Self-Reference – Lesson 11

Table of Contents

• Two types of self-reference and the connection between them
• Halakhic applications: moving from a person’s self-reference to a statement’s self-reference
• “Do not deviate” as an anti-paradox and the authority of the Sages
• The distinction between paradox and anti-paradox, with logical illustrations
• Institutional considerations: the need for interpretive authority and the example of the High Court of Justice
• Nachmanides and Maimonides: why a verse is needed and not just simple reasoning
• “Do not deviate” as clarification of the matter or as an additional prohibition, and the implications for meat and milk
• Minchat Chinukh: an ill person on the Sabbath, meat and milk versus pork, and two assumptions
• “These and those are the words of the living God”: pluralism versus monism and Rabbi Yosef Karo
• An attack on pluralism through self-reference and proof by contradiction
• The set paradox, axiomatic set theory, and Russell’s theory of types
• Removable discontinuity: making an exception in order to neutralize a loop
• Bava Metzia 30b: worker/slave, “it is satisfactory to him,” and the answers of Tosafot and the Ran
• A note from the Jerusalem Talmud and the continuation of the series

Summary

General Overview

At the beginning of the series, two kinds of self-reference are presented: the self-reference of statements, such as the liar paradox and Russell’s theory of types, and a person’s self-reference, which is not necessarily paradoxical but does require regulation. The claim is that there is a connection between them. After halakhic applications of the second type, the discussion moves to halakhic applications of a statement’s self-reference and to halakhic paradoxes, with the example of lo tasur—“do not deviate”—as a model of a logical loop that looks like an anti-paradox. Later, the statement these and those are the words of the living God is examined in a pluralist versus monist reading, and an attack on pluralism is proposed by applying the position to itself, alongside the possibility of a “removable discontinuity” that excludes a problematic case. Finally, the topic of niḥa lei—“it is satisfactory to him”—in the case of the red heifer / the heifer whose neck is broken, from Bava Metzia along with Tosafot and the Ran, is presented as another halakhic-logical model in which the rule collides with itself.

Two Types of Self-Reference and the Connection Between Them

At the outset there are two types of self-reference: statements that refer to themselves in paradoxes like the liar paradox, and a person referring to himself. In Russell’s theory of types, attempts are presented to solve paradoxes that arise from the possibility of a statement referring to itself. A person’s self-reference is not supposed to create a logical paradox, only specific definitional problems, but it is argued that there is a certain connection between the two types.

Halakhic Applications: Moving from a Person’s Self-Reference to a Statement’s Self-Reference

In the halakhic applications discussed up to this point, the focus was on self-reference of the second kind, such as a person encircling himself, and halakhic topics in which a person relates to himself. Now the focus shifts to a statement referring to itself and to the possibility of “halakhic paradoxes” or logical loops within normative structures. The move begins with examples that seem to sit on the boundary between the two types and are then reclassified according to their essential structure.

“Do Not Deviate” as an Anti-Paradox and the Authority of the Sages

In the verse, “Do not deviate from all that they instruct you,” a loop is claimed: the Sages interpret the verse as the basis of their authority, and the verse supposedly obligates accepting their interpretation, including their interpretation of the verse itself. The claim is classified as a statement referring to itself, because the essential question is whether the verse itself grants authority, not merely that the Sages, as agents, refer to themselves. The structure is defined as an anti-paradox because both positions remain consistent: not accepting the Sages’ interpretation of lo tasur leads to no general obligation to accept their interpretation, while accepting the interpretation leads to a general obligation, and in both cases there is no internal contradiction.

The Distinction Between Paradox and Anti-Paradox, with Logical Illustrations

A paradox is defined as a loop that does not allow a truth value to be assigned to a statement—for example, statement A: “statement A is false,” which leads to the result that if it is true, it is false, and if it is false, it is true. An anti-paradox is defined as a statement to which both truth and falsehood can be assigned consistently, such as statement B: “statement B is true,” where each of the basic assumptions—true or false—does not generate a contradiction. The example of lo tasur is presented as parallel to an anti-paradox, and in an anti-paradox one can bring in external considerations to choose between two consistent possibilities, something that is impossible in a paradox.

Institutional Considerations: the Need for Interpretive Authority and the Example of the High Court of Justice

A general line of reasoning is presented that a normative system has difficulty functioning without some body that has the authority to issue binding interpretations. The example of the High Court of Justice is brought as a parallel: one can appeal to an expanded panel, but in the end there is no body above the broadest panel. And if we say that a binding precedent is established by the authority of the High Court itself, we get an anti-paradoxical structure in which one may reject that determination and thereby not become bound by it, or accept it and become bound by it, and both routes are consistent. The decision in favor of obligation is presented as practical-institutional logic, not as a logical necessity.

Nachmanides and Maimonides: Why a Verse Is Needed and Not Just Simple Reasoning

A question is raised about Nachmanides’ view, according to which lo tasur teaches that the Sages can interpret—and if so, this seems like simple reasoning, so why is a verse needed? It is said that according to Maimonides as well, the verse teaches authority to interpret, although for Maimonides there is also the added point that they can legislate. The answer is that turning the reasoning into a verse creates a practical difference, such as the possibility of punishment, because “one does not punish unless there was prior warning,” and the warning has to be written. Therefore the verse of lo tasur is especially needed in the context of the rebellious elder.

“Do Not Deviate” as Clarification of the Matter or as an Additional Prohibition, and the Implications for Meat and Milk

An analysis is presented of whether violating the Sages’ interpretation creates only disobedience to lo tasur, or whether the act itself receives the status of violating the prohibition derived from the verse as interpreted. The claim is that when the verse obligates the Sages’ interpretation, then eating meat and milk is not only a violation of lo tasur, but a violation of the prohibition of meat and milk itself, because the Sages’ interpretation is “the binding interpretation.” Nachmanides’ objection to Maimonides in the first root is cited regarding poultry with milk: if lo tasur is a Torah-level prohibition, then doubt concerning poultry with milk should be treated stringently as a Torah-level doubt. The answer attributed to Maimonides is that lo tasur is not a prohibition added anew in every violation, but rather a clarification of the matter through which rabbinic laws are generated, and therefore the prohibition violated is “the prohibition of poultry with milk,” not “do not deviate.”

Minchat Chinukh: an Ill Person on the Sabbath, Meat and Milk Versus Pork, and Two Assumptions

In the case of an ill person on the Sabbath who must be fed something prohibited, the Minchat Chinukh argues that it is preferable to feed him pork rather than meat and milk, because with meat and milk one violates two prohibitions: the prohibition of meat and milk and also lo tasur. Two assumptions in his words are presented: first, that there are two separate prohibitions here, and second, that two Torah-level prohibitions are more severe than one Torah-level prohibition. In addition, a doubt is raised as to whether a prohibition learned by interpretation counts as a full Torah-level prohibition according to Maimonides, and a line of thought is suggested according to which even if meat and milk is intrinsically less severe, there could still be greater severity because of lo tasur as an explicit prohibition from a verse.

“These and Those Are the Words of the Living God”: Pluralism Versus Monism and Rabbi Yosef Karo

The Talmudic passage in Eruvin 13b is cited: a heavenly voice says, “These and those are the words of the living God, but the Jewish law follows Beit Hillel,” and it is said that there is apparently a contradiction between the two statements. On the pluralist reading, both Beit Shammai and Beit Hillel are “right,” and the halakhic ruling is presented as a functional or educational decision rather than a determination of truth, with the Talmud’s reason—that Beit Hillel were “gentle and humble, and they would mention the words of Beit Shammai before their own”—fitting a model of educational reward. Rabbi Yosef Karo, in Klalei HaGemara, offers a monist reading: the ruling follows Beit Hillel because they are closer to the truth, since one who first considers his opponent’s arguments is more likely to arrive at the truth, and therefore the reasoning is epistemic, not a behavioral prize. According to the monist reading, “the words of the living God” means the legitimacy of the arguments, not final truth—similar to the explanation that there are 150 reasons to declare the creeping thing pure and 150 reasons to declare it impure, but the balance tips one way.

An Attack on Pluralism Through Self-Reference and Proof by Contradiction

A “proof” in favor of monism is proposed by applying the pluralism/monism dispute to the statement of these and those itself: pluralism has two interpretations, and if the pluralist behaves pluralistically even toward the dispute about pluralism, inconsistency results, because monism and pluralism cannot both be correct together. It is argued that the motivation for pluralism is trust that the Sages do not err, and therefore excluding the dispute about these and those forces one to admit that the Sages can err, which undermines the basis for pluralism. This move is presented as parallel to the mathematical use of self-reference paradoxes as a “proof by contradiction” and as a tool that forces one to give up the assumption that allows the paradoxical loop.

The Set Paradox, Axiomatic Set Theory, and Russell’s Theory of Types

The set-theoretic paradox of “the set of all sets that are not members of themselves” is presented, leading to a contradiction whether it is a member of itself or not. The paradoxes of naive set theory are presented as the reason for the move to axiomatic set theory, which builds the world from the empty set upward in order to guarantee consistency. Russell is presented as one who concluded from similar paradoxes that language must not allow self-reference, and the speaker argues that this is an unnecessary overreaction, because there are cases of self-reference that are not paradoxical, and so there is no justification for “throwing them all out.”

Removable Discontinuity: Making an Exception in Order to Neutralize a Loop

A logical possibility is presented for solving a loop by excluding one specific point, similar to correcting a function at isolated points in order to remove a discontinuity. The proposal to say, “I am a pluralist in every dispute except the dispute about pluralism,” is defined as logically consistent, but it is argued against as an ad hoc solution that is not plausible, because it runs contrary to the motivation that gives rise to pluralism. The distinction between “logically possible” and “plausible” is preserved as a guiding line in examining solutions.

Bava Metzia 30b: Worker/Slave, “It Is Satisfactory to Him,” and the Answers of Tosafot and the Ran

In Bava Metzia 30b, Rav Pappa is cited regarding the written form and the read form—“slave / worker”—in the case of the heifer whose neck is broken: the written form and the read form produce an intermediate method in which an act done incidentally invalidates only if niḥa lei, that is, if the owner is pleased with what was done. Tosafot asks from the case of “a male mounted her,” since a red heifer is very valuable and the owner certainly does not want to lose it for the sake of a small gain. So the condition of niḥa lei seems impossible, because once the law invalidates it, it will always turn out that he is not pleased. Tosafot answers: “if she had been valid, he would have been pleased, and therefore one may not validate her,” and an explanation is brought that the displeasure generated by the law itself is not counted; satisfaction is measured according to what would have been desirable were it not for the law, as a model of excluding the point that creates the loop. The Ran in Shittah Mekubetzet brings a similar answer and adds another move: if we validate it, then certainly he is pleased and therefore it should be invalidated; and if we invalidate it, then he is not pleased and therefore it should be validated. In this way an infinite loop is obtained that illustrates internal self-reference, and the question remains why the Ran sees this as an answer rather than merely creating a situation of irresolvable doubt.

A Note from the Jerusalem Talmud and the Continuation of the Series

It is said that the Jerusalem Talmud gives another reason for the Jewish law following Beit Hillel: they would hear Beit Shammai and then withdraw from their own position, and this is aligned with the reason in the Babylonian Talmud as a deepening of the weighing of the opposing argument and even an admission of error in some cases. In conclusion, it is said that next time they will return to the Ran’s question and wrap up the series, and it ends with “Shabbat shalom.”

Okay, at the beginning of the series I spoke about two kinds of self-reference, and I discussed a bit whether there is some connection between them. The first kind is self-reference of claims to themselves, the various paradoxes like the liar paradox and the like. We spoke about Russell’s theory of types and attempts to solve the issue. And the second kind is self-reference in the sense of a person relating to himself and not a claim relating to itself, which on the face of it does not necessarily lead to problems, but we saw that even so it is something that requires recursion in some sense, and sometimes it can indeed create problems. We pointed out that there is some connection between these two kinds of self-reference. In the last few sessions I began dealing with halakhic applications of self-reference, and what I did until now was halakhic applications of self-reference of the second kind, a person relating to himself. And about that I spoke—someone encircling himself and so on, the whole expression, all the halakhic topics that discuss a person’s self-reference. What I want to deal with now is the second kind of self-reference, which is a claim relating to itself, a kind of halakhic paradoxes. I think I spoke about paradox and anti-paradox really at the very beginning of the series, and there I think I brought a few halakhic examples, if I remember correctly. I’ll start with a few examples that we can discuss a bit in terms of whether they belong to the first type or the second type. For example, once someone asked me on the website about “do not deviate.” The verse in the Torah, “do not deviate from all that they instruct you,” which is basically the basis for the authority of the Sages, or for the obligation to obey the voice of the Sages. And they said to me that the ones who interpreted the verse in that way were the Sages, and therefore the question is whether I am obligated to adopt this interpretation of the verse that grants authority to the interpretations of the Sages. Because the verse itself does not necessarily say that, and it was the Sages who interpreted the verse in a way that says I must accept their interpretations. So the question is whether I can really interpret this verse differently from the Sages, and then the verse itself would also not say that I have to adopt the interpretation of the Sages, and that remains consistent. In other words, I can basically interpret it differently and not be bound by the interpretation of the Sages. There is some kind of self-reference here, and there is a certain feeling that this stands somewhere between the two types we spoke about. Is this a claim relating to itself, or a person relating to himself? There is some strange combination of these two things here, because seemingly this is a person relating to himself. That is, the Sages interpret the verse in a way that grants themselves authority to interpret. So in a certain sense the Sages are referring to themselves; that is self-reference of the second kind. But I think that isn’t really right. In the essential sense this is self-reference of the type of a claim referring to itself, not a person referring to himself. Because in the end, what matters in my view is whether the verse grants authority to the Sages. The fact that the Sages interpreted the verse means that the verse tells me that there is authority to the interpretations of the Sages, and one of the interpretations to which it refers is the interpretation of the verse “do not deviate” itself. And therefore I think we have here a claim referring to itself and not a person referring to himself. And this belongs to the type I am dealing with now. In a certain sense, therefore—or let me put it differently—self-reference of a person to himself, on the face of it, should not lead to a paradox. A person refers to himself; there is no principled problem in that, aside from all the things I noted. In self-reference of a claim to itself, there, at least in some cases, a logical loop can arise, a paradox. And in this case of “do not deviate,” the feeling is that there really is some kind of logical loop here. In other words, there is some problematic feature here; it is not just a person referring to himself and creating perhaps some specific problems. That is, when a person refers to himself, is that considered referring to someone else, or can it be viewed as referring to someone else who just happens to be himself, or not? That is a different kind of question, but it is not a logical paradox. Here, in this context, the smell is basically the smell of a logical loop. And therefore that is another indication that we are dealing here with a claim referring to itself. The Sages interpret the verse “do not deviate” in such a way that the verse gives the Sages authority to interpret verses. And one of the things to which I apply the authority that the verse gives is the interpretation of this very verse itself. So in fact the verse refers to itself. It says that the Sages have authority to interpret me. And therefore this is of the type of a claim referring to itself, not a person referring to himself. How important is this distinction really? What? Why is this distinction important really, between reference to…? It’s an important distinction; the practical point is that there are two types, that’s all. One creates paradox, the other is not necessarily paradoxical. There are problems that need to be solved with the warning, but there is no paradox here, there is no loop when a person refers to himself. And in this case there does arise a logical loop, and that belongs to the family of paradoxical self-references. Because if I do not accept the interpretation of the Sages of this verse, then I do not need to accept the interpretations of the Sages at all, and therefore that is perfectly fine, it is consistent. And if I do accept the interpretation of the Sages of this verse, then I also have to accept the interpretations of the Sages in general, and that too remains consistent. So actually this is an anti-paradox. What? Right. If you remember, I distinguished between paradox and anti-paradox, and in fact what happens here is not a paradox but an anti-paradox. And what is the difference between them? Let me remind you that in an anti-paradox—paradox is for example… wait, I’ll share the screen for a moment. One second. I’ll share the screen for a moment. Yes, this is basically the liar paradox. Proposition A—what does proposition A say? That proposition A is false. Right? That is a kind of self-reference that creates a paradox. Now I’ll suggest a different formulation. Proposition B says that proposition B is true. So I said that this is an anti-paradox. Paradox. Why? Because paradox means some kind of logical loop that does not allow me to assign a truth value to the proposition. If the proposition is true then it is false, and if it is false then it is true, and so on and so forth. So you cannot assign any truth value to the proposition. Truth value means true or false. In proposition B that is not the problem. The problem in proposition B is that I can assign to this proposition both the value true and remain consistent, and the value false and remain consistent. Right? Because if I decide that proposition B is true, say for the sake of discussion—let us assume it is true—then what does this proposition claim? That it itself is true. Which is indeed a true claim, because it is true, so to say that it is true is a true statement. So that is consistent. But by the same token, if I were to assume that the proposition is false, then when I examine the proposition that proposition B says about itself that it is true, that turns out false, because after all it is a false proposition. So when someone says that this proposition is true, that is false. Right? Then it comes out that assuming that this proposition is false is also consistent. And therefore I called the second formulation an anti-paradox. A paradox is a proposition to which you cannot assign a truth value. A normal proposition is one to which you can assign a truth value, but only one: either it is true or it is false; it cannot be both. Proposition B can be assigned both truth values. You can say it is true and that will be consistent, and you can say it is false and that will be consistent. That is what I called an anti-paradox. Now in this example that I gave regarding “both these and those,” regarding “do not deviate,” that is basically parallel to an anti-paradox. Why? Because if the Sages tell me, interpret the verse “do not deviate” in such a way that “do not deviate” means I must adopt the interpretations of the Sages of the verses—that is how the Sages interpreted the verse “do not deviate.” So now there are two possibilities before me. I can fail to accept their interpretation of this verse, and then it comes out that I am not supposed to, not obligated to, accept the interpretations of the Sages of verses. Then it is fine that I did not accept their interpretation, because I am not obligated to accept their interpretations. So that is consistent. But by the same token I can accept their interpretation of the verse, and then it comes out that I must accept the interpretations of the Sages of verses, and that is indeed what I did also with regard to this verse. And therefore it can receive both the value false and the value true and remain consistent. And therefore this is basically parallel to an anti-paradox. Now, what is different between this and a paradox is that in this case I can say: you are right, that is true in principle, but there is logic in accepting the interpretation of the Sages of “do not deviate,” and therefore their authority to interpret. For example, the logic that says there has to be some factor that has the authority to interpret. Otherwise it would be hard to function. Just a general consideration like that, not a logical argument. Rather a general consideration saying that it is not reasonable for a normative system to function without there being some institution or factor that has authority to issue binding interpretations. Something like this I would say, for example, also in a legal system. So for instance, the question always arises: before whom can one appeal a ruling of the High Court? You can request leave to appeal before—or request a rehearing before a broader panel. If the panel was of three judges, you can request a hearing before a panel of seven judges or eleven judges. But that you request from them themselves. If you are dissatisfied with the decision of the broadest panel of the High Court, before whom will you appeal? You cannot appeal. So if I disagree with the High Court, I disagree with the High Court, but that will not help me at all. There is no way to attack a ruling of the High Court. Or in an even blunter way: I do not know, I don’t know if this is explicit law or just practice, but rulings of the High Court are binding precedent. Meaning, rulings of the High Court you have to accept. Now let us assume that the High Court itself determined this very thing. I don’t know; a lawyer is needed, I don’t know whether it was established by force of a statement of the High Court itself. And the High Court itself determines that statements of the High Court are binding, okay? So if that is indeed so, then you understand that this is completely parallel to what I discussed, to the anti-paradox I described in the legal context. Then someone can come along and say: okay, this statement of the High Court I do not accept, and therefore I also do not have to accept statements of the High Court. Because after all, accepting the statements of the High Court is itself based on an instruction of the High Court. So therefore basically I can—I have two options. I can fail to accept that instruction, and then I am not bound by the instructions of the High Court. I can accept that instruction, and then I will also be bound by the instructions of the High Court. But both ways are open, and both are consistent. But the logic, of course, says that there has to be some factor that has authority to determine a binding interpretation. And therefore I can certainly hear someone arguing that, true, both interpretations are logically consistent, but really one should adopt the second interpretation. And of course that exists only in an anti-paradox and not in a paradox. Because in an anti-paradox there really are two options, and both are consistent. You can adopt either one. So if there is some consideration that says, okay, adopt the second and not the first, that is perfectly fine; the situation is acceptable. And that consideration really says that I should adopt the second option and not the first. Regarding a paradox, of course, this is not relevant, because in a paradox I have no option at all. I cannot determine that it is true and I cannot determine that it is false; there is no truth value I can assign to it. So there some external consideration cannot come and tell me what the truth value of the verse nevertheless is. It has no truth value. But if you say that it is a simple matter of logic to accept the interpretations of the Sages of the biblical verses, then according to Nachmanides it comes out that there is no need for the verse “do not deviate” to teach this. Because the view of Nachmanides is that the verse “do not deviate” teaches that the Sages can interpret. But if you say this is simple logic that they can interpret, then seemingly there is no need for the verse. Is it also so according to Maimonides? No, according to Maimonides the verse says that the Sages can legislate, not only interpret. Fine. But according to Nachmanides—very good—but according to Nachmanides the verse teaches that the Sages can interpret. According to Maimonides too it teaches that. Yes, very good, but for Maimonides there is the added novelty that they can also legislate. You can ask why, according to Maimonides too, the verse is needed to teach me that they can interpret. According to Nachmanides, that is all there is in “do not deviate.” According to Maimonides, however, there is also that. So the question still exists according to Maimonides as well. There is a novelty in the verse regarding the ability to legislate, but Maimonides still says that this verse also teaches that they have authority to interpret. The question is why this is needed. The answer, I think, is that it is needed because after I have received this, now this thing is the result of a verse and not of mere reasoning. Like in the column “What does a verse come to teach?” What? Like in your column on the site, what is that column called? If every verse teaches the opposite. Yes, exactly. Why? How is that connected? Column 411. No, but why is it connected? It is connected because now you said that from reasoning we learn something and the verse comes to reinforce that reasoning. So like there in the column, when do we say that this is reasoning? That I explained that it is not necessarily true that a verse always comes to teach the opposite. Exactly; when there is weak reasoning, the verse turns the reasoning into a verse. Yes, right. Now once it is a verse, for example one implication is that punishment becomes possible. If this were only reasoning, then even if I say “Torah reasoning” in a certain sense, that is not enough for punishment, because one punishes only where there has first been warning. And the warning has to be written. Reasoning is not a warning. So for example, an elder who rebels, who disagrees with the interpretation of the Sages of a verse, is liable to death. And if this were only reasoning, one could not execute an elder who rebels. He would be a wrongdoer, he would be in the wrong, but you could not execute him. To execute him, it has to be a verse. Therefore, in practice the novelty of “do not deviate” in the power it gives the Sages to interpret is mainly with regard to the elder who rebels. One can find a novelty in this not only regarding the elder who rebels. Let us take an example. The Sages interpret or expound the verse “The Lord your God you shall fear” to include Torah scholars. I will leave aside for the moment Maimonides, who says that such a derivation is not Torah-level. We didn’t hear the beginning. What did you say at the beginning? We didn’t hear. I said that there may be a novelty in “do not deviate,” that it teaches that the Sages have authority to interpret not only regarding an elder who rebels, but also in a regular case. Let’s take an example. Suppose the Sages interpret “The Lord your God you shall fear” to include Torah scholars. So there is—no, not that one—“You shall not cook a kid in its mother’s milk.” The Sages interpret that there is a prohibition to eat, a prohibition to cook, and a prohibition to derive benefit. Now if the verse “do not deviate,” or if the authority to interpret were only a matter of reasoning, then the fact that the Sages interpreted that it is forbidden to eat poultry with milk—it is not written; what is written is that it is forbidden to cook. The Sages interpreted that it is forbidden to eat. If I were to eat poultry with milk, then I would be in the wrong in the sense that I am supposed to obey the Sages and I did not obey. But would I be in the wrong in the sense that I ate meat and milk—sorry, that I ate meat and milk? Is that act itself an act that is wrong? Or is only the disobedience expressed in it what is wrong? If this were only reasoning that one has to obey the Sages, then I would be in the wrong in the sense that I did not obey. But the fact that I ate meat and milk would not itself be an act that is wrong. Because after all I interpret the verse differently from the Sages, and in my view the verse does not say that it is forbidden to eat meat and milk. So I did not violate what the verse said. But once the verse itself says that one must listen to the interpretations of the Sages, this means that when I ate meat and milk, I was in the wrong also in the laws of meat and milk, not only in the laws of “do not deviate.” I violated the prohibition of meat and milk, not only “do not deviate.” Because “do not deviate” reveals that the interpretation of the Sages is the binding interpretation of the verse. So not only is it wrong to depart from their words, but what they say is the binding meaning of the verse. And once that is the case, then to eat meat and milk is in fact the prohibition of meat and milk, not only the prohibition of “do not deviate.” I’ll give you an example of what I mean. In Minchat Chinukh, he wants to argue: what happens if I have a sick person on the Sabbath whom I need to feed something prohibited? Now before me are two kinds of prohibitions—sorry, meaning, I have either meat and milk or non-kosher meat, pork. And he has to eat meat; the doctors said he has to eat meat, and I have no other meat. Either meat mixed with milk or non-kosher meat, pork. What should I feed him? What is preferable to feed him? So Minchat Chinukh argues that it is preferable to feed him pork. Why? Because if I feed him meat and milk, then he violates two prohibitions: both the prohibition of meat and milk and “do not deviate,” because it was the Sages who interpreted “You shall not cook a kid in its mother’s milk” as a prohibition to eat meat and milk. So it comes out that I violate both the prohibition of meat and milk and “do not deviate.” And that is more severe than merely eating pork, which is one Torah prohibition, but not two. There are two novelties here in Minchat Chinukh. One novelty is that indeed there are two prohibitions here, because one could have said there is only “do not deviate,” or that there is only meat and milk. Do you understand why? One could have said there is only the prohibition of “do not deviate.” After all, if I interpret the verse differently, maybe I am right; there is no guarantee that the Sages are right, only that I am obligated to obey them. There is an obligation to obey them, but that does not mean they are right. So if I interpret the verse differently, then who says I violated the prohibition of meat and milk? I claim the verse does not prohibit meat and milk. True, I have to obey them, so I violated “do not deviate.” So one could interpret it that way. One could also interpret the opposite—that the verse “do not deviate” is not an independent prohibition. It comes to tell you that the verse “You shall not cook a kid in its mother’s milk,” the binding interpretation of it, is the interpretation established by the Sages. And now the prohibition you violate is only the prohibition of meat and milk, not a prohibition of “do not deviate.” “Do not deviate” is only a disclosure, a clarification. “Do not deviate” only reveals that the interpretation of the verse is the interpretation given by the Sages. But it does not mean that now, when you violated this prohibition, you violated “do not deviate.” You did not violate “do not deviate”; you violated the prohibition of meat and milk. Because what the Sages interpreted is the binding interpretation of the verse. So now, when you ate meat and milk, you violated “You shall not cook a kid in its mother’s milk.” Ah, you interpret it differently? You interpret it incorrectly, because the binding interpretation is the interpretation of the Sages. And according to this direction, the only prohibition I violated is just the prohibition of meat and milk; there is no prohibition of “do not deviate.” “Do not deviate” is only a clarification saying that the verse—after the Sages determined it—means that it is forbidden to eat meat and milk. Why do I say this? Because for example think about the famous question on Maimonides. Maimonides says that “do not deviate” is also the basis for rabbinic prohibitions, for legislation by the Sages, regarding poultry with milk, not meat with milk. The Sages forbade eating poultry with milk, as a decree because of meat and milk, a rabbinic prohibition. Why must one obey the Sages? Because of “do not deviate,” according to Maimonides, because of “do not deviate.” So everyone asks about Maimonides: if so, then in eating poultry with milk there is a Torah prohibition? Because besides the fact that you eat poultry with milk, you also deviated from the words of the Sages, and there is a prohibition of “do not deviate,” and a doubt about poultry with milk should have to be treated strictly because it is a Torah-level doubt—Torah-level doubt goes stringently. Yes, that is the question they ask on Maimonides; Nachmanides already raises this point against Maimonides in his glosses to the first principle. What is Nachmanides assuming? According to Maimonides, the verse “do not deviate” is not itself a prohibition; the verse “do not deviate” is a clarification that tells me: know that what the Sages say is indeed prohibited; you really must obey. So when the Sages forbade eating poultry with milk—now I am speaking of their legislation and not of their interpretation—then when the Sages forbade eating poultry with milk, the verse “do not deviate” tells me that now there is a prohibition of poultry with milk. So when I eat poultry with milk, I did not violate “do not deviate.” “Do not deviate” is not a prohibition; “do not deviate” only tells me that now there is a prohibition of poultry with milk, and that is the prohibition I violated—the prohibition of poultry with milk, not the prohibition of “do not deviate.” “Do not deviate” only reveals that such a prohibition exists. Then the question on Maimonides is incorrect, because according to Maimonides it is not that I violate the prohibition of “do not deviate”; I violate the rabbinic prohibition of poultry with milk. The verse “do not deviate” only reveals that there is a rabbinic prohibition in eating poultry with milk. But it is not the case that every time I violate—every time I eat poultry with milk—I violate the rabbinic prohibition of poultry with milk and the Torah prohibition of “do not deviate.” So on the Torah level too, it is the same. When I eat meat and milk—not poultry with milk, meat and milk—then what prohibition did I violate? I violated the prohibition of meat and milk, but not “do not deviate.” “Do not deviate” only reveals that there is a prohibition of meat and milk; from that point on, the prohibition that exists here is the prohibition of meat and milk, not the prohibition of “do not deviate.” Minchat Chinukh, who says that there are two prohibitions here, assumes a third conception. When could one say that there is only “do not deviate”? One could have said there is only meat and milk. Minchat Chinukh argues that there are two prohibitions here, both “do not deviate” and meat and milk. That is Minchat Chinukh’s first assumption. The second assumption of Minchat Chinukh: two prohibitions are more severe than one, right? Not only that two prohibitions are more severe than one, but that we are dealing here with two Torah prohibitions in every respect. Meaning, the severity of each prohibition is the full severity of a Torah prohibition. Then, once there are two, it is more severe than one. But that assumption too is not simple, because for example according to Maimonides, a prohibition learned from an interpretive derivation is not at all a Torah prohibition; it is a prohibition from the words of the Sages. Then it is much more logical. Okay, so according to Minchat Chinukh’s first assumption, one can still remain with his conclusion even without the assumption that meat and milk is a full Torah prohibition. Fine, that is just a side remark. In any case, here too in “do not deviate” there is some kind of self-reference that leads me to an anti-paradox. Either I accept the interpretation of the Sages of “do not deviate,” and then I am supposed to accept the interpretations of the Sages in general, or I do not accept the interpretation of the Sages regarding “do not deviate,” and then I am also not supposed to accept the interpretations of the Sages in general, and once again I remain consistent. There is a similar case—I may have mentioned it, I no longer remember—regarding “both these and those are the words of the living God.” I think I did not mention it. In “both these and those are the words of the living God” there are several ways to interpret that statement. Maybe I’ll give some introduction. The Gemara in tractate Eruvin, on page 13, brings that Beit Shammai and Beit Hillel disagreed for years and could not decide the dispute, and then a heavenly voice came forth and said: “Both these and those are the words of the living God, and the Jewish law follows Beit Hillel.” So I discussed this in other contexts; I will not now go into the whole topic there, but that is what the heavenly voice said. Now, seemingly the two statements of the heavenly voice contradict one another. On the one hand, “both these and those are the words of the living God,” so both are right, both Beit Shammai and Beit Hillel. On the other hand, “the Jewish law follows Beit Hillel,” that means Beit Hillel are right and not Beit Shammai. So there are two ways to read this. One way to read it is the pluralist way, which says “both these and those are the words of the living God” means both these are right and those are right too, like the judge’s wife: everybody is right. According to the pluralist reading, I understand the sentence “both these and those are the words of the living God,” but the sentence “the Jewish law follows Beit Hillel” is not clear. If both are right, then in what sense does the Jewish law follow Beit Hillel? You have to say that “the Jewish law follows Beit Hillel” is not because the truth is with them, but because something has to be decided. Both are right from the standpoint of truth. But since one has to determine some agreed-upon bottom line, the heavenly voice said: act in accordance with Beit Hillel—not because the truth is with them. And indeed the Gemara there later says that the reason the Jewish law was ruled like Beit Hillel is that they were pleasant and humble, and they would state the words of Beit Shammai before their own. On the face of it, that sounds like a reward for good behavior. Yes—they behave very nicely, they are polite, they teach the words of Beit Shammai before their own, so let us give them a prize and rule the Jewish law like them. That explanation seems to be one that does not say: because the truth is with them therefore I rule like them; rather, I rule like them in order to educate the public to behave nicely, to gain some educational benefit, not because the truth is with them. That is the pluralist reading of the Gemara. But Rabbi Yosef Karo, in his book Kelalei HaGemara, suggests another explanation. He argues that when the Gemara says that the Jewish law was ruled like Beit Hillel because they were pleasant and humble and stated the words of Beit Shammai before their own, this is the explanation of why Beit Hillel are closer to the truth. It is not a prize for good behavior. Because one who first weighs the arguments of his interlocutor before… and therefore this explanation of the Gemara, that the Jewish law was ruled like Beit Hillel because they stated the words of Beit Shammai before their own, is not to show us that they behaved nicely and were rewarded for good behavior by the Jewish law following them, but because they conducted themselves that way, apparently they were closer to the truth. And therefore the Jewish law was ruled like them. That is, when you issue a halakhic ruling, you need to weigh very carefully also the opposing arguments before you formulate a view of your own, and then you have a higher chance of getting at the truth. Yes, like what the Gemara says, that anyone accepted to the Sanhedrin had to bring 101 reasons to declare a creeping creature pure and 101 reasons to declare it impure. So Rabbenu Tam asks there: what do we need these empty pilpulim for? Why do we need empty dialectics to purify the creeping creature? The Torah says the creeping creature is impure. So the Maharal says these are not empty pilpulim. There really are 101 reasons why the creeping creature is pure, and they are correct reasons, and there are 101 reasons why the creeping creature is impure. The Torah says that the reasons why the creeping creature is impure outweigh the reasons why it is pure, not that there are no reasons to declare it pure. There are reasons to declare it pure. Only the reasons to declare it impure outweigh the reasons to declare it pure, and therefore the creeping creature is impure. But a good judge, one who wants to sit on the Sanhedrin, has to be someone who understands very well also the reasons of the opposing position before formulating a position of his own. He has to understand well all the sides of why the creeping creature is pure, and afterward understand why the sides saying the creeping creature is impure are weightier or more significant. Therefore one accepted to the Sanhedrin had to be tested by giving 101 reasons to declare the creeping creature impure and 101 reasons to declare it pure. Like Beit Shammai and Beit Hillel, where Beit Hillel weighed the arguments of Beit Shammai first and only then formulated a position of their own, and therefore their chance of coming closer to the truth was higher. And if so, then in Rabbi Yosef Karo we see that the reason the Jewish law was ruled like Beit Hillel is not because it was a reward for good behavior, but because they were right—or most likely right. Which means that Rabbi Yosef Karo was a monist and not a pluralist. He read the Gemara in a monistic way: the Jewish law follows Beit Hillel because the truth is with them, not because there is a multiplicity of truths. Of course, that then raises the question: so what does “both these and those are the words of the living God” mean according to Rabbi Yosef Karo? If he is a monist and the truth is with Beit Hillel, then in what sense are the words of Beit Shammai also the words of the living God? About this I spoke in another context. I said that their being the words of the living God means that their position is a legitimate position. Their arguments are correct arguments, as I said earlier about the reasons to purify and the reasons to impurify the creeping creature, but in the bottom line they really are mistaken; the truth is with Beit Hillel. Because the arguments raised by Beit Hillel carry more weight than the arguments raised by Beit Shammai. But that does not mean that the arguments of Beit Shammai are incorrect; they are correct. It is only the weight they assign them that is not correct. The arguments of Beit Hillel are arguments of greater weight, and therefore the words of Beit Shammai are the words of the living God because their arguments are correct arguments. In the bottom line they are mistaken; Beit Hillel are right, according to the monistic reading. Fine, but that is just a side remark on how to read this in a pluralist way and in a monistic way. Now I ask: okay, who is right? Is the monistic reading right or is the pluralist reading right? Depends on your intuition? What? It depends on your approach, your intuition, what your intuition is, no? So I wanted to claim that I have a proof that the monistic approach is correct. What is the proof? Let us apply the monist-pluralist debate to “both these and those” itself. After all, there too there are two interpretations, right? A monistic interpretation and a pluralist interpretation. Now the pluralist, in order to be consistent, basically has to say that also regarding “both these and those” one should accept all the interpretations. Or in other words, on the question of pluralism versus monism too, he has to relate in a pluralist way. But that cannot be; that is a logical contradiction. Because it cannot be that both monism is right and pluralism is right. Because if monism is right, that means the pluralist is mistaken. It means there are incorrect positions. Say, in the debate whether a rival wife in the case of a daughter is permitted or forbidden, the dispute of Beit Shammai and Beit Hillel. If you are a monist, then once you say she is permitted, the person who says she is forbidden is mistaken. If you are a pluralist, you are essentially saying both this position is right and that position is right. But the monist clearly holds that the pluralist is mistaken. So you, as a pluralist, cannot say that both the monist is right and the pluralist is right in the dispute about pluralism itself; you have to admit that it is impossible to apply the pluralist position. Here is the self-reference. If you apply your pluralist position to the dispute regarding pluralism itself, you come out inconsistent, not coherent. But who says one has to be pluralist in all disputes? There are places—most places—where one should be pluralist. The pluralist position means that the Sages are never mistaken. After all, what is the basis of pluralism? The basis of pluralism basically says that every halakhic sage who raises coherent arguments is by definition not mistaken. An authorized halakhic sage, yes, a major halakhic sage cannot be mistaken. In the case of the Sages, say. Why do people always say there are no disputes about reality? Yes, that is what is commonly said in yeshivot: there are no disputes about reality. Why? Because in a dispute about reality it is clear that one side is mistaken. But the assumption in the yeshivot is that among the Sages, when there are disputes, “both these and those are the words of the living God,” meaning neither side made a mistake. Both are right. Therefore it cannot be that there are disputes about reality, because in a dispute about reality it is clear that one of the sides is mistaken. Fine, that is of course nonsense; clearly there are disputes about reality. The dispute, for example, about what they did in the Tabernacle, regarding carrying in and out with the beams and the wagons—that is a dispute about reality. What happened in the Tabernacle? Fine, I spoke about this once, that there is an explanation of Rabbi Yitzhak Hutner. But for my purposes I just want to show you what the motivation is for the pluralist interpretation of “both these and those.” The motivation is the confidence that the Sages cannot be mistaken. Or that sages cannot be mistaken. Yes, but that is not what I asked. I asked whether maybe the pluralist really is a pluralist in most all cases, but there are a few exceptional cases where he is not a pluralist. Pluralism does not necessarily mean one has to be pluralist everywhere. So I said: if you look at the reason why he advocates pluralism, then everything I said now is the answer to that question. Why? Look at the reason a person adopted a pluralist position. Because of that assumption—that he thinks a halakhic sage who advances a coherent position cannot be mistaken. Fine, I am not talking about a halakhic sage. So if you take the halakhic sage who advances a coherent position about “both these and those,” he too cannot be mistaken. So you need to be pluralist also with respect to this very dispute. Because the very same basis you have for pluralism in general should also exist here, and by the same token on the other side. If you tell me this is an exception, what are you really saying? That sages who interpreted this in a monistic way made a mistake here. Or vice versa. And sages who interpreted it in a pluralist way made a mistake here. Oh, so sages can make mistakes? Then the ground has fallen out from under your pluralist position. Here, sages can make mistakes. I understand. So it basically comes out that once you apply—and by the way, this is often Gödel’s kind of move and a lot of mathematical moves—they are basically moves that apply a certain position to itself and try to reduce it to absurdity, thereby proving that it is not correct. Yes, paradoxes like the paradox of sets: they divide sets into sets that contain themselves as an element and sets that do not contain themselves as an element. For example, the set of all sets. It itself is also a set, right? So it is itself one of the elements in that set of all sets. Or for example, no matter. Now there are sets that contain themselves as an element—they themselves are one element of themselves—and there are sets, and you already see self-reference here, and there are sets that do not include themselves as an element, that are not an element of themselves. Let us collect all the sets that do not include themselves as an element, that are themselves not an element of themselves, and form a set from them. Is that set an element of itself or not? If it is an element of itself, who are its elements? All the sets that are not an element of themselves. So if it is an element of itself, it is not an element of itself. But if it is not an element of itself, then it is one of the sets inside itself, so it is an element of itself, because after all it is the set of all sets that are not an element of themselves. That is a paradox. This is one of the paradoxes that basically brought down set theory in mathematics, naive set theory. Yes, there are all sorts of paradoxes in naive set theory that caused mathematicians to give it up, to understand that it leads to paradoxes, and to begin reconstructing set theory on an axiomatic basis—axiomatic set theory. Yes, they start from the empty set, then a set containing the empty set is a set with one element, and so on, and in this way they build set theory from scratch in a way that is supposed to be consistent. Now notice: on the one hand there is self-reference here. A set that is an element of itself is self-reference. So we are not especially surprised when we discover that such self-reference creates some paradoxical loop. But on the other hand, mathematicians see this and make constructive use of it—or constructive destruction—and you are basically using self-reference to produce a paradox, and thereby to prove that something in the infrastructure that led to this paradox is incorrect. Very often self-reference is a tool to prove something by contradiction. Let us assume it is correct; we will see that this leads to a paradox, and that is the proof that it is not correct. In this case we assume that one can define a set in a simple intuitive way. I show you that this assumption leads to a paradox, and that is the proof that one cannot define sets naively. So this is a constructive use of paradoxes of self-reference. I simply generate self-reference in a way that creates a paradox, and then that shows me that I must give up some assumption that led to this paradox. Something like this is what I tried to do in the dispute between pluralism and monism. What did I do there? I took pluralism and said: if you are a pluralist, you should apply your pluralist position also to the dispute about pluralism itself. You see the self-reference, but I am making constructive use of it. Why? I do not stop at saying this is a paradox; rather, from the fact that we reach a paradox, it is proved that pluralism is not correct. This is a proof by contradiction against pluralism, and in favor of monism. Because I claim that if you adopt a pluralist position, you get caught in a paradoxical loop. A vicious circle, yes. So this use of self-reference that creates paradoxes basically says that this is in effect a proof by contradiction, or reduction to absurdity, against the claim that stands behind and allows the self-reference. By the way, the theory of types that I discussed at the beginning of the series—this is basically what Bertrand Russell does in a very similar way. He basically says that all the paradoxes, or a whole collection of paradoxes, are possible only because in our language it is legitimate for a claim to refer to itself. And these paradoxes are the proof of that. That is how he built the theory of types. Basically, these paradoxical loops are a proof by contradiction against the thesis that allows self-reference. And from here a proof that self-reference is impossible. But I said there that I think he is throwing out the baby with the bathwater. There are many self-references that do not create paradox, and therefore I do not see why one should forbid them all. So I will not return to that here; I only want to draw your attention to the fact that Bertrand Russell too made the same use of self-reference. It is a constructive use. Mathematicians often make use of self-reference, and many times it is in order to show that you enter a loop, and therefore you basically need to give up some assumption that made this loop possible. So you do not remain with a paradox and throw up your hands—there is a paradox here. Rather, the paradox is proof that the assumption that made it possible is not correct. And now you have a solution to the paradox: one must give up that assumption. We have proved that assumption is not correct. And this is a mathematical tool, these paradoxes of self-reference. It is not a matter of: there is a paradox and I remain with my hands in the air. The paradox is an instrument. It is an instrument by means of which I prove by contradiction that some claim is incorrect, the claim that allows the paradoxical loop. So also in this context of the dispute between pluralism and monism, I am basically claiming that I can make use of self-reference to attack pluralism, to prove that pluralism is not correct. The suggestion Eliav made earlier, when he said basically: let us say I am a pluralist everywhere except with regard to the dispute about pluralism itself. On the logical level that is a possible solution. And you suggested something more moderate, that there might be a group of disputes with respect to which I am not a pluralist. I am proposing something minimal: only in the dispute about pluralism am I not a pluralist. There I am a monist. What is the monism? My monism is that there is only one truth. What? That there is not one truth. Yes, meaning that on this question there is only one truth, and that truth is that there is not one truth. Because that is basically the dispute about pluralism. I often say that in my view there is nothing in the world that is certain. And I am very unsure whether this claim itself is certain. The claim that nothing is certain—am I certain about that? Am I one hundred percent convinced that it is true that nothing is certain? Maybe yes. I am not sure whether this claim itself is certain or not. So here, in this sense, I am showing you that the pluralist in fact reveals a monistic position on the question of pluralism. On the question of pluralism, the monist is right. So that means that I, as a pluralist, am actually a monist. On this question there is only one truth, the pluralist truth. Okay, so can I really solve paradoxes that way? By making an exception for the problem that creates the paradox, but keeping the claim that is under attack in general? Yes, that is basically what I argued against Bertrand Russell. What I said was: do not throw out all self-references; throw out only the self-references that lead to paradoxes. Because there are self-references that do not lead to paradoxes, so why give them all up? I think that in the Jerusalem Talmud there is another explanation of why the Jewish law follows Beit Hillel, because they would listen to Beit Shammai and retreat from their own view. And then… What? Can’t hear? I’m saying: in the Jerusalem Talmud there is another explanation why the Jewish law follows Beit Hillel: that they would hear Beit Shammai and retreat from their own view. Meaning that they changed their mind and accepted the view of Beit Shammai, so they themselves did not think that they could not make mistakes. It is the same reasoning. What is written in the Babylonian Talmud, that they stated the words of Beit Shammai before their own, means that they weighed the argument of Beit Shammai before they formulated a position of their own. They weighed it—meaning that sometimes that weighing led them to the conclusion that Beit Shammai really were right and they did not formulate another position. They admitted the mistake, yes. “Beit Hillel later ruled like Beit Shammai” is found in several places. I think it is the same reasoning as in the Babylonian Talmud. In any case, for our purposes, what I really want to point out here is the possibility of solving problems of self-reference by removing the point that creates the paradoxical loop—but only that point. Not giving up the whole claim that this attack targets. Say I attack pluralism by creating a loop in the dispute about pluralism itself. I say: I remain a pluralist except in this dispute itself. Or what mathematicians call a removable discontinuity. Meaning there is a function that is continuous except at isolated points. So if we redefine the function at those isolated points, it can become a completely continuous function. Yes, it is a discontinuity that can be removed. Change the definition of the function at specific points and you get a continuous function. Here too: change the definition of pluralism at specific points and you get a coherent claim, a coherent pluralist claim. Let me maybe bring two more examples. So wait—so in conclusion, can one or can one not? So in conclusion, your proof does not hold? I am saying on the logical level it is possible. It is a logically coherent claim to say that I am a pluralist in all disputes except this one. That is perfectly fine. There is no paradox here; one can make such a claim. What I told you earlier is that my argument against this solution is that it is ad hoc. It does not really have any logic behind it. The logic that underlies pluralism should have led to a pluralist attitude also with respect to this dispute itself. Therefore I claim that this position is an unreasonable position. But on the logical level it is a possible position. Meaning, on the logical level it solves the paradox, the loop. But it is not reasonable? But it is not reasonable. I think it is not reasonable, yes. Okay, let me bring two more examples of such removable discontinuity. One second. I lost it in column 406. Here. I’ll share the screen for a moment. The first example is a Gemara in tractate Bava Metzia on page 30. The Gemara there brings the following statement. Rav Pappa said—it is talking about the heifer whose neck is broken; some say the red heifer, it does not matter at the moment; let us say the heifer whose neck is broken. Yes, the heifer whose neck is broken is what they bring when a corpse is found and they do not know who murdered him. So the elders of the city closest to that place go to a rough wadi and bring the heifer whose neck is broken. But with regard to that heifer there is a rule that it has to be a heifer upon which no yoke has been placed: “which has not been worked with and upon which no yoke has come.” Rav Pappa says, the Gemara says: if it had been written “worked” and we had read “worked,” I would have said even by itself. What happens if a yoke came upon it, but I did not place a yoke on it, I did not work with this heifer, but it happened on its own? Something fell on it and it carried it. So a yoke came upon it, but on its own. If it had been written “which was not worked with,” do you understand the difference between “was not worked with” and “did not work”? “Did not work with it” means I did not work with it. “Was not worked with” means no work was done with it regardless of me, even if it happened on its own. So the Gemara says that if it had been written “worked” and we had also read “worked,” I would have said that even if a yoke came upon it on its own, it would be disqualified. Because the main point is that no work was done with it; it is not necessary that I not have worked with it. So then I would have thought even if it happened on its own. And if it had been written “did work” and read “did work,” I would have said only if he worked with it, not if it happened on its own. Now that it is written one way and read another—there is here a written-reading discrepancy; it is written without a vav, but we read it with a vav—Rav Pappa says: what does this teach? It teaches that both of those first extreme readings are wrong. We require “worked with” analogous to “he worked with it”: just as “he worked with it” is when it is pleasing to him, so too “worked with” means when it is pleasing to him. Yes, the two extreme possibilities basically say either that if it happened on its own then it does not disqualify it, or that if it happened on its own then it does disqualify it. What happens because there is a written-reading discrepancy? We arrive at an intermediate position. What is the intermediate position? That even if it happened on its own, it can still be disqualified, but only if I, the owner of the heifer, am pleased that it happened. If it happened on its own but I am not pleased with it, then not. But if it happened on its own, not through me, yet I am pleased with what happened, because it happened on its own but in the end something came out that was to my advantage, then it is disqualified. So says the Gemara. Tosafot there in Bava Metzia ask: and if you say so, then why is it disqualified if a male mounted it? Surely he does not want to disqualify a heifer whose value is so great for such a small thing. For example, if a male mounted it, then basically a yoke came upon it by itself; I did not do this, they did this by themselves. But if I am pleased by it—why am I pleased? Because if a calf comes from this, then I gain a calf, so I am pleased that a yoke came upon it. Therefore the Gemara says that in such a situation the heifer is disqualified. Tosafot ask: why? Surely if the heifer is disqualified, then I am obviously not pleased with that, why? Because after all the red heifer is worth a fortune. The red heifer is something very valuable. And now if I am pleased that a yoke came upon it, that pleasure itself causes the heifer to be disqualified, or the red heifer to be disqualified. I may gain the calf that will be born, but I lost a red heifer worth like a hundred cows. So in the end I am not pleased with what happened here. But if you say that, then in every case I will not be pleased. In what case would I be pleased? So Tosafot say: once you qualify it and say that if a yoke came upon it by itself it is only if he is pleased, then the rule is dead. There will never be pleasure here, because the moment you disqualify it, he will always not be pleased. So when does the law ever apply that the heifer is disqualified when it happened on its own because I am pleased? It will never happen. That is Tosafot’s question. You need to put a limit on what counts as “pleasing.” You hear? You need to put a limit on what counts as “pleasing.” Okay, that is why I am bringing it here. Tosafot say: and one can answer that if it had been valid, he would have been pleased, and therefore we should not validate it. What is the answer? That were it not for the prohibition, he would have been pleased. What? Were it not for the prohibition, he would have been pleased. Yes. Meaning, all my lack of pleasure stems from the law that disqualifies the heifer because of the pleasure. Meaning my displeasure is not because of the reality itself. In the reality itself a calf was produced here, and I am only happy about that. My displeasure stems from the law, the law that says that the moment I am pleased, the heifer is disqualified. Once the law disqualified the heifer for me, then I am not pleased. Tosafot say that displeasure stemming from the law does not count. Only displeasure that stems from the reality is taken into account. You understand that this is exactly a removable discontinuity, right? At the end of the day, you ask: is he pleased or is he not pleased? Clearly he is not pleased. Right, it is because of the law, but at the end of the day he really is not pleased with it. So what? So if he is not pleased with it, he shouts “I’m not pleased, I’m not pleased,” and we say: it won’t help you, your heifer will be disqualified regardless. Why? Because in this situation, basically… were it not for the law. But now with the law I am not pleased; what do you want from me? In practice you ask whether I am pleased or not. I am not pleased. Rather, we make some sort of correction, a removable discontinuity, because we remove the displeasure that stems from this law itself—it does not count—and all other displeasure does count. The rule that says that when I am pleased the heifer is disqualified—sorry, that when I am not pleased the heifer is not disqualified—is true, except where the displeasure stems from the very law itself. You understand that this is exactly what Bertrand Russell does in the theory of types. And what Eliav suggested earlier regarding the attack on pluralism. Let us simply make an exception for the problematic case itself and say that the rule does not apply to it. Once we do that we neutralize the loop, and now there is no difficulty. So you see that it is reasonable to do this? So you do see that it is reasonable to do this? First of all, what I see is that it is logically possible, not that it is reasonable. It is logically possible; now we need to discuss whether it is reasonable or not. Regarding pluralism, I claim it is not reasonable. Here it is not so simple. Here I may perhaps explain why it is also reasonable, not only logically possible. Why? Why? Because it may be that a person’s pleasure is not a principle measured by the question of what his psychological state is. If that were the question, then in the end his psychological state is that he is not pleased; why should I care why he is not pleased? He is not pleased. But it may be that this is only a criterion for what is happening here. When something happens and it is pleasing to a person, then for me that is a thing that disqualifies the animal. Do you understand what I am saying? And then it makes a great deal of sense to say that if my displeasure is because of the law, that is irrelevant, because all I am really asking is what happened here in reality. Did what happened here in reality, in principle, add something for the owner of the heifer? Certainly yes. So what if he is displeased because of the law? But if displeasure is not itself the criterion, and is only an indication—acts that a normal person, were it not for the law, would be pleased by, these are the acts that disqualify. That is certainly something one can accept. There is logic here. If I interpret the displeasure as not a requirement about the person’s psychology, about what is in the person’s soul—if it is a requirement about what is in the person’s soul, then in practice he is not pleased. Why should I care why he is not pleased? He is not pleased. But if I claim this—I think this is what Tosafot means, and therefore I think it is also reasonable and not only logically possible, to answer you, Eliav. My claim is that Tosafot want to say that what is not really required is the person’s actual pleasure; rather, they are giving you a criterion for what type of acts are disqualifying acts. Acts such that if you ask a non-Jew who does not know the Jewish law, “Is this an act that you would be pleased to have happen to your heifer?” and he answers yes, that belongs to the family of disqualifying acts. Exactly. It is a sign and not a cause. In yeshivot, yes, that is what they say: it is a sign; “he is not pleased” is a sign, not a cause. It is not that displeasure disqualifies or pleasure disqualifies, but rather pleasure is an indication that this act belongs to the type of disqualifying acts. Then there is also logic to it. In the minute I have left, I just want to finish with something the Ran does here, and we will return to it next time. The Ran, who appears there in Shitah Mekubetzet, also brings two answers. He brings the same question as Tosafot. And one can say that since the act in itself is pleasing to him, we do not validate it on account of its disqualification, for then its disqualification would become the cause of its validation. This is seemingly like the answer of Tosafot, although he has a certain addition, and I am not sure it is really exactly like Tosafot’s answer. But it goes in the direction of Tosafot’s answer: he makes this case an exception to the rule and solves the problem. But he adds another explanation. And furthermore, if you validate it, he certainly is pleased. What is he saying here? This is a very charming loop. What are you asking? You are basically saying this: if we disqualify the heifer—say a male mounted it—you ask the owner of the heifer, “Are you pleased?” He says, in principle yes, but if you disqualify the heifer for me, then no. So in practice I am not pleased; that is Tosafot’s question. If I am not pleased, the heifer should be valid—that is what Tosafot asked, right? The Ran says: why are you stopping there? Let us continue further. If we validate it, he certainly is pleased. So the heifer is valid now? Fine, so if it is valid, then yes, I am pleased. But then if I am pleased, the heifer should be disqualified. But if the heifer is disqualified, then I am not pleased. But if I am not pleased, then it is not disqualified. But if it is not disqualified, then yes, I am pleased. In other words, what the Ran is saying is that Tosafot stopped the objection after one step. Why doesn’t he continue further? You can continue this loop forever. Now an interesting question is why the Ran thinks this is an answer. Fine, you can continue forever—and therefore what? Therefore the heifer really will be disqualified if I am pleased? No, it is a paradox. It will both be disqualified and not be disqualified, and I do not know what to do with that. Seemingly the question remains in place; it is just a different question. Tosafot asked: let us validate the heifer. According to the Ran, one should ask: let us place it in a state of uncertainty; it is possibly disqualified, possibly valid, and I cannot decide. But the question still remains: why does the Ran see this as an answer? That is a question. We will return to that question next time. Okay, I’m done. Does anyone want to comment or ask? Yes. Fine then, goodbye, Sabbath peace. Next time I think we will already finish this series; maybe we will need a little more, but I think next time we will already finish this series, I think. And when is the next series? I don’t know, we’ll think about it more; I’ll send a message. Okay, goodbye, Sabbath peace. All the best.