Positivism in Halakha and in General, Lecture 3

Table of Contents

• Paradoxes and initial examples
• Aristotelian definitions and types of statements
• The liar paradox versus an anti-paradox
• A halakhic example of an anti-paradox: a heavenly voice, “It is not in heaven,” and majority rule
• The answer of “against the majority” and the dilemma between a quantitative majority and a qualitative majority
• The strange structure in Tosafot regarding Rabbi Yehoshua
• Anti-paradox as justification for the need for a heavenly voice, and its implication for disputes over authority
• A halakhic example of a paradox: Rav and Shmuel on a condition regarding overcharging
• The connection to the dispute between Rabbi Meir and Rabbi Yehuda, and analysis of “she knew and waived it”
• The liar paradox in deciding Jewish law: money law versus a reversing prohibition
• Tosafot, Rabbenu Chananel, and the argument whether this is “prohibitions” or “civil law”
• Critique of the “word game” solution and grounding paradox in real content
• Behavioral solutions versus an analytical solution: compromise, passive omission, and a heavenly voice
• Buridan’s donkey, randomness, and rationality
• Determinism, symmetry, and “Buridan’s person”

Summary

General overview

The speaker continues from the previous lecture on paradoxes, systematically defining a paradox as opposed to an anti-paradox through Aristotle’s concepts of a “sentence” and a “proposition,” and shows how logical structures of self-reference also appear within halakhic rulings. He suggests that there are four categories of propositions: true ones, false ones, ones that cannot consistently be assigned a truth value, and ones that can consistently receive both truth and falsity. He illustrates this through passages in Tosafot and the Talmud about a heavenly voice and about making a condition regarding overcharging. He argues that the attempt to dismiss paradoxes as “meaningless word games” is inadequate, because in similar structures there is also a real question of halakhic and practical decision-making. He concludes with a discussion of Buridan’s donkey, rationality, randomness, and determinism, and examines whether a random solution solves problems of justification or only makes it possible to “get out alive.”

Paradoxes and initial examples

The speaker notes that last time examples of paradoxes were brought up, including self-referential paradoxes like the liar paradox. He also brings another kind of paradox, such as the surprise exam paradox, in which the very attempt to infer when the “surprise exercise” will happen cancels the possibility that it will in fact be a surprise. He wants to move on to the question of what one does with paradoxes, but before that he distinguishes between a “paradox” and an “anti-paradox,” both in a general context and in a halakhic one.

Aristotelian definitions and types of statements

The speaker attributes to Aristotle a distinction between “sentences” and “propositions,” where a proposition is a sentence to which one can attach a truth value of true or false. He states that a question like “What time is it?” is not a proposition, because one cannot attach truth or falsity to it, whereas “It is dark outside right now” is a proposition. He defines a paradox of the liar-paradox type as a sentence to which one cannot consistently attach a truth value, because if it is true it turns out false, and if it is false it turns out true.

The liar paradox versus an anti-paradox

The speaker formulates “Sentence A: Proposition A is false” as a paradox, because attributing either truth or falsity to it generates a circular contradiction. He formulates “Sentence B: Sentence B is true” as an anti-paradox, because, in his view, one can assign it truth and remain consistent, and can also assign it falsity and remain consistent. He sums up four types of propositions: a true proposition, a false proposition, a proposition with no consistent truth value at all, as in the liar paradox, and a proposition to which both truth values can consistently be assigned, as in the anti-paradox.

A halakhic example of an anti-paradox: a heavenly voice, “It is not in heaven,” and majority rule

The speaker brings an example from an article he wrote in HaMa’ayan and presents a passage in Eruvin 13 about the dispute between Beit Shammai and Beit Hillel, which lasted “two and a half years,” after which a heavenly voice went out and said: “These and those are the words of the living God, but the Jewish law follows Beit Hillel.” He quotes Tosafot, who ask how one can follow a heavenly voice when in the story of the Oven of Akhnai it is said, “It is not in heaven,” and therefore one does not pay attention to a heavenly voice. He presents Tosafot’s answer that in the heavenly voice of the Oven of Akhnai, “it went out only for his honor,” meaning for Rabbi Eliezer’s honor, and therefore “it was fooling us,” whereas a heavenly voice that genuinely means what it says does decide the matter. In that case, “It is not in heaven” is not a principled rule, but a local statement about a heavenly voice that is not serious.

The answer of “against the majority” and the dilemma between a quantitative majority and a qualitative majority

The speaker brings Tosafot’s second answer: in the Oven of Akhnai, the heavenly voice was “against the majority,” and therefore the rule “follow the majority” applies, so one does not heed the heavenly voice. He quotes Tosafot saying that in the dispute between Beit Shammai and Beit Hillel, “Beit Hillel were the majority,” but the heavenly voice was needed “because Beit Shammai were sharper.” The speaker interprets this to mean that the dilemma was between a quantitative majority and a qualitative majority. He argues that this creates a structure in which each side is internally consistent: if one adopts a quantitative majority, then the quantitative majority decides in favor of a quantitative majority; and if one adopts a qualitative majority, then the qualitative majority decides in favor of a qualitative majority. So this is an anti-paradox that requires an external deciding factor like a heavenly voice.

The strange structure in Tosafot regarding Rabbi Yehoshua

The speaker quotes Tosafot asking, “And if you say so, then what does Rabbi Yehoshua mean?” and bringing the answer, “ ‘It is not in heaven’ implies that one should pay no attention at all to any heavenly voice.” He argues that this “pulls the rug out” from under the previous distinction and leads to the result that both Beit Hillel and Beit Shammai are acting against Rabbi Yehoshua, while in the Oven of Akhnai they still reject Rabbi Eliezer because of the majority against the individual. He presents an interpretive difficulty according to which Tosafot come out saying that the reasoning of “It is not in heaven” is not actually correct in practice as Jewish law, and the rejection of Rabbi Eliezer really rests on majority rule, a reason not presented there as the central issue in the passage. He defines this as a comment on the odd structure in Tosafot.

Anti-paradox as justification for the need for a heavenly voice, and its implication for disputes over authority

The speaker formulates the dispute between Beit Shammai and Beit Hillel over the decision-making rules themselves as an anti-paradoxical structure in which there is no internal resolution, and therefore “that is exactly why you need the heavenly voice.” He adds an analogy from the world of halakhic authority after the redaction of the Talmud, arguing that there is an autonomous view according to which “after the sealing of the Talmud there is no formal halakhic authority,” and therefore “one can disagree.” He contrasts this with a precedent-based approach that developed around the Shulchan Arukh and its commentators, and argues that someone who does not accept precedent will also not accept the precedent-based binding ruling itself. He describes this too as a parallel structure in which a rule validates itself.

A halakhic example of a paradox: Rav and Shmuel on a condition regarding overcharging

The speaker brings a passage in Bava Metzia 51: “One who says to his fellow, on condition that you have no claim against me for overcharging”—Rav says, “He still has a claim against him for overcharging,” and Shmuel says, “He has no claim against him for overcharging.” He explains the laws of overcharging approximately in terms of “one-sixth,” and the meaning of the condition that seeks to bypass the Torah’s law. He presents a rule for deciding disputes between Rav and Shmuel according to which “in monetary law” the Jewish law follows Shmuel, while in “prohibitions” the Jewish law follows Rav, and emphasizes that the problem here is that the sides also disagree over how to classify the dispute itself.

The connection to the dispute between Rabbi Meir and Rabbi Yehuda, and analysis of “she knew and waived it”

The speaker presents the Talmudic move linking the discussion to the dispute between Rabbi Meir and Rabbi Yehuda in Kiddushin over the condition concerning “food, clothing, and marital rights,” and quotes: according to Rabbi Meir, “his condition is void,” while according to Rabbi Yehuda, “in a monetary matter his condition stands.” He comments on the question among the medieval authorities (Rishonim) whether “marital rights” are considered monetary, and brings directions among the medieval authorities (Rishonim): a narrow interpretation that applies only to food and clothing, versus an interpretation that also defines “marital rights” as an interpersonal obligation that can be waived like a contractual obligation. He quotes the Talmud’s rejection of the simple identification and shows how Rav argues that he can work even “according to Rabbi Yehuda,” because there “she knew and waived it,” whereas here “did she know what she was waiving?” And Shmuel argues that he can work even “according to Rabbi Meir,” because there “he is certainly uprooting” the Torah law, whereas here “who says he is uprooting anything at all?”

The liar paradox in deciding Jewish law: money law versus a reversing prohibition

The speaker concludes that according to Rav, the dispute takes on a monetary character of waiver and contracts, while according to Shmuel, the dispute takes on the character of the category “making a condition against what is written in the Torah” as a question of when a condition can take effect. He argues that this yields a paradoxical structure: if one rules like Rav, then this is a “monetary discussion,” and therefore according to the rule one ought to rule like Shmuel; but if one rules like Shmuel, then this is a “prohibitory discussion,” and therefore according to the rule one ought to rule like Rav. He presents this as a structure parallel to the liar paradox, in which each ruling flips itself.

Tosafot, Rabbenu Chananel, and the argument whether this is “prohibitions” or “civil law”

The speaker quotes Tosafot in Bava Metzia 51, who bring Rabbenu Chananel ruling like Rav on the grounds that “the Jewish law follows Rav in prohibitions.” He quotes Tosafot’s difficulty: “This is puzzling, because they are not arguing about whether it is permitted to do this, but about whether he must return the overcharge, and the Jewish law follows Shmuel in monetary law,” and explains that Tosafot see this more as contract law than as prohibition and permission. He argues that apparently, according to his analysis, both Rabbenu Chananel and Tosafot assume an agreed-upon character for the dispute, even though in his view the passage itself creates a split in which Rav frames it as monetary while Shmuel frames it in a way that is not classic monetary law. He emphasizes that it is hard to understand how Rabbenu Chananel can rule like Rav when, according to Rav’s own approach, this is monetary law, which should have led to ruling like Shmuel.

Critique of the “word game” solution and grounding paradox in real content

The speaker cites, in the name of Rina Aharoni, the claim that sentences like “This sentence is false” and “This sentence is true” are word games that “assert nothing,” and therefore there is no point in asking about their truth value. He argues that the halakhic examples show that paradoxical and anti-paradoxical structures also exist in propositions with real content, like “one can make a condition about overcharging” or “do we follow a quantitative majority or a qualitative majority,” and therefore one cannot solve the logical problem simply by declaring that the classical cases are meaningless.

Behavioral solutions versus an analytical solution: compromise, passive omission, and a heavenly voice

The speaker rejects the suggestion to “do half and half” as a solution that replaces principled decision-making with technical conduct that does not resolve the question of halakhic validity. He argues that if the condition does not take effect, then any partial solution leaves a problem of theft or uprooting the law, and therefore it is not a halakhic ruling but a behavioral suggestion. He returns and emphasizes that he is looking for a real solution to the problem, not a trick that gets one out of the mess, and connects this to the motif of an external resolution like a heavenly voice in the anti-paradoxical case.

Buridan’s donkey, randomness, and rationality

The speaker mentions Buridan’s donkey, which stands at an equal distance between two feeding troughs and dies of hunger because of symmetry and the lack of any reason to prefer one side. He suggests that going randomly is a way to survive, but it does not provide justification for choosing right rather than left, and therefore it does not solve the problem of rationality as a demand for a reason. He proposes a solution in which the donkey “hooks itself up to a random generator” that physically compels it, so that the justification lies in the rational decision itself to hand the choice over to a mechanism that gets it out of paralysis.

Determinism, symmetry, and “Buridan’s person”

The speaker says that in the book The Sciences of Freedom he used the example to examine a deterministic worldview, in which a person is a machine driven by laws of nature. He argues that in a completely symmetrical world, in which the person or robot is perfectly symmetrical before two identical options, a purely physical system will not break symmetry and therefore “will die of hunger,” and he sees this as a mirror held up to the determinist, if he is really willing to accept that conclusion. He responds to the claim that the probability of a symmetrical state is zero by saying that this is a principled thought experiment, and distinguishes between a solution to rationality by means of a random generator and the problem of determinism, where “in a deterministic world there is no random generator either,” and therefore harnessing randomness is not a solution to the deterministic issue.

I once wrote about the elections for the Chief Rabbinate in this context of Zionist and non-Zionist rabbis, and following the last elections, when Rabbi David Lau and Yitzhak Yosef were chosen, there was this kind of breast-beating, some crisis in Religious Zionism. And in those elections the question was which son would be chosen in each case. They were all sons, that was obvious, but I mean beyond that, the question was whether it would be Zionist or non-Zionist. So people said: we failed to unite, and therefore the Haredi rabbis were elected. If there was a split among the Religious Zionist candidates, that was simply a complete misunderstanding of the map, completely ridiculous. Meaning, there was no split at all; there was total unity among the Haredim, and therefore Haredim were elected, because the only one there who wasn’t Haredi was David Stav. Meaning, all the rest were Haredi, and he wasn’t elected because he really was in the minority, that’s all. There were all kinds of Haredim, ones who recite Hallel and ones who don’t recite Hallel, fine, that’s not the point, but they were all Haredi. What? Hallel on Independence Day, that’s what I meant. I’m saying that in the general elections it’s going to be exactly the same thing, in the same style as what’s happening right now. Wait, there’s nothing new, don’t worry. What? New names will be switched in? You mean new names. Fine, every time there are some; they bought some old name, Bennett bought some name, no? There’s some party name that already existed, I don’t know, I don’t really understand this stuff. The name of someone who withdrew, The Jewish Home, supposedly the name of someone who withdrew; he was thinking of starting a party, and basically The Jewish Home is Pritzky’s name. Oh really? Yes, they took it from him, and then he didn’t run, so he sold the brand. He said, if I’d known, I wouldn’t have sold the shell company. And what does that mean, to buy it, I didn’t understand that. There’s a name that’s already registered as a shelf company, it’s ready-made. You don’t need now—no, because there’s a party, he set up a new name for the list; there’s a party and it’s sort of inactive. Why can’t he just make another party? He wanted that name. No, it also has organizational significance. I don’t know, maybe he needs a few thousand people who want to register for the party. No, there are also timing issues before it goes through and gets registered, and sometimes you don’t have time. I hope you’re enjoying this; important things, names too. Well, actually my printer didn’t work, and speaking of names, Haneen Zoabi filed a complaint with the Knesset committee that The New Right is stealing their name, because they’re called Hadash. Not for real. In any case, The New Right is the registered name in the Knesset. No, but Haneen Zoabi is Balad. They called themselves the new right-wing, not The New Right, and then it’s fine, then the difference will be clear. If they call themselves The New Right, then it’s not clear. Anyway, I hope my battery somehow holds up, because I just couldn’t print, my printer didn’t work. Last time I spoke a bit about paradoxes, and at the end I finished with various examples of paradoxes. I said there are paradoxes that stem from self-reference, like the liar paradox. Fine, maybe on WhatsApp? What? Everything gets sent to the group. These are files, I don’t know how to send that, I don’t understand this stuff. Maybe you can, probably you can, but I’m not the person for it. And I brought various examples of paradoxes, some self-reference paradoxes, some paradoxes of other kinds, like the surprise drill paradox, yes, I mentioned it, where the commander says there’ll be a surprise drill next week. It can’t be on the last day, because then the day before they’d know; but then it also can’t be the day before that, and so on, so there can’t be any surprise drill at all. And I want to move on a bit and see what we actually do with these paradoxes, but before I move on I’ll try to define two types—maybe we talked about this once, I don’t remember anymore—two types that I call paradox and anti-paradox, both in the general context and in the Jewish context. Basically, you can formulate paradoxes like the liar paradox and define them as follows. Aristotle defined sentences and propositions. Sentences are just bits of speech that say something. Propositions are those sentences to which you can assign a truth value, either true or false. Two truth values: true or false. So for example, “it’s dark outside now” is a proposition. For example, that proposition is either true or false. If I ask you, “what time is it?”, that’s not a proposition. I’m not asserting anything, I’m asking, and you can’t assign that an אמת or false value, because that sentence is neither true nor false, since it doesn’t assert anything. Okay? So that’s why it isn’t a proposition. So propositions are sentence-type things in terms of truth or falsehood, and therefore there are true propositions and false propositions. A paradox like the liar paradox is a paradox because it is a sentence to which you cannot assign a determinate truth value. If it’s true then it’s false, and if it’s false then it’s true, so in fact it’s a sentence of which you can say neither that it’s true nor that it’s false. That’s what defines the paradox, at least paradoxes of this type. Yes, so if I say: Proposition A: Proposition A is false—then that’s a paradox. Why is it a paradox? Because if we say it’s true, then it turns out to be false, because if the proposition “Sentence A is false” is true, then that means it is false, because this sentence itself is false, and so on. So basically this is a sentence to which you cannot assign any truth value, neither true nor false. But there is another statement—or not a proposition, but another sentence—which also seems strange in the question of how to define it. Let’s say it like this: Sentence B: Sentence B is true. In the liar paradox it was Sentence A: Sentence A is false. So if it’s false then it’s true, if it’s true then it’s false, therefore it’s a paradox. What do you say about this sentence? Sentence B: This sentence is true. Sentence B is true. It lacks value. What do you mean it lacks value? We didn’t learn anything from it. No, we didn’t learn anything from the liar paradox either. That doesn’t define it. The question is rather: how does it map onto this landscape of paradoxes, true statements, false statements? Seemingly there’s no paradox here. Why? A sentence saying that Sentence B is true, and that’s it, I said it. How can I keep going here? It doesn’t keep rolling, there’s no wheel here. Right? But it still isn’t a simple statement, not a proposition in the usual sense. So I called it an anti-paradox, because in the liar paradox I assign it a truth value—that it’s true—but then it comes out false, and then it comes back out true, and back out false, and the wheel keeps turning. In this sentence I can say it’s true, and I can say it’s false, and in both cases I remain consistent. Right? If I say it’s true, then it really does come out true, so that’s consistent. And if I say it’s false, then it really is false, because after all it says of itself that it is true, and if it’s false then it really is false. So this means that the sentence receives both truth values: both true and false. It lives peacefully with both of them. Meaning, you can assign it the truth value true and that comes out consistent; you can assign it the truth value false and that too comes out consistent. That’s why I called it an anti-paradox. So in fact we have four kinds of propositions. There is a true proposition, there is a false proposition, there is a proposition that has no truth value at all—meaning, if it’s true then it’s false and if it’s false then it’s true, that’s the liar paradox—and there are propositions to which you can assign both truth values, both true and false. Now on this point I want to bring two halakhic examples. This is from a paradox—from an article I wrote in HaMaayan. The first example is an example of an anti-paradox. And we already talked about this. The Talmud in Eruvin 13 describes how Beit Shammai and Beit Hillel disagreed for two and a half years, I think, and were unable to reach a decision. Then a heavenly voice emerged and said: “These and those are both the words of the living God, but the Jewish law follows Beit Hillel.” So Tosafot there—this is on page 13—Tosafot on page 6 asks: how do we follow the heavenly voice in such a case? After all, in the oven of Akhnai it says “It is not in heaven,” so we do not heed a heavenly voice. So how can it be that here they did follow the heavenly voice? Tosafot says as follows: here it was after the heavenly voice. “And if you say, what is different that we do not rule in accordance with the heavenly voice of Rabbi Eliezer,” who said there that we don’t follow a heavenly voice, “whereas here we do follow a heavenly voice? One can say that there it only emerged in his honor, as is evident there.” Here Tosafot gives a few more interesting answers. The heavenly voice in the story of the oven of Akhnai came out only in honor of Rabbi Eliezer, but the truth is that the Jewish law is not in accordance with him. It tricked them; it said that the law followed Rabbi Eliezer, but it did so only in his honor, and in fact it did not really mean to render a legal ruling, and therefore they did not heed it. But a heavenly voice that truly means it—yes, that one we do heed. So everything written there, “It is not in heaven,” is not really a general principle that it is not in heaven in the way we usually understand it. “It is not in heaven”—the sages there simply said that “it is not in heaven” means specifically that this heavenly voice came out only in honor of Rabbi Eliezer, but in truth it did not seriously mean what it said, and therefore we do not heed it. But there isn’t really some general rule saying “it is not in heaven.” That’s the first answer. The second answer is: and also, there it was against the majority, and the Torah said, “incline after the majority.” In the case of the oven of Akhnai the heavenly voice came out against the majority; the majority were against him. Therefore we do not heed a heavenly voice when it goes against the majority, because the halakhic rule is that we follow the majority. But if the heavenly voice does not contradict the rules of halakhic decision-making, then yes, we do heed it. And he says: but here, on the contrary, Beit Hillel were the majority. Beit Hillel were in fact the majority. Fine, so what’s the problem? Why do you need the heavenly voice at all? Then just follow the majority and that’s it. So he says: no, and the heavenly voice was needed only because Beit Shammai were sharper. Quality or quantity? What? Yes, we talked about this once. You count feet. Yes, exactly. So we’ve discussed this more than once, and I said that basically the dilemma was which majority you need: the quantitative majority or the qualitative majority. And therefore there was a dilemma, and therefore the heavenly voice emerged. And this answer of Tosafot is a bit strange, because whichever way you look at it: does the rule “incline after the majority” mean follow the quantitative majority or the qualitative majority? If you tell me it means the quantitative majority, and therefore it doesn’t really contradict the rules of halakhic decision-making, then the question comes back: so what was the dilemma? Why did they need the heavenly voice? So what if Beit Shammai say, “we’re the qualitative majority”? But what counts is the quantitative majority. And if you say that’s not so, then what did you gain from the whole move? Then in any case there isn’t really a halakhic decision here. So it’s not true that this heavenly voice fits the rules of Jewish law, that we follow the majority, because here there is a dispute about the rules of Jewish law. I think the claim here is that from the standpoint of the rules of Jewish law there really was a dispute between Beit Shammai and Beit Hillel. There is a rule of “incline after the majority.” Beit Hillel said: we follow the majority of feet. Beit Shammai say: we follow the majority of heads. So there is a dispute about how to interpret the rule of “incline after the majority.” The heavenly voice came and said: we follow the majority of feet. Fine? Now what does that mean? It’s true that it isn’t following the rules of Jewish law—because then what was the dilemma? There was a dispute about the rules of Jewish law. But on the other hand it also isn’t going against them. There isn’t a rule that goes against it. Maybe there was one opinion like this and one opinion like that, and we have no way to decide. In such a situation we follow the heavenly voice. Fine? That’s acceptable. Meaning, Tosafot does not mean to say that we follow the heavenly voice when it matches the rules of Jewish law, as seemed at first. It’s not that Beit Hillel were the majority and therefore there’s no problem following the heavenly voice. The point is not that Beit Hillel were the majority, but that it does not go against the rules of Jewish law. Where it does go against the rules of Jewish law, we do not heed the heavenly voice, as in the case of Rabbi Eliezer and Rabbi Yehoshua in the oven of Akhnai. Because there the heavenly voice came out against the majority, and then it’s obvious—it’s directly, frontally against the rules of Jewish law—so we do not heed the heavenly voice. In our case there was a dispute over what the rules of Jewish law actually say. In such a case the heavenly voice can decide who is right in that dispute. Why? Because we have no other halakhic ruling that is opposed to the heavenly voice. In such a case you can follow the heavenly voice. Fine? That is the claim in the second answer. And then he continues and asks: “And if you say, if so, what of Rabbi Yehoshua?” Rabbi Yehoshua said “we do not heed a heavenly voice”—but Rabbi Yehoshua only said that regarding Rabbi Eliezer’s heavenly voice. He is already saying here that this goes according to Rabbi Yehoshua, who says we do not heed a heavenly voice. But Rabbi Yehoshua doesn’t say any such general thing. He says we do not heed a heavenly voice only when it is against the Jewish law. What does that have to do with Beit Hillel and Beit Shammai here? “One can say that ‘it is not in heaven’ implies that—” when Rabbi Yehoshua said “it is not in heaven,” Rabbi Yehoshua really holds that we never heed a heavenly voice at all. That is Rabbi Yehoshua’s view, and therefore Rabbi Yehoshua here too would not accept relying on a heavenly voice. But the Talmud here says—but the Talmud here does not follow Rabbi Yehoshua, and therefore they did heed the heavenly voice. Fine. So it turns out that both Beit Hillel and Beit Shammai go against Rabbi Yehoshua. So what? Then we should also have changed the ruling in the oven of Akhnai. This Tosafot is very strange in terms of its structure. But why both Beit Hillel and Beit Shammai? I understand why Beit Hillel go against Rabbi Yehoshua, because they accepted the heavenly voice, whereas Rabbi Yehoshua holds that one does not heed a heavenly voice at all. But Beit Shammai accepted it too. And that’s what decided the dispute; otherwise what did the heavenly voice help? Beit Hillel knew they were right even without the heavenly voice; they didn’t need it. The heavenly voice determined the law according to everyone. Meaning, after there was a dispute, the heavenly voice came and said the law follows Beit Hillel. The plain meaning is that everyone accepted this as a decision. What does it mean that only in later generations—never mind. Bottom line, in the end they accepted this decision, and this decision is not in accordance with Rabbi Yehoshua. Yes, but why? If it’s not in accordance with Rabbi Yehoshua, then in the oven of Akhnai they also should not have ruled like him. No, there it’s because of the majority. It’s not because of Rabbi Yehoshua. What do you mean? In the dispute over the oven of Akhnai, Rabbi Eliezer was an individual against the majority; everyone else was with Rabbi Yehoshua. And afterward, in the statement of “it is not in heaven,” that is Rabbi Yehoshua’s own opinion; it doesn’t say that others joined him. But what Rabbi Yehoshua says there in the oven of Akhnai, namely “it is not in heaven,” isn’t true. He isn’t right that it is not in heaven. Okay. So why then can you not accept Rabbi Eliezer’s opinion concerning the oven? Well yes, heaven supports him. Fine, but he was one against the many, and the Jewish law follows the many. Let’s leave Rabbi Yehoshua aside. Yes, so this is really strange. We reject Rabbi Eliezer’s opinion, but not because of the reasoning Rabbi Yehoshua gives there, because that reasoning is not correct. Rather we reject it because of a reason that doesn’t appear in the passage there at all—the reason that one simply follows the majority, and the majority are right, therefore they rejected Rabbi Eliezer’s opinion. So that’s odd. The whole sugya there says we don’t accept Rabbi Eliezer because Rabbi Yehoshua said “it is not in heaven.” Then Tosafot tells us: what are you talking about? Rabbi Yehoshua isn’t right at all in what he says there; we don’t rule like him. But still it’s true that we don’t accept Rabbi Eliezer, for what reason? For a reason that doesn’t appear there in the sugya at all—simply because there is a majority. In the end, from the standpoint of how the Talmudic passage is constructed, that’s strange. Anyway, I don’t know, that’s just a comment on Tosafot. But for our purposes, what does this mean? Let’s now try to think through the process according to the second answer of Tosafot. There is a dispute between Beit Shammai and Beit Hillel as to whether the decisive majority is the quantitative majority or the qualitative majority. Right? Beit Hillel say it’s the quantitative majority, and Beit Shammai say it’s the qualitative majority. Okay? This is really a case of anti-paradox. Right? Because what do we do within that very dispute? We wait for the heavenly voice. Before the heavenly voice: if Beit Hillel are right that the quantitative majority decides, then even in the dispute about whether the quantitative majority or the qualitative majority decides, we follow the quantitative majority. And the quantitative majority says that the quantitative majority decides. Right? Beit Hillel, who were the quantitative majority, said that the quantitative majority decides. We move down one level. Okay? So in the methodological dispute over which majority decides, the quantitative majority or the qualitative majority, there too the dispute is between a quantitative majority and a qualitative majority. Right? Because Beit Hillel said the quantitative majority decides and Beit Shammai said the qualitative majority decides. Now if we adopt the opinion of Beit Hillel, then there is a quantitative majority in favor of the view that the quantitative majority decides. So we rule like the quantitative majority and it comes out consistent. But on the other hand we could have ruled like Beit Shammai, that the qualitative majority decides, and then what does the qualitative majority say? That the qualitative majority decides. So we rule like the qualitative majority, and that too comes out consistent. So this is really an anti-paradox. If we decide that it’s true, then it’s true, and if we decide that it’s false, then it’s false. Meaning, we gain nothing from the rules of halakhic decision-making, and precisely for that reason we need the heavenly voice. Since when there are two opinions, each of which is self-consistent, I can assign either one and each is legitimate. If one of them were illegitimate, we could discard it. But both opinions are legitimate. So we have no way to decide on the basis of majority rules, and we follow the heavenly voice. That is what Tosafot is saying. This is basically an anti-paradox. It’s an anti-paradox in which there are two—the heavenly voice comes and says this sentence is false or true. Sentence B: Sentence B is true. Now about this sentence I can say it’s false and that is consistent, and I can say it’s true and that is consistent. Unlike any ordinary claim, where it’s either true or false and you can’t say both, here you can say both. So how will it be determined? The heavenly voice will determine it. Meaning, the heavenly voice will decide whether it is true or false, because both answers are possible. In a paradox, though, the heavenly voice cannot decide, because in a paradox no answer is true, so what can the heavenly voice say? That the sentence is false—that isn’t right, because if it’s false then it’s true, and if it’s true then the heavenly voice won’t help at all. The heavenly voice can enter the picture only in a case of anti-paradox. It cannot say of a false sentence that it is true, because that would go against the rules of Jewish law. Right? If according to the rules of Jewish law it’s false, the heavenly voice can’t say it’s true. If according to the rules of Jewish law it’s true, the heavenly voice can’t say it’s false. So where can the heavenly voice act? In a paradox, the heavenly voice can’t say anything at all, because here it is neither true nor false. Only in a case of anti-paradox are we stuck, because it could be true and just as well it could be false, and then the heavenly voice decides. Whatever it decides, that’s what it will be. Okay? Exactly that. But why can’t I say that in the dispute between Beit Shammai and Beit Hillel, if in that dispute itself—meaning, it will determine things for the future, but as for right now, what determines it? Why can’t I say that I cannot rule not because of an anti-paradox, but because this is a principled question on which they disagree, and it will affect the future, and I can’t already now decide it. Therefore I need the heavenly voice. Why? That’s exactly what this is called—that’s called an anti-paradox. No, I need the heavenly voice because there is a principled issue here with which I can’t proceed. Why can’t you proceed? Because it’s a case of anti-paradox. Because if Beit Hillel are right, then Beit Hillel are right, and if Beit Shammai are right, then Beit Shammai are right. Meaning, you can’t decide the dispute before you’ve already decided it. That’s what you’re saying. I can say that I don’t want to decide the dispute, because for such a question, before I go further, I need a heavenly voice. Not that you don’t want to—you can’t decide it. Since each side is self-consistent. If you rule like Beit Shammai it comes out consistent, and if you rule like Beit Hillel it comes out consistent, so what can you do? So maybe I’ll give you an example—I just remembered one. I once wrote an article on—surely I spoke about this here too at some point—on autonomy in halakhic decision-making. And my claim was that basically after the Talmud—not only my claim, the medieval authorities already say this, and it’s even explicit in the Shulchan Arukh essentially—that after the sealing of the Talmud there is no authority—not authority really, in the sense of a formal sphere of authority—there is no formal halakhic authority. Okay? Meaning only the Talmud has authority, and therefore what the medieval authorities and later authorities or the Geonim or whoever else may say, with all due respect, can be disputed. Meaning, if I think otherwise, I can rule otherwise. So that’s an autonomous conception, and I tried to show that historically too this really was the conception until the beginning of the modern era, in the period of the medieval authorities. From the Shulchan Arukh onward—and this was part of the polemic around the Shulchan Arukh—somehow a conception took shape that gives status to earlier halakhic opinions. Let’s say, in the period of the medieval authorities, later authorities grant status to the medieval authorities; and also in the period of the later authorities, the great later authorities have some special status—from the Shulchan Arukh certainly, but afterward maybe also the Mishnah Berurah or, in our time, and so on. So this is a kind of precedential conception. So people said to me: fine, if so, then the Jewish law has been decided against you. Because the halakhic world accepted the position of the Shulchan Arukh, which is a precedential position—that there are certain texts that have authority and you can’t disagree with them. So I said: true, and in that very dispute too I disagree with those who accepted that ruling, and I do not accept it. Exactly the same structure. Meaning, the question is whether I am bound by precedents or whether I can rule autonomously. It turns out that all the important precedents say one must rely on precedents. Right? All the important decisors from the sixteenth century onward, almost all of them—or at least in recent centuries, certainly. At the beginning it still wasn’t so; the Shakh wasn’t like that yet. But the commentators. What? The Vilna Gaon and the Alter Rebbe also—The Vilna Gaon. Right, there are rare exceptions. All the commentators on the Shulchan Arukh, in any case. The commentators, Maharal, everyone. Okay. The commentators certainly, the earlier ones disagree with the Shulchan Arukh. Right, which is why I said—I corrected myself and said that at the beginning of that period it wasn’t true, but certainly in the last one or two hundred years it has become accepted. And then they say to me: look, so yes, there were opinions this way and opinions that way, there is a dispute here, but the law has been decided—somehow it has become accepted that precedents are binding. And again, of course this is very rough; the question is which precedents and in what sense, not important now, I’m speaking only at the principled level. So I said: true, the law was decided regarding precedents on the basis of precedents, and if I do not accept the precedential conception, then I also will not accept that ruling. Meaning, in this matter too I am not willing to bind myself to precedents that tell me I must bind myself to precedents. It’s exactly the same structure as Beit Shammai and Beit Hillel. Now there is also—No, but if the Rabbi said that the authority of the Talmud stems from the fact that it was accepted by all Israel, then that is different from mere precedents. No, that’s another claim. That claim has also been made. If there is agreement of the whole public about something specific, true, then it will receive a status like the Talmud. No, but that itself—that itself is the very question, the agreement of the public. No, but that’s another claim. That’s not the claim I made earlier. You’re now raising a different claim. I’m talking about the issue of authority; I can talk about that claim too. What I raised earlier was a different claim. Leave the authority of the Talmud aside. Even if the Talmud had no authority, that claim could still be self-consistent. Meaning, however Jewish law happened to settle or develop in such a way that people do go by precedents, independently of that principle. You’re asking another question, with which I also agree: if the whole public agrees regarding the Talmud, then the Talmud has status. Fine, so what’s the difference with the Shulchan Arukh? If the whole public agreed regarding the Shulchan Arukh too, then I should accept its authority upon myself—what difference does it make? Fine, but that isn’t the claim I was discussing earlier. Not necessarily the Shulchan Arukh, but even the principle that there is precedent and people rely on earlier precedents. Same thing, but that’s another claim, not the one I was talking about. What I want to bring now is also an anti-paradox, again a halakhic example. Not anti-paradox, sorry—a paradox. That was the anti-paradox. So the Talmud in Bava Metzia 51 says that Rav and Shmuel disagree on the question of stipulating against what is written in the Torah with respect to stipulating about overcharging. “It was stated: one who says to his fellow, ‘on condition that you have no claim of overcharging against me’—Rav said: he still has a claim of overcharging against him; and Shmuel said: he has no claim of overcharging against him.” Yes, he says: I’m selling you some object. Now there are laws of overcharging. If I sell it to you at a price one-sixth above the market price of the item, then the sale is void, okay? That is overcharging; you return the money. If it’s exactly one-sixth, then the money is returned but the sale stands, and if it’s less than one-sixth then the sale stands and the money is not returned either. Now someone sells and makes a stipulation: I make this sale conditional on the fact that even if there is overcharging, the sale will remain valid and you won’t be able to claim that I overcharged you. Fine? The question is whether such a stipulation is effective or not, because seemingly it goes against the Torah. The Torah itself says there is a law of overcharging. Here you are making a stipulation against the Torah’s laws; you want the Torah’s law of overcharging not to apply. So in monetary matters, is that possible? Here is the dispute; we’ll see in a moment. So Rav said: he still has a claim of overcharging, meaning the stipulation is ineffective. And Shmuel said: he has no claim of overcharging. What takes effect? Meaning, he has no claim of overcharging—I agreed. But then he violates Torah law. What? Even according to Shmuel does he violate Torah law? Not necessarily. Who says? If there’s agreement—yes, they agree. We’ll see in a moment. So the Talmud asks—meaning, how can such a law be decided? At first glance, in disputes between Rav and Shmuel there is a rule, already found in the Talmud: in monetary matters we decide like Shmuel, and in ritual prohibitions we decide like Rav, right? So it’s actually a simple rule. You need to check whether the dispute is a monetary dispute or a dispute involving prohibition, and that determines whether the law follows Rav or Shmuel. But what can you do when Rav and Shmuel also disagree on where exactly the dispute is located? And according to Rav this is a monetary dispute, while according to Shmuel it is a dispute of prohibition? Look. The Talmud says that this matter apparently depends on the tannaitic dispute regarding stipulating against what is written in the Torah in a monetary matter. The Talmud says as follows: “Shall we say that Rav speaks like Rabbi Meir and Shmuel like Rabbi Yehuda? For it was taught: one who says to a woman, ‘Behold, you are betrothed to me on condition that you have no claim upon me for sustenance, clothing, and conjugal rights’—she is indeed betrothed and the condition is void; these are the words of Rabbi Meir. Rabbi Yehuda says: in a monetary matter, his condition stands.” There is a well-known tannaitic dispute, appearing in several places in the Talmud, between Rabbi Meir and Rabbi Yehuda: what happens if a man betroths a woman on condition that she has no claim upon him for sustenance, clothing, and conjugal rights. He owes her sustenance, clothing, and conjugal rights by Torah law, but he stipulates, and she agrees, yes? She agrees to the betrothal and is willing to forgo sustenance, clothing, and conjugal rights. The question is whether it takes effect or not. Rabbi Meir claims it does not take effect because he is stipulating against what is written in the Torah; but Rabbi Yehuda says this is stipulating against what is written in the Torah in a monetary matter, and although in general, if one stipulates against what is written in the Torah, the condition is void—the act stands and the condition is void—but in a monetary matter the condition stands. That’s what Rabbi Yehuda says. Conjugal rights are monetary? What? We’ll get to that; I’ll comment on it. So according to Rabbi Yehuda you can stipulate concerning sustenance, clothing, and conjugal rights because it is a monetary matter. And incidentally, in Jewish law we rule like Rabbi Yehuda, that in a monetary matter the condition stands. It really is a question, because sustenance and clothing are monetary matters—I have to provide for her—but conjugal rights are sexual relations. What does that have to do with money? So the medieval authorities already comment on this—the Rashba as well, and others. There is a very interesting dispute among the medieval authorities on this point. Some say—I don’t remember who says what—but some say that it refers only to sustenance and clothing. Granted, it says “sustenance, clothing, and conjugal rights” because those always appear together, but the intention is only sustenance and clothing, because conjugal rights really are a matter of prohibition. On that one cannot stipulate. But I think the Rashba holds the second opinion—I don’t remember; I just remember that the Rashba addresses it. But there are medieval authorities who argue: no, it applies to conjugal rights too. Why? Because I owe her conjugal rights, and if she waives that, then it’s like a contract. A contract to provide a service is also a monetary matter. What do you mean no? It doesn’t matter. If I owe you something, and that thing is a service, and now—yes, of course only figuratively, but never mind—I owe to provide something, and the woman agrees, and we both agree that I am exempt from providing that thing, then this is called a monetary matter. It doesn’t matter that the Torah—what is written here is that the obligation of conjugal rights is an obligation between one person and another. The Torah obligates me to provide this to the woman if she demands it. If she waives it, then what’s the problem? In that sense it is exactly like money. It doesn’t matter; in our language, say, this is contract law. It doesn’t matter that the contract does not obligate me in a monetary payment; it obligates me to provide something. But this is contract law. Contract law belongs to civil law. I can stipulate if both sides agree; there is no problem. Fine, so back to our issue. The Talmud says—let me just repeat—the Talmud basically says that the dispute between Rav and Shmuel over stipulating about overcharging apparently depends on the dispute between Rabbi Meir and Rabbi Yehuda about stipulating against what is written in the Torah in a monetary matter. Rav, who says the condition is void—he says there is still overcharging against him, the stipulation didn’t help you—holds that even in a monetary matter the condition is void; you cannot stipulate against what is written in the Torah even if it is a monetary matter. And Shmuel, who says yes, says that you can. So that is apparently the dispute; that’s what the Talmud says. Then the Talmud says no. Actually this would create a difficulty for Rav, because we know that in every place the law follows Rabbi Yehuda, and therefore Shmuel can align himself with Rabbi Yehuda, but Rav cannot align himself with Rabbi Meir because the law follows Rabbi Yehuda. In any case, the Talmud rejects that and makes the classic move: it shows us how both Rav and Shmuel pull both tannaim in their own direction. Each one shows that both tannaim support him. Though in principle they only needed to do this for Rabbi Yehuda, but never mind, they do it for both. How does it work? It says as follows. Rav says: “I can state my view even according to Rabbi Yehuda. Rabbi Yehuda only said it there because she knows and therefore waives it. But here, does he know what he is waiving?” Meaning, Rabbi Yehuda says that if one betroths a woman on condition that she has no claim for sustenance, clothing, and conjugal rights, the condition stands. Why does the condition stand? Because she knows what is involved; she knows that in marriage a husband is ordinarily obligated to his wife in sustenance, clothing, and conjugal rights. She waives it, so she waives it. One is allowed to waive rights. That is what Rabbi Yehuda says. But in our case he does not know whether there is or is not overcharging here. He may be assuming that the market price really is the price at which he is buying, that that really is the market price. He doesn’t know the market price. Therefore here, even though he has essentially waived this right to void the sale if overcharging occurred, since he did not know that this was actually the case, he did not really certainly waive anything. So such a waiver might be something Rabbi Yehuda does not agree with. In such a case it would still be considered stipulating against what is written in the Torah, and one cannot do that. Therefore Rav says: I can fit even with Rabbi Yehuda, not only with Rabbi Meir. Okay? And Shmuel says: “I can state my view even according to Rabbi Meir. Rabbi Meir only said it there because he is definitely uprooting the law, but here who says he is uprooting anything?” Rabbi Meir, who does not accept betrothing a woman on condition that she has no claim for sustenance, clothing, and conjugal rights—that is because there it is clear that he is uprooting Torah law. Meaning, almost the same argument is used in both directions. Here it is clear that he is uprooting Torah law—why? Because we know there is an obligation of sustenance, clothing, and conjugal rights, and he is cancelling it. That one cannot do, even with the woman’s agreement. But in stipulating about overcharging, if the price is a fair price, then you have not uprooted the Torah’s law; if the price is not fair, then you have uprooted the Torah’s law. So it is not clear that the Torah’s law has been uprooted. Incidentally, that was exactly Rav’s reasoning in drawing Rabbi Yehuda to his side. The very same reasoning leads Shmuel to draw Rabbi Meir to his side. Rabbi Meir, who does not agree with stipulating against what is written in the Torah in the case of betrothal on condition that there is no sustenance, clothing, and conjugal rights—there it is clear that he is uprooting, and therefore one cannot stipulate to uproot Torah law completely where one certainly uproots it. But if you stipulate a condition such that Torah law may perhaps be uprooted, then yes, because maybe it won’t be uprooted and maybe it will, so this condition can in fact take effect. Now let’s pause and think: what does that really mean? It turns out that according to Rav, what is the dispute between Rabbi Meir and Rabbi Yehuda? It is a dispute in contract law, right? Therefore he says: if the contract is a contract that both of us understand, and one side waives, then he can waive. In our case, why can’t he waive overcharging? Because one side doesn’t really know there is anything problematic in this contract. Therefore his waiver is not truly a waiver. The whole discussion is a discussion in civil law, right? That is clear. There is some contract here, and the question is whether the waiver is a serious waiver or not, what the contract says, what it doesn’t say; it is a dispute in civil law entirely. And that is what Rav says, right? What does Shmuel say? Shmuel says this is a dispute over the question of where the prohibition of stipulating against what is written in the Torah was stated—this ritual rule that a condition contrary to what is written in the Torah cannot take effect, right? This is not about contract law. It has to do with contract law, but it is a rule in contract law laid down by the Torah. What’s called mandatory law—you can’t stipulate against it. Okay? Therefore this is basically a dispute in prohibition and permissibility, over the question of where you are considered to be stipulating against what is written in the Torah and where you are not. He says: only where you definitely uproot the Torah’s law does the rule apply that you cannot stipulate against what is written in the Torah. If you do not definitely uproot it, then this rule does not apply. It’s not exactly a prohibition—I’m not formulating it precisely, because there is no prohibition against stipulating against what is written in the Torah; rather, the condition simply does not take effect. Fine, but the Torah determines that such a condition does not take effect. This is not contract law; it is prohibition and permissibility—the Torah determines where conditions can take effect and where they cannot. This is a dispute over what the Torah says, right? Basically this is ritual law, not civil law. It’s like a prohibition: you are not allowed to do such a thing. It does not belong to evaluating the intentions of the two sides, or what the contract says, or whether the parties agreed or did not agree—that’s a legal discussion in civil law, right? So what comes out? According to Rav, this is a monetary discussion; according to Shmuel, this is a discussion of prohibition. And this is really the liar paradox, right? Compare it to Beit Shammai and Beit Hillel, which was an anti-paradox. There I said that if I go with Beit Shammai, then the law really is like Beit Shammai, and if I go with Beit Hillel, the law is like Beit Hillel—that’s an anti-paradox. Here it goes exactly the other way. If I go like Rav—if Rav is right—then this is actually a monetary discussion, and in monetary discussions the law follows Shmuel. If Shmuel is right, then this is a discussion of prohibition, and in matters of prohibition the law follows Rav. So it really comes out as a paradox, right? There are some very interesting points here, because among the medieval authorities—I brought a few sources here too—when they discuss whom the law follows regarding stipulating about overcharging, the medieval authorities disagree. Tosafot there in Bava Metzia 51 brings the words of Rabbenu Hananel, who ruled like Rav. Why? He says: “and the law follows Rav in matters of prohibition,” therefore he ruled like Rav, the law follows Rav in prohibition. Tosafot objects: “That is astonishing, because they are not disagreeing about whether it is permitted to do this, but about whether he must return the overcharge, and the law follows Shmuel in monetary matters.” Rav says this is a dispute of prohibition—sorry, Rabbenu Hananel says this is a dispute of prohibition, and therefore we should rule like Rav. And Tosafot objects: what are you talking about? They are not discussing whether it is permitted or forbidden to stipulate this way; they are discussing whether the stipulation takes effect or not. This is contract law. Therefore the law should follow Shmuel, because it is a monetary dispute. That’s not exactly what I said earlier. It’s very interesting, because according to what I said earlier, neither Rabbenu Hananel nor Tosafot is really right. Because according to Rav this is a monetary dispute, and according to Shmuel it is a dispute of prohibition. Yet here both Rabbenu Hananel and Tosafot assume that the nature of the dispute is one agreed nature, according to both Rav and Shmuel. The only question is what that nature is—whether that nature counts as a dispute of prohibition or a monetary dispute, right? That is the disagreement between Rabbenu Hananel and Tosafot. That is not what I said earlier. Why? Because I think Tosafot understands the dispute the way I analyzed Shmuel earlier. The dispute is indeed a dispute of prohibition, except that—he says what I noted before, that I wasn’t being precise. There is no prohibition in the Torah against stipulating against what is written in the Torah, right? If you make such a stipulation, the condition simply isn’t valid. The mechanism of the condition is not valid in Jewish law if you stipulate against what is written in the Torah, that’s all. There is no prohibition to do it. So Tosafot says: true, the dispute is a dispute in the Torah’s laws, but it is not a dispute about something that is forbidden or permitted for me to do, and therefore this is not called “the law follows Rav in prohibitions.” Because although it is not monetary law—according to both Rav and Shmuel this is not monetary law, yes?—on the other hand it is not really a matter of prohibition either. So Tosafot says it has the status of monetary law, not of prohibition, and therefore the law follows Shmuel. Fine? Because he argues—I said before that according to Shmuel this is a dispute of prohibition. Tosafot says that even according to Shmuel it is not really a dispute of prohibition. Why? Not because my earlier analysis is wrong—he clearly accepts exactly the analysis I gave earlier; you can see it, he says it. Rather, he says that even according to that analysis it is not a dispute of prohibition, because a dispute of prohibition is only where the Torah forbids or permits something, and here, even according to Shmuel, that is not the case. The question is what the condition takes effect on—that is the dispute—but there is no dispute here over whether I am permitted or forbidden to do something. That is not called a dispute in matters of prohibition. And since Shmuel says that, the law follows Shmuel in such a case. But it also isn’t monetary. Fine, but still you can’t say the law goes against Shmuel, because Shmuel himself agrees it’s prohibition—no, Shmuel does not agree that it’s prohibition, because this isn’t called prohibition. Fine? Therefore Tosafot says that one should rule like Shmuel. Rabbenu Hananel says: what are you talking about? If even Shmuel agrees this is a matter of prohibition, then we must rule like Rav, because this is called prohibition, since the dispute is over whether one can or cannot stipulate this way. For me, Rabbenu Hananel is very difficult. Tosafot does not contradict what I’m saying; Rabbenu Hananel does. Why? Because according to Rav, clearly this is a monetary dispute. According to Rav there is no doubt this is monetary. As for Shmuel, my earlier analysis said this is not monetary—that’s clear—but I also said it is a dispute of prohibition. Here Tosafot says: no, because it’s not about what is forbidden and what is permitted. True, it’s not monetary, but it’s also not prohibition; it’s something of another type, and never mind for now what type. Okay? So Tosafot, even if he accepts my earlier analysis, can still disagree with me and say: according to Shmuel this is not a dispute of prohibition such that the law must follow Rav. So Shmuel remains self-consistent. But according to Rav this is certainly monetary, and then the law follows Shmuel. Okay? Therefore Tosafot is right to say: true, I can’t tell you this is a monetary dispute, but it is certainly not a dispute of prohibition. Right? And since that is so, the law follows Shmuel, because if Rav agrees that the law follows Shmuel, and Shmuel himself certainly doesn’t say the law follows Rav—it remains open—then we must rule like Shmuel. So Tosafot is right even according to my analysis. But Rabbenu Hananel goes all the way in the opposite direction, and that clearly is not right according to the analysis I gave earlier. According to my earlier analysis, Rav certainly says the law follows Shmuel. Shmuel perhaps does not say the law follows Rav, so what basis is there to rule like Rav? There certainly is none. You can say: I don’t know what to do here. You can say like Tosafot, that in any case we will rule here like Shmuel, because Shmuel himself certainly thinks the law follows him, and Rav according to his own position should also rule like Shmuel. So for that reason we rule like Shmuel, even though it is not monetary, because it is also not prohibition. Fine? But how can you say what Rabbenu Hananel says? That is really hard. Because Rabbenu Hananel assumes that if we go by Rav, then certainly this is a dispute in monetary law, and then the law follows Shmuel. So how can one rule like Rav? That certainly cannot be. You can say either we rule like Shmuel, as Tosafot says, or that I don’t know what to do—throw up my hands, wait for a heavenly voice, I don’t know. Okay? But to rule like Rav is really difficult here. Anyway, perhaps he has ideas; maybe one can explain Rabbenu Hananel on this point. But for our purposes, what I wanted to demonstrate here is that in halakhic decision-making, the paradox and the anti-paradox that I brought earlier—which at first glance seem, as Yossi said before, like a sentence that says nothing—both the paradox and the anti-paradox, of course, a kind of construction that in any event says nothing. Why should I care whether this sentence is true or false? It has no content at all. So what does the sentence mean? A true sentence means its content is correct; but this sentence has no content at all. Go read Shmuel’s friend—what’s his name? Rona Aharoni. Rona Aharoni is actually a friend of mine. Yes, I first heard of him from you. Your anti-friend? No, I don’t understand. The first time—from you. Mathematician, mathematician, perfectly fine, yes. In any case, he really argues that these sentences are word games; they assert nothing, and therefore there is no point discussing whether they are true or false. That is basically how he solves the paradox, or the anti-paradox, of these sentences: they say nothing. But here I’m now giving an example showing that that is not true, because in our example there is the same construction as paradox and anti-paradox, and here there is a question how to rule in Jewish law. Meaning, it does say something. These sentences—“Sentence A: Sentence A is false,” or “Sentence B: Sentence B is true”—those sentences say nothing; they talk about themselves when they themselves say nothing. So if I am not me, then who am I anyway? Right? It doesn’t say anything, so you can say there that these are just sentences and nothing more. There is no issue here; it’s a non-issue, because the sentence says nothing. So what does it mean to say the sentence is true or the sentence is false? There is supposed to be some correspondence between the content asserted by the sentence and something happening in the world. But the sentence says nothing. You can say maybe it’s nonsense. But here I’m showing you that the same structure as the liar paradox and anti-paradox also exists in relation to things that definitely say something about Jewish law, about reality, whatever. There is a real question: do we rule like Rav or like Shmuel? Do we rule like Beit Shammai or like Beit Hillel? And the structure is really a structure of paradox and anti-paradox. And that shows that you cannot solve the logical problem of paradox and anti-paradox the way our friend Rona Aharoni solves it. Because that may be true regarding the original examples used to illustrate paradox and anti-paradox, since those claims really don’t say anything. But what will you do here? Fine, here there is a real question. What does it mean—Rav and Shmuel say nothing? Of course they say something. You get stuck because of the rules of Jewish law, but they are saying something, namely whether one may stipulate concerning overcharging or whether one may not stipulate concerning overcharging, or whether one may stipulate—yes, Beit Shammai and Beit Hillel, it doesn’t matter, in all the halakhic disputes between Beit Shammai and Beit Hillel. Do we follow the majority in wisdom, or do we follow the majority? Halakhically he says this regarding free choice, body and soul. No, I’m talking about the specific claim here. And regarding the specific claim here, I’m saying that he may perhaps be right about the original claims by means of which the paradoxes were introduced, because those claims really say nothing; they’re some kind of game with truth values. But when I show that a similar structure exists also with claims that make assertions about Jewish law, about reality, whatever, that means there is a real problem here. Meaning, again: how do you decide the dispute? There is such a dispute. How do you decide it? Give him half of the overcharge. What do you mean? I mean some sort of compromise—take—You can’t. What do you mean, give him half the overcharge? That isn’t—to not give the woman the full conjugal rights you owe her, that is stipulating against what is written in the Torah. No, to stipulate about conjugal rights, not overcharging. And how would that help? Return only half the overcharge. That’s not—you are obligated to return all the overcharge. Yes, if it’s not—That isn’t a solution to the paradox. It’s just a practical rule of conduct—how we should behave. How to rule in Jewish law? So do half, like a compromise ruling in a court in a case of uncertainty. Yes. Fine, that’s only a question of what to do in practice. But of course it is not a resolution of the problem, because it still goes against the Torah. The Torah obligates returning the entire overcharge. So that doesn’t help. You are equally a wrongdoer according to the one who says that this condition doesn’t take effect, understand? Because you are a thief; you are taking half of the overcharge, and it isn’t yours. If the condition does take effect, then it also isn’t yours, and then you’re a thief on half the overcharge. Fine, you can say that the court can confiscate half the money, and then you won’t be a thief. That’s a technical solution, but you can’t really solve the problem. You can’t offer a halakhic ruling here. You can offer us a way to behave. Fine. Yes, like we talked about the African king—I don’t remember—yes, with the diamond. Take your son, marry him to his daughter, and everything will be fine. Solve the problem; leave me alone with gimmicks. That’s Litvak’s question about that story. Fine. So this is an introduction to paradox and anti-paradox in the halakhic context. It may be that the Rif—after all, you asked why the Rif ruled like Rav—maybe, as you said, according to the Rashba’s explanation of conjugal rights, anything that is not prohibition perhaps gets called monetary. It may be that the Rif says exactly the opposite: anything that is not monetary I call prohibition. And if I—And which is monetary? Sustenance, clothing, and conjugal rights? No, sustenance, clothing, and conjugal rights is the dispute between Rabbi Meir and Rabbi Yehuda. I’m talking about stipulating concerning overcharging. Rav and Shmuel are disputing about stipulating concerning overcharging, not about sustenance, clothing, and conjugal rights. Okay. They’re disputing whether sustenance, clothing, and conjugal rights is—No, sorry, no—they’re disputing the question regarding overcharging, whether overcharging is a monetary matter or a matter of prohibition. Stipulating concerning overcharging. So if the Rif thinks it is prohibition, then fine, he rules like Rav. But why does he think it is prohibition? Rav himself says it is a monetary problem. So how can you rule like Rav because you think this is a matter of prohibition, when Rav himself, whose view you are adopting, says it is a monetary matter? Maybe he sees it as—You understand, it’s problematic. Meaning, to rule like Rav but not for Rav’s reason—but then again, what are you doing, disagreeing with both Amoraim? Interesting question, I don’t know. In any case, one might have said, on the face of it, that the obvious solution—if one wants to rule like Rav and not like Tosafot—would be to say that here this is indeed a case of the rule that the law follows Rav in prohibitions. And with Rav and Shmuel in monetary matters we won’t be able to derive a ruling from it, so we would decide this as an exception to the rule. But the Rosh doesn’t say that. Right, the Rosh really doesn’t. The Rosh rules this way because it is prohibition and the law follows Rav in prohibitions. Fine. Finding circumstances to explain how he rules is one thing, but how to understand the Rosh is another. Okay, so that is regarding this. Now with respect to the paradox of self-reference there are proposals—I don’t remember whether I mentioned this last time. Maybe another example I mentioned now is Buridan’s donkey, yes, Buridan’s donkey, which stands at equal distance between two troughs full of good things and dies of hunger, because it has no way to decide whether to go to the trough on the right or the trough on the left because of symmetry considerations. Basically this is a somewhat similar situation. Right? Meaning, obviously the true solution is to go to one of the troughs at random, but the random solution is exactly the kind of solution you suggested. Meaning, okay, we’ll find some solution that gets us out alive, but you still haven’t really explained to the donkey why to go right or why to go left; for that there really is no reason. So in that sense I am looking for a genuine solution to the problem—how to behave in the hypothetical problem, not in the halakhic question, yes? It’s like when Buridan originally presented this question, he presented it as an illustration of what it means to be rational. What does it mean to be rational? Seemingly it means to take steps that have justification, right? So what does it mean to be rational in the case of this donkey? If he goes right, he took a step with no justification—why not go left? And vice versa. So being rational really means doing nothing at all: passive omission is preferable, and dying of hunger. What is rational about passive omission is preferable? Because if you don’t act, you don’t need a reason in order not to act. You need reasons in order to act. That’s the idea of passive omission. The idea of passive omission is preferable is like “the burden of proof is on the one seeking to take from another.” If you want the court to act, they need a reason in order to act. In order not to act they need no reason, because they are doing nothing, so no reason is needed in order not to do; a reason is needed in order to do. Okay, so he brought this as an illustration of the question of rationality, okay? And then he says: basically the point is that there is no rational solution here. And you’re suggesting to me: okay, but there is a kind of supra-rationality, yes, a higher rationality, that says first of all one must stay alive. Forget behavior according to reasons—you want to stay alive. So that’s a different matter. That’s the kind of solution you were suggesting here. But I’m really looking for the definition of rationality in such a situation. If someone says: I want to take a step that is genuinely justified, what am I supposed to do? The truth is, I can offer a justification for a rational step in such a situation. The donkey will attach itself to a random generator, okay, that decides whether to go right or left at random, and this compels the donkey—it drags the donkey along against its will. So that’s not rational. Completely rational. Because the attachment—the attachment to the random generator—is completely rational, because only that way does it stay alive, right? Like tossing a coin. No, but if I toss a coin then afterward I still have to do what the coin says, and then they’ll ask me: why are you going right? Why not left? Why not against the coin? Why according to the coin? So that doesn’t solve the problem. I’m saying: attach yourself to a random generator, and that random generator will decide right or left at random and will force you—you tie yourself to the generator and it will take you by force. It’s like tossing a coin that is connected to a machine so that the coin itself also takes you to the solution. Sit in a car, toss a coin, and the car drives. Why? Because the very attachment to the generator is completely rational, since only that way do you stay alive. Right? There’s no question as to why I attached myself to the generator, correct? And from that point onward, it already takes me; those are not my decisions, and the generator doesn’t need to be rational. I am rational; the generator is a machine, it doesn’t need to be rational. In my opinion this is a genuine solution to Buridan’s problem of rationality. So for example—I’ll just give you—I think I need to write a column about this. Maybe in the dispute between Rav and Shmuel one could do the same thing. Tie ourselves to a random generator that will decide whether to go like Rav or like Shmuel, and give this generator absolute authority in all issues of stipulating against what is written in the Torah. Stipulating concerning overcharging. The ruling in Jewish law would be that both of you go to that generator, put the money with it, and the generator will take the money and give it to whoever it wants. That is the ruling. But the generator will act randomly? Yes, sometimes it will give to this one and sometimes to that one. Not according to halakhic judgment. Correct, correct. I think that is the right passive omission for this case. That seems to me—I don’t know, I have to think about it. It just occurred to me now; I need to think about it. Fine. “One who wishes to become wise should go north; one who wishes to become rich should go south.” If the donkey wants this in order to become wise, then it should go one way. If it wants to live, not to become wise, then to become rich it should go south. So it should go toward the heap. Which direction? There are two heaps. It wants to eat. Fine, so let it go to the left—what can you do? Why? Why not right? Because it’s not rational. But on the right too there is the—Not on the right, why not? Because “one who wishes to become wise should go north”—that’s behind, leave it, you’re giving me homiletics. There are two troughs here. What is this? One who wants to eat should go either right or left. First of all they’d call him a donkey. He wants to eat, so let him go right. Donkey? That’s Dov. What’s his name, from the Gashashim. Yes, “the nuclear superpower,” what’s his name, Ziegel and so on. Fine, yes. I started to say that with Buridan’s donkey I used it in a somewhat different context, because my claim really was—and it fits here very well. I need to think about it; it’s interesting. I wrote this in the book Science of Freedom. I brought the example of Buridan’s donkey and called it Buridan’s man. And think about the deterministic worldview. In the deterministic worldview, basically the human being is a machine, right? A machine that makes decisions in an entirely mechanical way. There is no decision in the free sense, meaning that there are two possibilities and you decide freely in favor of possibility A or possibility B. Rather, you are driven by all sorts of causes. And if you have some illusion of deciding, that is only an illusion, but in fact you are driven by the laws of nature. Yes, the laws of nature. Now what I argued is that if a deterministic picture stands, I ask now a deterministic or materialist-determinist person, okay? A person like you, whom you conceive as a deterministic machine, standing between two troughs at equal distance, perfectly symmetrical. What will happen? So you’ll say: what do you mean? He’ll toss a coin because he has to live, right? But a person doesn’t toss a coin; a person is a deterministic machine. If he acts, if he makes a decision, then there has to be a cause producing that decision, right? Because of the laws of nature. A physical cause. Not a reason in the justificatory sense. Maybe there is a physical cause. Now I say: the whole world—I’m speaking now of the whole world—is perfectly symmetrical between right and left, and I am a pointlike person, okay? A pointlike person with absolute symmetry between right and left, two identical troughs and I’m in the middle. Everything else is the same. Only my body structure is different—well yes, but that’s just physics, it shouldn’t make a difference. The fact that the person is pointlike isn’t interesting. No, it doesn’t matter. It does matter. Why does it matter? Because your body structure is not an imperfect mirror image. The deterministic person will have to conclude that in such a case the person will die of hunger. Why does he have to be deterministic? Suppose you put a robot there. Right, I’ll show you what the answer is. The robot too will die of hunger. Obviously. No, it won’t die. I’ll show you what the answer is. The answer is: true, but the probability that such a situation will arise, because there are additional factors—It’s not clear; this is a theoretical question now. The probability is zero that it will really be like that. True. So the answer is yes. So what? What does that say? Nothing. It says nothing except that no determinist agrees to that. Why? Because it is obvious to him that he won’t die of hunger. It’s obvious to him that he won’t die of hunger because it won’t happen. Not because it won’t happen, but because he’ll decide to toss a coin. But he can’t decide. Exactly. He claims he can’t decide, but what does he believe? He believes he can decide. That is exactly what I’m claiming. A thought experiment—you can always derive from it: yes, he’ll die of hunger. What’s the problem? Even the answer he gives you is itself deterministic. That is not—if he is right that he is deterministic, then he didn’t give you an answer. I think he didn’t. I’m trying—after all he’ll die of hunger. Obviously. A thought experiment is always like that. You can always say: yes, certainly, in that possible case. That is the claim. If so, fine, if he says to you yes, then yes, he’ll die of hunger. But why would a robot die of hunger? Why would a robot die of hunger? What do you mean? Unless it’s a rational robot. But no—a mechanical robot. What is rational? I don’t care; it’s irrelevant to rationality. It’s a mechanical robot. Meaning, it is affected by the laws of physics; only the laws of physics operate. A perfectly symmetrical robot, right and left, in software too, in hardware too, perfectly symmetrical. Everything, clearly. I’m saying the human too is symmetrical. All the physics is symmetrical. The human—the physical dimensions of the human too—everything is symmetrical. Fine? Except that he has a spirit, I don’t know, or something, if I think he has one. If you don’t think he has one, then the human is a physical creature, and if everything is symmetrical he’ll stand there and die of hunger. There is a theorem in mathematics—that is, a statement saying that if there is a system, say a differential equation or whatever, some system of laws, the solution has at least the symmetry of the problem. A theorem in mathematics. So if the problem is symmetric between right and left, the solution too will be symmetric between right and left. The point is that the probability that such a fully symmetric situation will occur always tends to zero. I don’t care about probability. I’m talking about a hypothetical world in which it is perfectly symmetrical. The answer is spontaneous symmetry breaking. The answer is yes, he’ll stand there and die of hunger. Yes. I’m saying that this thing will never happen. He puts himself in front of a mirror. I’m saying: you’re a determinist; see that this is what follows from your view, and now decide whether that really is your view or not. That’s all. If yes, then so be it. In my opinion an argument like this won’t persuade any determinist. I’m not sure. I think an honest determinist could indeed be persuaded by it—someone who really thinks he’s a determinist. I think the robot too won’t stand there and die of hunger. What? Determinist—I didn’t understand. I think the robot too won’t stand there and die of hunger, because there’s no reason this should specifically be passive omission. Passive omission is preferable is one particular principle in certain cultures. Not true, not true. Newton’s second law says that if no force acts on you, you don’t move. I’m now talking about forces, not rational considerations. If equal forces are acting from both directions, for the sake of argument. No, there are physical forces. In the end the robot is a physical creature. Why should I care? You’re talking about the software level; that’s not interesting. Software only operates hardware. In the end there are electrons moving here, and a force acts on them. So now if everything is perfectly symmetrical, the robot cannot move right. What would move it right? Everything is symmetrical physically. Even if there is software in it, looking at software is already looking at too high a level of integration. I’m saying: show me in the physics how the electrons move right. It will stand there and die of hunger, that’s obvious. What? Yes, and the donkey too. I’m saying the donkey really will stand there and die of hunger. It’s not a joke. The donkey will stand there and die of hunger, that is clear, if it has no choice. Unless donkeys have free choice, but if they don’t then they really will stand there and die of hunger in the hypothetical case where everything is of course completely symmetrical. In that hypothetical case the donkey really dies of hunger. And the question whether the human also dies of hunger or not depends on whether you are a determinist or not. There is a main point here that maybe is causing the difficulty: the very assumption that there can be a symmetric situation—beyond the fact that it’s impossible, that things can’t line up that way because it isn’t plausible—I think that if there were such a person, a symmetric person, then assuming consciousness is a materialistic matter, his consciousness would not be the kind of consciousness I know. It would be a different consciousness, and so what seems to me—I think of myself, I imagine that I or any other person—No, fine, you’re returning to Shmuel’s argument. You’re basically saying: true, he will die of hunger, and that’s it. Fine. The question is whether that’s what you believe. If so, then it is not a counter-argument. But it’s not simply that he’ll die of hunger. You say “he”—it won’t be a human being as we know one. It will be a human being. It will be a human being. It won’t be a human because his consciousness won’t be—If you’re a determinist. A human being is not symmetric; if he were symmetric he wouldn’t be a human being, he’d be something entirely different. If you’re a determinist. But if you’re not a determinist, there is no obstacle to there being a symmetric human being. So I’m saying, again, you’re returning to Shmuel. If you’re a determinist, then indeed, he will die of hunger. You’re only providing the explanation of how it happens. Fine, that doesn’t matter. You’re still saying that the determinist stays inside his own loop. I’m saying that removes the sting of the question. No, I don’t think so, because if you really think about it honestly, I assume at least some determinists will say okay. I think what bothers you—something bothers you about this thought—is that you are thinking of a human consciousness, and then you say: a human consciousness can’t fail to choose, it will decide in some direction. And that is true. Human consciousness is not symmetrical; it is not a symmetric thing. I’m saying, once more, that is if you’re a determinist. If you are a determinist, then you make my present consciousness depend on my physics. And you say: since I am not symmetrical, my consciousness is not symmetrical either, and if I were symmetrical my consciousness would be symmetrical. But I am presenting the anti-thesis, the non-deterministic one. And the non-deterministic anti-thesis says that consciousness is not a function only of my physics. It has an effect on the physics, but that’s not all there is. So again we come back to this: the determinist will assume determinism and remain where he is. The interesting question, of course, is whether a deterministic person can, in a deterministic fashion, make a decision to harness himself to a random generator in order to live—exactly like with the issue of rationality. Right, to harness himself to it is a symmetrical action. I harness myself to a random generator, right? That is a completely symmetrical action. The generator is here; so far there is nothing asymmetrical in it. Now this generator produces, at random, either a movement to the right or a movement to the left, and I harness myself to it, meaning it will take me with it. So in fact I have solved the problem here and broken the symmetry without breaking the laws of determinism. A deterministic person doesn’t make decisions. If he is deterministic he doesn’t make decisions; it happens to him, it happens to him. Doesn’t matter. He’ll “decide” in order to live, of course as a mechanical result. What I call—what he calls a decision is what’s called a decision. Not in order to live. Not in order to live; if it’s in order to live, then it’s already not deterministic. No, “in order to live” as a computation. Never mind—he feels it’s in order to live, but he is built with a survival instinct. Fine, so you call that the libertarian illusion, that it’s in order to live. That’s why we use that language. You’re right. But what we call the survival instinct, which is really just mechanics, will lead him to harness himself to a deterministic machine that will take him to one of the two sides. Here it won’t be a solution. Unlike Buridan’s problem, where the problem was rationality—there it would be a solution. For the problem of determinism it won’t be a solution, because in a deterministic world there is no random generator either. A random generator is also non-deterministic. Meaning, how can it choose randomly right or left? What does random mean? If it is asymmetrical then it will choose according to the direction dictated by the asymmetry. If it is symmetrical then it simply won’t go anywhere, and there won’t be any random generator either. Right. So it solves Buridan’s problem, but it doesn’t solve my problem. Harnessing to a random generator doesn’t solve it. Okay, fine. Today we played around a bit, but…