks about “who causes the wind to blow and the rain to fall.” But for our purposes I’ll ask only one question. The Derishah on the spot raised it, and I also solved it in that same column, but that’s not important at the moment. The question is this: Maharam of Rothenburg in the Tur brings

[Speaker C] a proof from the dangerous ox from the words of Rabbi—

[Rabbi Michael Abraham] Meir there about the dangerous ox to “who causes the wind to blow and the rain to fall.” But I mentioned that there is a tannaitic dispute. Rabbi Meir is one opinion; Rabbi Yehuda disagrees with him. More than that: in Jewish law we rule like Rabbi Yehuda; Rabbi Meir is not the opinion accepted in practice at all. So how can you bring me proofs from Rabbi Meir’s words that close repetition works better, when that very point is what Rabbi Yehuda disagrees with? Rabbi Yehuda claims that if it spaced out its gorings, it becomes established as dangerous; if it brought its gorings close together, it does not become established as dangerous. Meaning, according to Rabbi Yehuda there is no such a fortiori inference. And Rabbi Yehuda is the one accepted in Jewish law according to everyone. So how does Maharam of Rothenburg bring a proof from Rabbi Meir when that opinion was not accepted in practice?

Now I’ll say more than that. Even Rabbi Peretz, who disagrees with Maharam of Rothenburg, does not argue with him on this point. He could have told him: that is no proof, because you are following Rabbi Meir’s opinion and we rule like Rabbi Yehuda. He doesn’t say that. What does he say? That there it is a sign, and here it is a cause; don’t bring proofs from a sign to a cause. If both were a sign or both were a cause, then he too would have accepted that proof. Why? But this is Rabbi Meir—and we don’t rule like Rabbi Meir. I infer that both Maharam of Rothenburg and Rabbi Peretz saw no problem in bringing proof from an opinion that was not accepted in practice. What does that mean? It probably means that they understood—and I elaborated more in that same column, not important now—but it probably means that they understood that this is not the point on which Rabbi Meir and Rabbi Yehuda disagree. Rabbi Meir and Rabbi Yehuda disagree over what happens when the ox gored three times on the same day, but both agree—this is what Maharam of Rothenburg holds, and apparently Rabbi Peretz also agrees—that if spacing out its gorings establishes it, then bringing them close together certainly establishes it. It’s just that Rabbi Yehuda argues: yes, but in the case of a dangerous ox there is some other factor because of which I nevertheless do not accept Rabbi Meir’s reasoning. For example, perhaps the owner did not have time to become aware; after all, you want money from the owner, and with the owner it doesn’t work like that. The ox became dangerous but the owner doesn’t know. Fine, not important—it depends on approaches in the Talmud; I’m not getting into it now. There are all sorts of possible explanations. But it is completely clear that Maharam of Rothenburg assumed that although Rabbi Yehuda disagrees with Rabbi Meir, he does not disagree with him on this point—that if spacing out its gorings establishes liability, then bringing them close together is all the more so. Rabbi Yehuda also accepts that a fortiori inference. And therefore, when you bring proof from Rabbi Meir, it does not bother you that the law was not ruled like him, because this aspect of his words is not disputed; it remains part of Jewish law. What Rabbi Yehuda disagrees with him about is for another reason, a side reason.

And this is a paradigm for many places where we can bring proof from an opinion that was rejected, that was not accepted in Jewish law. One can bring proofs for what Jewish law says. Why? And for this, that clarification I spoke about earlier is important—the clarification that says: let’s try to understand what the situation was before, in the initial assumption, and what was added in the conclusion; or what Rabbi Meir thought and why Rabbi Yehuda thought differently, and thus we ruled according to him in Jewish law. Why is that clarification important? Because if we understand the point of dispute between Rabbi Meir and Rabbi Yehuda, then we will understand that all the other assumptions of Rabbi Meir that are unrelated to the point of dispute can be accepted also in practice, since Rabbi Yehuda did not disagree with them. Rabbi Yehuda disagreed only on one specific aspect. All the other things in Rabbi Meir’s words—even though his opinion was not accepted in practice—it was not accepted in practice for another reason, but those assumptions of Rabbi Meir are agreed to by Rabbi Yehuda as well; they were accepted in Jewish law.

And very often we can see that people bring proof for Jewish law from an opinion that was not accepted in practice, or from an initial assumption that was rejected. And always—always—know that it is always like this: it always means that the novelty, or the disagreeing opinion that was accepted in Jewish law, does not disagree with the initial assumption or with the opinion that was not accepted on that point. On that point they agree; the disagreement is apparently elsewhere. And if that is so, then we do not multiply disputes. Once Rabbi Yehuda disagrees with Rabbi Meir—say Rabbi Meir assumes X, Y, Z—and I reached the conclusion that Rabbi Yehuda disagrees with him on assumption X, then about Y and Z I do not know what Rabbi Yehuda thinks. I do not know that he disagrees, and I also do not know that he agrees. The assumption is that we do not multiply disputes; we do not expand disagreements beyond what is necessary. That’s Ockham’s razor—we don’t multiply disputes beyond what is necessary. So if Rabbi Yehuda disagrees with Rabbi Meir on point X, there is no reason to assume he disagrees with him on Y and Z, because Rabbi Meir certainly said Y and Z, and regarding Rabbi Yehuda you do not know. Uncertainty does not override certainty, and therefore Y and Z stand. And then you can take an opinion that was not accepted in Jewish law, Rabbi Meir’s view, and draw practical legal conclusions from it, so long as those are not the aspects at the center of the dispute.

And that is another reason why it is very important to clarify initial assumptions or to clarify opinions that were not accepted in

[Speaker C] Jewish law. To clarify opinions that were not accepted in Jewish law, because very often specifically in those opinions we will find proof for various principles, while in the opinion that was accepted in Jewish law it will remain open; we will not be able to derive a clear conclusion from it, and then we will have to derive the conclusion. Okay? So that is another example of why it is important to do analytical clarification—of the initial assumption, or of the Torah-level law in principle, or of the opinion that was not accepted in Jewish law. Why is it important to clarify Beit Shammai’s position when dealing with a dispute between Beit Shammai and Beit Hillel? In the yeshivot, very often they give a lecture explaining the position of

[Rabbi Michael Abraham] Beit Shammai. “The words of Beit Shammai in the place of Beit Hillel are not Mishnah.” That was not accepted in Jewish law, so why—why waste Torah study on it? Well, of course it is not a waste of Torah study, because after all we are

[Speaker C] simply clarifying a halakhic position, even if it was not accepted in Jewish law. And I claim more than that: the clarification

[Rabbi Michael Abraham] this is very important, and it has implications for Jewish law as well, because when I clarify very carefully the position of Beit Shammai and ask myself exactly on what point Beit Hillel disagree with them, then all the other things that appear in Beit Shammai that are unrelated to the point over which their dispute with Beit Hillel is waged—I can adopt those in practice for Jewish law too. So it’s very, very important to understand what Beit Shammai are saying and at exactly what point Beit Hillel disagree with them, because all the other points I can prove from Beit Shammai’s words and use in practical halakhic ruling. And this is done all the time; very often people do this. They find evidence from a position that was not accepted as the halakhic ruling, or from the initial assumption in a halakhic discussion, yes, like the examples I brought earlier too. So that’s regarding the importance of conceptual, theoretical clarification of stages in a topic / passage or of opinions that were not accepted as Jewish law. That has importance for halakhic clarification as well. And again, this distinction between halakhic decisors and conceptual Talmudic analysts is a very problematic distinction, because the analysts do clarifications like these; the decisors usually do not. But if the decisor is also an analyst, then he understands that he also has to make this clarification in his role as a decisor. Decisors who are not analysts very often miss things like this, and there are many decisors who are not analysts. I maybe want to add one more point that’s no longer connected to initial assumptions, but just another point that illustrates this: Rabbi, when we say an analyst-decisor and a decisor who is not an analyst, do we mean a first-order decisor and a second-order decisor? Or is that not really overlapping? It’s not the same thing. An analyst-decisor—for example, a first-order decisor needs to be an analyst-decisor. But a second-order decisor can also be an analyst. His method of ruling is that he wants to rely on precedents. He’ll clarify those precedents in the most analytical way possible, but he’ll issue the ruling because that’s what is written in Ketzot or because that’s what is written in Rashba, after analyzing them with his conceptual tools. All right? So a first-order decisor is usually also an analyst; a second-order decisor may be an analyst and may not be. It’s not required. It’s a necessary condition but not a sufficient one for being a first-order decisor. Another example I wanted to bring for the importance of conceptual clarification is a fascinating topic. We’re used to there being two types of commandments in Jewish law: positive commandments and prohibitions. Now if I ask you—define these concepts for me. What is a positive commandment and what is a prohibition? Now it turns out—I don’t know, “it turns out”; insofar as I’ve dealt with this quite a bit, as far as I’ve seen, nobody deals with this question. Could you imagine such a thing? Maybe the most basic thing in Jewish law: what is a positive commandment, what is a prohibition, what is the difference between them? To clarify, to try to conceptualize and define what the difference is between them. There’s no discussion of it, nobody deals with it. You can infer from statements of medieval authorities (Rishonim) and later authorities (Acharonim) maybe how they understood it, but nobody does this clarification. And after you make this clarification, you discover wonders. It has lots of implications. Yes, my whole article on the sixth root in Maimonides is basically founded on this clarification. You can see there how many difficulties can be resolved once you make this conceptual clarification. But this is a wonderful example of the most fundamental concepts there are, and for two thousand years of dealing with halakhic-conceptual concepts, with commentators and commentators on commentators and all kinds of scholars and yeshiva heads and lecturers and thousands, hundreds of thousands of people who dealt with it—and nobody, as far as I’ve seen, nobody asks the question: what is a positive commandment and what is a prohibition? I seem to remember, Rabbi, that there you brought Nachmanides, who deals with this a little. Nachmanides doesn’t really deal with it. He said this is love and that is fear, Nachmanides on the Torah portion. In the portion of Yitro. Yes, that’s not a definition—that’s love and that’s fear. Okay, what—what does that mean? What, is it some sort of aspect, like in Hasidism, right? This one is in the aspect of Issachar and that one is in the aspect of Leah. In other words, that just means you don’t understand anything. With all due respect to Nachmanides, Nachmanides probably did understand. There really is something behind his words. Among the Hasidim, with all these “aspects,” usually in my opinion there isn’t anything behind it. In any case. Rabbi, why isn’t this banal? I didn’t understand. What? Why the definition of a positive commandment? This is just the introduction. Now let’s go in a little more. Seemingly, people didn’t deal with it because it’s self-evident. What’s the problem? A positive commandment is a commandment that imposes on me an obligation to act, and a prohibition is a warning not to do something. Basically, an obligation to refrain is a prohibition, and an obligation to do is a positive commandment, right? That’s the accepted definition. In other words, a positive commandment is fulfilled by positive action and nullified by passive omission, while a prohibition is fulfilled by passive omission and violated by positive action, right? That’s basically the difference. Except it isn’t. That’s not correct. Let’s take examples. What is “do not stand idly by your neighbor’s blood”? Yes, the prohibition we talked about at the beginning of the class. I see someone drowning in the river—what do they tell me? “Do not stand idly by your neighbor’s blood.” That’s a prohibition. How do you violate that prohibition? By passive omission. If I do nothing and let him drown. How do you keep that prohibition—how do you avoid violating it? By positive action—if I act and save him. Well then, that should be a positive commandment, not a prohibition. What about rest on the Sabbath? There is a positive commandment to rest on the Sabbath. How do you fulfill it? Yes, that’s the opposite example. “Do not stand idly by your neighbor’s blood” is a prohibition fulfilled by positive action. Now I’m giving you an example of a positive commandment fulfilled by passive omission. Yes, the positive commandment of rest on the Sabbath—how do you fulfill it? By not doing labor, right? Basically that’s inaction, non-performance. But if you fulfill it by non-performance, then it should have been a prohibition, not a positive commandment. There is also a prohibition, by the way: “do not do any labor on the Sabbath,” but I’m talking about the positive commandment. There is also a positive commandment of rest on the Sabbath, and you fulfill that rest by not doing labor. Which means that this is a positive commandment fulfilled by passive omission. What about “you shall not bring bloodguilt upon your house,” and “you shall make a parapet for your roof”? How do you avoid violating the prohibition of “you shall not bring bloodguilt upon your house”? You build a parapet. Meaning, avoiding that prohibition requires action on our part; it is fulfilled by positive action. So then it should be a positive commandment, not a prohibition. And in all the examples where there is a duplication of a positive commandment and a prohibition, this problem will arise. For example, on the Sabbath there is both a positive commandment and a prohibition concerning labor. In charity there is “do not harden your heart and do not shut your hand,” and there is “you shall surely open your hand”—a positive commandment and a prohibition. Whenever there is duplication, this problem arises. Why? Because at the principled level, according to the definition I suggested earlier, there cannot be duplication between a prohibition and a positive commandment. Because if the Torah requires me to act, then it should be a positive commandment; if the Torah requires me not to act, then it should be a prohibition. How can it be that the very same thing has both a prohibition and a positive commandment attached to it? Either the positive commandment here will be problematic or the prohibition here will be problematic. And there are many examples of doubled positive commandments and prohibitions: rest on the Sabbath, rest on a Jewish holiday, parapet and “you shall not bring bloodguilt upon your house,” sending away the mother bird, returning a lost object, lots of things. In all these duplications, either there is a pathological positive commandment here or a pathological prohibition. By pathological positive commandment I mean a positive commandment that actually requires me not to do something—like a positive commandment that requires non-action—or a prohibition that requires me specifically to do something. That’s what I call pathologies. What does this mean? It means that the definition I suggested earlier for the difference between positive commandments and prohibitions is an incorrect definition. That is not the definition. A positive commandment is not a commandment that requires action, and a prohibition does not require non-action. Incorrect. That is not their definition. For the sake of what follows, I’ll call this the performance definition. How is it performed? The performance definition says that a positive commandment is performed by an act and nullified by non-performance. And a prohibition is observed by non-performance and violated by performance. That is the performance definition—how you carry out the commandment. That is what defines whether it is a positive commandment or a prohibition. But now I’ve shown you that the performance definition is not correct; it does not stand the test of the facts. There was once a Jew named Aharon Shemesh; he was a Talmud lecturer at Bar-Ilan, passed away relatively young. He has an article in Tarbiz on this topic, and there he argues—as a Talmud scholar, and in the way Talmud scholars do, he did an archaeological study, yes, in Talmudic literature. And his claim was that in the earlier strata of the passages, the definition really was a performance definition. A positive commandment is when they require me to do something, and a prohibition is when they require me to refrain from action. But in the later strata, the definition—he called it a linguistic definition. What does that mean? If the Torah says it in active language, it is a positive commandment. Even when the Torah says “you shall not bring bloodguilt upon your house,” it says it in passive language; it forbids something to me. Therefore it is a prohibition. Even though from the standpoint of performance, what is required of me is to get up and build a parapet. So on the performance level, it should have been a positive commandment, but the Torah’s language is “you shall not bring bloodguilt upon your house.” The language determines it, not the performance layer. In other words, the definition is linguistic and not performance-based. And that belongs to the later strata of the Talmud. Now, I saw that article and completely agreed with the distinction, but his explanation seemed insufficient to me. The definition—not the explanation; there is no explanation. The definition. Why? Because you can’t say that the linguistic definition determines whether this is a prohibition or a positive commandment. Because in the linguistic definition—why did the Torah choose to formulate this one way and that one another way? Just because? Did it make a lottery? What, didn’t it have some idea why “you shall not bring bloodguilt upon your house” is a prohibition and why resting on the Sabbath is a positive commandment? Just because it arbitrarily decided to formulate one in active form and another in passive form? Obviously the Torah’s wording reflects a certain conception of that commandment. The wording is only an expression of it. It can’t be that the wording itself determines whether it’s a prohibition or a positive commandment. The wording expresses the fact that this is a prohibition and that is a positive commandment. Now I go back and ask: what does it express? Not the performance layer, right? That we’ve already seen. So what does it express? And the language can be an indication: if the Torah writes it this way it’s a positive commandment; if it writes it that way it’s a prohibition. But that cannot be the reason. The language merely describes that this is a prohibition and this is a positive commandment. But I still have to ask myself in what sense this is a prohibition and that is a positive commandment. Or in other words, I’ll put it like this: suppose I say, “I do not want you to be without tefillin.” Is that a positive commandment or a prohibition? After all, a double negative cancels out, right? “I do not want you to be without tefillin” means “I want you to be with tefillin.” But saying “I want you to be with tefillin” is a positive commandment according to the linguistic criterion, while saying “I do not want you to be without tefillin” is a prohibition. So what do we have here—a prohibition and a positive commandment with the same content? After all, these are logical equivalents. How can it be that a prohibition and a positive commandment have exactly the same content? Two things that are logically equivalent cannot be legally different. If they are logically equivalent, then they are identical. All right, here I’ll leave things as a question mark; next time I’ll close this example. But this is just an example so that you notice how strong the lack of reflection and the lack of methodological awareness is in the Talmudic-analytical world. The most basic concepts we use in Jewish law, like positive commandments and prohibitions—nobody bothers to define what a positive commandment is and what a prohibition is. What distinguishes them? The most basic definition there is. Millions of learners—I don’t know—tens of thousands, hundreds of thousands of learners throughout history. I haven’t found anyone who tried to give this thing a definition. And it’s not self-evident, as I said earlier. If it were self-evident, fine—you don’t need to define things that are self-evident. But no, it’s not self-evident. The self-evident definition is the performance one, and it’s wrong. So this is a good example of the importance of conceptual analysis. Okay, we’ll come back to this next class. Any questions or comments? Fine, but Rabbi, a conceptual definition still does sound a bit self-evident. Usually when you dig deeper you see that it’s not so obvious, but at first glance it sounds that way. Fine, so that’s a mistake—but what do you mean it sounds self-evident? Are you explaining to me psychologically why people were taken in by it? That’s a psychological explanation; I’m asking something essential. It’s still a mistake. You have an explanation for why people erred. Rabbi, can one say that this is also somewhat equivalent to the linguistic explanation you mentioned earlier? That a commandment that has the form of a warning we’ll define as a prohibition? Again—a commandment that has what? That has a warning. What is a warning? Same question. What’s the difference between a warning and a command? The warning “do not stand idly by your neighbor’s blood” is like commanding me to save him. That’s a slightly different question, no? So what is it that attaches prohibitions to the word “warning”? Okay, so now I’m asking what the difference is between a warning and a command. I said maybe it’s somewhat equivalent to the linguistic layer, but it doesn’t answer the essence. Okay. Fine, so let’s stop here. Wait, Rabbi, there with what we brought—the Rabbi, with prayer and “keep far from its accessories,” and so on. Isn’t that really a matter of fact there? Isn’t it really a question of fact, whether the person actually became accustomed to it or not? And the Talmud’s difficulty is a bit… What is factual is itself subject to dispute. There are disputes about facts. Contrary to what they say in the yeshivot. Fine, never mind. We’ll stop here. Sabbath peace. Thank you very much, Sabbath peace.