Rabbi Gedaliah Nadel’s Thought – Reasoning in Halakha – Lecture 5

Table of Contents

• The style of the Torah and its implications for interpretation and Jewish law
• The example of “when brothers dwell together” and Rabbi Gedaliah Nadel’s rationale
• The dispute over the meaning of “to establish a name” and alternative explanations
• The question of the formal cutoff and whether it “comes out of the verse”
• Interpretive authority, changes across generations, and the parallel to periods in Jewish law
• Opening Chapter 3: reasoning versus first principles
• Non-Euclidean geometry, mathematics versus physics, and a priori propositions

Summary

General Overview

The central message is that the Torah is written in a literary-poetic style, not as an informative law code, and therefore interpreting the Torah cannot be a dry, linear reading of words. It requires attentiveness to “what blows between the words” and to the interpreter’s conceptual world, while even the narrative sections themselves take part in generating Jewish law. The central example is the rabbinic derivation from “when brothers dwell together” regarding the law of “his brother’s wife whom he was not in the world with,” for which a simple rationale in the style of Rabbi Gedaliah Nadel is proposed, alongside a debate over whether such reasons explain the formal line drawn by the law or only its general direction. Later, Chapter 3 opens on reasoning, which is distinguished from first principles, and Rabbi Gedaliah’s position is presented regarding axioms as “truths” that the Holy One, blessed be He, implanted in a person, as opposed to modern approaches that see them as arbitrary assumptions, including a discussion of non-Euclidean geometry and the relationship between mathematics and physics.

The style of the Torah and its implications for interpretation and Jewish law

The written Torah appears in language that includes prose, rhetoric, and poetry, and its meaning is not limited to dry information or to messages that are found linearly in the sentences. Interpretation changes from the outset when one approaches the text as a “poetic” text rather than as an encyclopedia, because the atmosphere and narrative framework are part of the halakhic meaning and not merely a literary addition. The Oral Torah continues this form of presentation in an associative way, and Maimonides’ attempt to formulate Jewish law in a defined legal style is seen as contrary to the halakhic tradition, not as a problem of “primitiveness” or inability to formulate things clearly. Interpretation is not merely a “technology,” because in every exposition there is a textual trigger, but the decision of what to learn from it depends on logic and on the interpreter’s choice, and therefore the interpreter’s own world becomes part of the interpretive product.

The example of “when brothers dwell together” and Rabbi Gedaliah Nadel’s rationale

The example is the opening of the section on levirate marriage: “when brothers dwell together,” which is written in the language of narrative rather than as dry legislative wording, and this narrative framework enables the Sages to derive a precise law from it. The Sages learn from here the law of “his brother’s wife whom he was not in the world with,” according to which if the surviving brother was born after his brother’s death, the law of levirate marriage does not apply, and it is established that the story is not just “atmosphere” but an actual source for Jewish law. Rabbi Gedaliah Nadel explains that the commandment of levirate marriage applies when the two brothers lived “in the same generation” and in the same way of life, because the surviving brother takes over the deceased’s inheritance, can conduct the life and property as the brother would have conducted them, and can father a son and raise him in the same way in order “to establish a name for his brother,” as the passage says. According to this explanation, when the brother is born only after his brother’s death, he already belongs to a different world, and therefore the home he establishes cannot be considered a real continuation of the home that was lost, even though there is genetic closeness.

The dispute over the meaning of “to establish a name” and alternative explanations

An alternative claim is raised in the name of Abarbanel about a “soul” that enters a “new body,” and that the preferred place for this is the brother, but it is argued that this too can be reconciled without contradiction by saying that the new brother himself is the “continuation” and therefore does not need to perform levirate marriage. It is argued that Rabbi Gedaliah does not usually explain in mystical terms, but rather “on the plane of everyday, tangible human psychology,” and it may even be that he does not speak in the language of souls at all. Questions are raised from family reality, such as hatred between brothers or the woman’s attitude toward her husband, and the answer is that the idea of “establishing a name” is not a matter of appreciation, symbols, or “hanging up pictures,” but of leaving something of the structure and mentality in the world, in a way that does not depend on love or hatred. It is asked whether levirate marriage also existed in other societies, and it is said that it is known that such a custom existed, and that in the story of Judah and Tamar a kind of levirate marriage appears even before the giving of the Torah.

The question of the formal cutoff and whether it “comes out of the verse”

It is said that one could have “continued the idea” of “together” and limited the obligation to brothers who literally lived together, or derived additional conditions such as age, but “from the precision of the verse” the binding formal shape of the law emerges: “that they had one shared dwelling in the world.” It is argued that it is hard to see how the wording specifically requires even “one second” of overlap, and that a formal cutoff is necessary in every legal system even if the general rationale is understood, so there is no necessity that the line itself be learned from the verse; rather, it may have been determined by the Sages. A comparison is made to Maimonides’ approach to the reasons for the commandments in The Guide for the Perplexed, according to which the reason explains the main point of the commandment but not necessarily the details of the cutoff, because “you have to draw the line somewhere,” and it is said that the attempt to derive even the formal line from the verse is not persuasive. A criticism is presented of the sharp claim that seeing the Torah as a collection of ideas that do not obligate precision is a “Christian view,” and it is said that Christianity is not merely another interpretation but claims that explicit halakhic parts are “no longer relevant” because of a “new covenant,” so the dichotomy is not necessarily accurate.

Interpretive authority, changes across generations, and the parallel to periods in Jewish law

It is explained that cultural distance changes one’s ability to understand and to argue, and therefore a hierarchy of periods such as the Tannaim, Amoraim, Geonim, medieval authorities (Rishonim), and later authorities (Acharonim) is described in terms of “changes across the generations” and not only “decline of the generations.” It is argued that the advantage of earlier generations is not only hierarchical greatness but closeness to the same milieu and understanding of the connotations and contexts, and therefore their authority is connected to mediation and not only to a formal rule. The question is raised of the “cutoff line” between periods and the fact that it is sometimes retrospective and not sharp, including examples such as “Rav is a Tanna and may dispute,” and the question of the Kesef Mishneh at the beginning of the laws of rebellious elders—why later Tannaim disagree with earlier ones but Amoraim do not disagree with Tannaim. It is said that the possibility of disputing the canon itself or the very authority of the tradition is a different discussion, and that considerations of order and framework can play a role in accepting authority even without full identity with “the truth.”

Opening Chapter 3: reasoning versus first principles

It is said that reasoning, in the language of the Sages, is not what philosophers call “first principles,” but rather something that could have been said differently and yet the Sages thought this is the correct way, whereas a first principle is something whose truth is clear to a person without proof and one cannot think otherwise. A modern debate is presented over whether axioms are arbitrary assumptions that can be exchanged, or “an unshakable primary truth,” and it is said that this is more a philosophical debate than one “within science.” Rabbi Gedaliah argues that in practice there is “no point at all” in this debate when dealing with exercises in formal logic, because one can build consistent systems from different assumptions, but the true first principles are “the truths that the Holy One, blessed be He, implanted in a person,” which every person is convinced of.

Non-Euclidean geometry, mathematics versus physics, and a priori propositions

The example of Euclid and parallels is brought, and it is explained that someone who replaces an axiom and obtains non-Euclidean geometry is “talking about something else, not about space,” and that one can find an application of it on the surface of a sphere, where “any two such lines must intersect.” A distinction is drawn between the mathematician’s approach, which sees such systems as consistent structures without commitment to the world, and the physicist’s approach, which determines which system describes physical space of a certain kind. The difficulty is raised of how one knows that axioms are true claims about the world if they cannot be fully confirmed observationally, and it is emphasized that the certainty comes from strong intuition and not from experiment. The discussion is connected to the idea of synthetic a priori propositions and to the question of the relationship between the structures of thought and the structure of reality, and it is said that by the end of the chapter the associative connection to matters of Yom Kippur had not yet been completed.

We were near the end of the second chapter, on page 15. It starts on 14 and we got to 15. I’ll just finish that. The next section of chapter 3—we’ll see how much I manage to get through. It seems to me it connects, at least associatively, somehow also to matters of Yom Kippur, so maybe we’ll even manage to make some connection. In any case, in the second chapter, when he talks about Scripture, I remind you that he is talking about the sources, the sources of Jewish law: Scripture, midrash, reasoning, a law given to Moses at Sinai. So here he was talking about Scripture. And in that context he begins—yes—that Scripture, the Torah, is written in a style unique in kind, unlike anything else, in a language of prose, rhetoric, poetry, and so on. And somehow we wandered a bit into discussing what poetry is as opposed to prose, how to define those things.

And it seems to me that he doesn’t mean only—he does do that—but he doesn’t mean specifically to marvel at the quality of the poetic writing, or of what he calls prose in the literary sense, not in the sense of an encyclopedia. Rather, he wants to point out that this is not writing of an encyclopedia or computer code. And that means that when we interpret the Torah, we have to know in advance that we approach it in a way that says this is not a text whose meaning lies linearly in the words or the sentences. In other words, it’s not something that just conveys information or dry details. There is a lot between the lines no less than in the lines themselves, metaphorically speaking. In other words, there is a poetic dimension.

And that’s not only in the Written Torah. He is speaking about the Written Torah, but I think I mentioned a bit that this is true also of the Oral Torah. The fact that the Talmud is not written like the Shulchan Arukh or like Maimonides, but rather in some more associative form, means that the Talmud too continues this mode of presenting things. And conversely, Maimonides, who tried to put things more into a defined legal formulation, got hit over the head for it, because that somehow ran against the mode of thought, against the halakhic tradition. And I don’t think that reflects primitiveness or lack of expressive ability. Rather, there is some kind of statement here: it is not right to present things in a cut-and-dried way as a collection of commands; you have to let some of the surrounding atmosphere take part in the interpretation of the commands.

These commands cannot be written in a merely dry and informational way, because then we miss the spirit of the matter—not in the ideological sense; the interpretation itself will be wrong. That is, if we relate to a certain text as a collection of informational details, then we are very limited in interpretation. Meaning: what the text says—that’s its meaning. There are not many degrees of freedom there. Again, you can’t close it off entirely, but there aren’t many degrees of freedom. But when something is written—and already when they tell you it’s actually a poem, before you even begin to read it and be impressed by the thing itself—you already come with a different mindset. You come with the sense that you have to understand what air is blowing between the words, what this is really trying to say. And that takes part in the interpretation itself. Not that it gives you this or that sort of experience, but the interpretation given to the text itself is different once the text is defined as poetry and not prose—prose in the sense not that he means, but informational dryness, an encyclopedia.

So that was up to the middle of page 15, and he ends the chapter with an example. A nice example, I think—interesting, and very characteristic of Rabbi Gedaliah Nadel, by the way. Rabbi Gedaliah Nadel, and his students following him, renewed something that maybe in the period of the medieval authorities (Rishonim) would have seemed self-evident, but somehow we lost it—or at least, I don’t know, I as a yeshiva student, the yeshivot lost it: to relate to things and try to understand that they have some simple meaning. Not to jump immediately to abstract theoretical constructions. You can find explanations even for things that seem to us to be what’s called a decree of Scripture. We’ll still talk about the concept of a decree of Scripture. But you can understand the meanings of these things. And in yeshivot, “decree of Scripture” is a synonym for something that has no explanation, or has no explanation—there’s no reasoning behind it. So we’ll still talk about that; Rabbi Gedaliah Nadel also speaks about it explicitly, and we’ll still get to it. But here, let’s look at this example.

“Let us take one example, and there are countless others like it. The Torah begins the passage of levirate marriage with the words, ‘When brothers dwell together.’ This is a beautiful opening in narrative language.” And again I say: “beautiful” here does not mean merely to admire it. It means: notice that there is a sentence here that is not informative. That is, if they wanted only to write the information, they should have said: if someone dies, his wife must enter levirate marriage with his brother. That’s all. What is this “when brothers dwell together”? Meaning, the story here, the narrative framework here, is part of the passage. It is not written like the Shulchan Arukh or like Maimonides. And in that sense, this is what he is talking about here, regardless for the moment of whether this is a “beautiful” opening. Maybe it is a beautiful opening, but that’s not the point. The point is that this is an opening that is a story, not a dry law book. That is what he means to say.

“It could simply have said that if a man dies without children, his brother is obligated to marry his wife in levirate marriage. But the Torah prefers narrative language in order to describe the idea of levirate marriage this way. And behold, the sages learned from the language ‘when brothers dwell together’ a certain law.” The narrative part of the passage not only gives us the atmosphere, not only has literary or artistic value; it takes part in the interpretation itself. In other words, laws emerge from it. So this illustrates everything he said in the first part of the chapter.

So what do the sages learn? “The wife of his brother who was not in his world.” The Talmud in tractate Yevamot says that if the levir was born after his brother’s death, there is no law of levirate marriage. Meaning, yes, if a married man dies, and at the moment of death his brother is not yet in the world, and afterward his mother gives birth to another child, so now he has a brother—the question is whether this brother obligates the woman who remained, the widow, in levirate marriage. So the sages say no: “the wife of his brother who was not in his world.” Meaning, when he died they were not—he was not yet in the world. Is that a decree of Scripture or logic? So, right, in a moment we’ll see. Fantastic logic. Excellent logic. Yes, so that’s what he explains here; that’s the point.

Now again, I, as a yeshiva student—okay, “when brothers dwell together,” together probably means together, so therefore we don’t do levirate marriage. You don’t think about the meaning of the matter, what idea lies behind it. That’s not the sort of thing a yeshiva student does. And with him—Rabbi Gedaliah Nadel—you very often find these things. It’s one of the main things he, I think, renewed: really to look with simple eyes, to try to understand the idea. That behind these things sits some idea. More than that, you have to understand—and I think I’ve spoken about this, and we’ll probably still speak about it more—that this is true in derashot and true in almost everything: there is no such thing as something without an idea behind it. In other words, if there is an explicit verse, then maybe you can argue about it. Even there, Maimonides says there is no such thing; there is no commandment without some purpose, some logic, some idea behind it. But there one can still argue: the Torah said it, so that is what it said; either it meant something or it didn’t mean something; maybe it meant and we can’t understand. Fine. About that one can argue.

But everything that the sages derive—here it says “when brothers dwell together,” and the sages derive that the wife of his brother who was not in his world does not require levirate marriage—you could have not made that derivation. “When brothers dwell together” is not some compelled derivation. I could have extracted other things from it too. It’s clear that once they extract this, the sages had some idea behind it, even though here we are dealing with Torah law, not rabbinic law. In rabbinic law, obviously—they enacted an enactment because they wanted to achieve something. But in interpretation of the Torah, most Torah laws we know—not rabbinic ones—are the result of interpretation by the sages. There has to be logic there. Why? Exactly—why did the sages choose specifically this?

An etrog, whatever. Yes, exactly. Meaning, everything… As I think about it now, I remember—I think I brought this example—of “You shall fear the Lord your God,” to include Torah scholars. Shimon HaAmsuni used to expound every occurrence of the word “et” in the Torah, until he reached this verse and said, “Just as I received reward for the exposition, so I will receive reward for withdrawing from it.” Now take this verse. Fine, let’s say it says “et,” so suppose we already have some assumption that when “et” appears it comes to include something. Okay, accepted. But what does it include? “You shall fear the Lord your God”—to include holy books, paper towels, or tables? I don’t know—what do you derive? Obviously the interpreter has to apply some logic here, meaning to understand what is most reasonable to include as something that one must fear as one fears the Holy One, blessed be He. So the interpreter’s conclusion there, Rabbi Akiva’s, was Torah scholars. Torah scholars. Fine, maybe one could argue about that too, but what?

I heard Rabbi Zolti say that the obligation to fear God also applies to Torah scholars. “The rabbi”—that he accepts. Fine. In any case, when you make a derivation, you have some trigger in the text. The word “et” appears, and from the word “et” you include something. But what to include—that is always your interpretation. You have many ways of including, many things you could include. Therefore there is no interpretation in which the interpreter’s logic is not involved. There is no interpretation that is technology alone.

And therefore, the poetic dimension of the Torah on the one hand really does allow us a certain interpretive breadth that is not attached only to the words. But one must note that on the other hand this also means that the interpretive product does not really come out of the text. That is, it is also a function of the interpreter. The world of the interpreter is an inseparable part of the interpretive product. And therefore this is not only a statement about the text—that it is written in the form of poetry and not in the form of prose. It also means, first, that it is called for that we interpret it more broadly. And second, it also means that the interpretation does not come solely from it. A text that is prose-like, an encyclopedia—in the end what you read is what is written. You don’t have much involvement of the reader in the interpretive product; there’s not much interpretive act there at all. What is written is what is written; there aren’t many tricks. And the poetic form of the text basically says that the interpreter is involved in the product no less than the text itself. Maybe not no less, but he too is involved, like the text itself.

Now back to our subject. Here: “the wife of his brother who was not in his world,” meaning if the levir was born after his brother’s death, there is no law of levirate marriage. And then he explains—now Gedaliah Nadel explains—“The commandment of levirate marriage belongs specifically where two brothers lived in the same generation, in the same way of life. The levir receives the inheritance of the deceased, and if he belongs to the same generation, the same way of thinking, as his brother, he will be able to conduct life and property as his brother would have conducted them.” But that’s not… that’s logic, not Jewish law. It’s logic. Say if they overlapped one day and that already… Wait a second, we’ll get in a moment to where you draw the line; where you draw the line is always a question. But first the question is whether the idea itself works; afterward we’ll see where you draw the line.

“He will be able to father a son and educate him in the same way, and thus establish a name for his brother.” After all, the passage explicitly says that the goal of levirate marriage is “to establish a name for his dead brother.” It says so explicitly in the Torah—that’s the interpretation. The Torah says: what does it mean “to establish a name for his dead brother”? It means, in some form, to continue the brother who died, because he died without children, he has no continuation. So you have to make sure that in some form he has a continuation. So Gedaliah Nadel says: that is the idea behind “the wife of his brother who was not in his world.” Meaning, if you were still with him in the same environment, in roughly the same world, then when you build a home, that home will in some fashion continue the home that he built, or could have continued had he lived. And therefore the law of levirate marriage is relevant only when you really belong to the same atmosphere, the same air, the same form of life, form of thought. If you belong to another generation, then it is already a different world. So the fact that you are his brother means you share genetics, but something very essential is missing from the home you will build, in the sense that it will not resemble, or be a continuation of, the missed home, the lost home. And therefore, basically, the claim is that there is no law of levirate marriage here.

An interesting idea I heard. Why don’t you agree, Yossi? Why is this important? What does it mean to establish a name for his brother—because it will be in the same style? What is “to establish a name for his dead brother”? “Name”—do you take that just as a name, as if the family name will remain? What is “to establish a name for his dead brother”? I claim it means to let the soul enter a new body. So? Then once the soul is available after he dies, where better can it enter than into his brother? But if his brother wasn’t alive, then his brother produces for him the body closest to him. Okay. Not me—Abarbanel. Right, fine.

In any case, by the way, I’m not sure that contradicts this. Meaning, it could be—what idea lies behind that? The idea behind it is that it explains why half a minute after the first brother dies, if the second brother is born, then already he does not have to perform levirate marriage. And Nadel’s story doesn’t explain that. But what if the soul… Let’s continue a moment—if the soul entered this newly born brother, then on the contrary, now he can establish a name for his dead brother. He establishes it. Right. So why shouldn’t he perform levirate marriage? He himself, he himself, he himself constitutes the name, so he doesn’t need to marry the woman. He himself is the continuation. So no need anymore. No need.

Did you really need to write that Pinchas did not die? Why should my grandmother care that Pinchas didn’t die? It’s not just reincarnation. Trace it down to Samuel and see that it’s the same one. Fine, okay. Also an interesting interpretation. But in any case, Rabbi Gedaliah Nadel’s claim is this claim. By the way, of course he would not have accepted such a claim. I’m not sure he spoke in codes; he wasn’t that open—no, no, no. That’s not the kind of thing he would say. No. He wouldn’t say it. Souls entering available bodies now—that’s not his kind of thing. His explanations are always on the psychological, human, everyday, concrete plane. He doesn’t go into mysticism and things like that at all; it didn’t speak to him. I think he didn’t believe in all that. I don’t know if “didn’t believe,” but he didn’t speak that language.

So his explanation doesn’t hold water through the whole poem? Fine, one can argue, but I’m saying: right now I’m learning his explanation. I think it’s an interesting explanation, an explanation—I don’t know—thought-provoking. And what if the brothers hated each other? I didn’t understand. If two brothers hated each other? That doesn’t matter. So what if they hated each other? Does that produce halitzah? Does it mean they aren’t similar? Besides, he can also do halitzah. But beyond that, if they hate each other, so they aren’t similar—what does that have to do with anything? He won’t establish what he says, to establish the dead man’s name in the house in the same form; it won’t be the same thing. Why won’t it be the same thing? It will be exactly the same thing because he is similar to him. Not exactly—it’ll be the same thing because he’s similar to him. What difference does it make whether he hated him or not? It doesn’t have to do with hanging his brother’s pictures on the wall. They differ on ideological grounds, lifestyle. One is this way, one is that—no, the woman, the woman hated her husband with a deadly hatred; she can’t be a co-wife. So what? She can’t. You’re saying that if they force her to marry him she’ll make a home as opposite as she possibly can to the previous brother’s. Maybe she will and maybe she won’t. But no, not necessarily at all.

What does “as opposite as possible” mean? The home that would have been created from the brother and the woman would be a home stemming from the character of both of them. It doesn’t matter if you hate him, so long as the characters involved here are similar characters. It could be that he was wicked and this one is wicked too. So what? What difference does it make? He’ll build such a home. Again, we are not talking about a wicked person’s home; that is exactly the point. To leave him a name doesn’t mean to leave him a name in the sense of esteem. It’s not a matter of leaving someone a name for admiration or whatever, for his personality, hanging his pictures on the wall. The point is that something of him remains, almost biologically I’d say—not biologically, but now as long as it resembles him, it doesn’t matter whether you hate him or love him, you will resemble him. It doesn’t matter. It still leaves him in the world. What difference does it make whether you hate him or not? It is not relevant at all. The fact that you hate him or don’t, that you won’t hang his pictures on the wall—that’s all. Fine, you won’t hang them. That’s not the levirate marriage under discussion here. According to his interpretation, the levirate marriage under discussion here is to leave this mentality, this family structure that was created there, to leave something of it in the world.

Yes, but that really sounds like a very modern kind of explanation, totally simplistic, for such an enormous Torah, something huge that doesn’t even come close to this. Okay. And I’m sure he knew that too. Maybe—but you can’t say that if speaking to students he’d talk like that. No, no, you’re mistaken. Here you’re definitely mistaken about Rabbi Gedaliah. About the interpretations one can argue, but Rabbi Gedaliah I knew a bit, and I know the students too. What would Maimonides in Guide for the Perplexed have said in his head? Not a single word there is this, not simple meaning. Believe me, if he had thought what you are saying, he would have said it. Rabbi Gedaliah was not someone who held back his tongue. What he thought, he said. That’s also why he took blows. So he didn’t hesitate and say things only for students; he said what he thought. On the contrary, often there were complaints against him: why are you saying things you shouldn’t say? “Sages, be careful with your words.” Yes—even if it is true. He was not that type. Now you can argue with him; you can say this is not the right interpretation. Okay.

Rabbi? Yes. Does levirate marriage exist in other societies besides Jewish society? I think so. I haven’t done research, but yes, it is known that there was such a thing. In Greece it certainly existed. No, it also existed in the past, certainly. It was some kind of custom. Look, with Judah and Tamar the Torah describes a kind of levirate marriage even long before the giving of the Torah. So I assume it is not the result of a commandment. That goes against Rabbi Gedaliah, because he was born—the argument is that a brother born after… No. Not that there wasn’t a little child there. A question. Yes. They wait until he grows up. Yes, yes, yes. But that also doesn’t matter so much, which is why I say it also doesn’t matter that much, because I don’t think it has to fit all the halakhic patterns of what happened there. But the idea was there. The idea existed there. After all they discuss whether there really was levirate marriage there or not.

Completely. What did Onan do? He said, “I know that the offspring will not be mine.” What I produce is actually for my brother now. So he didn’t want it, he spilled on the ground, because the offspring would not be his. According to Nadel’s approach, on the contrary, he is making a name for his brother. He is making a name for his brother when he does… He didn’t want it, he spilled on the ground, because the offspring would not be his. According to Nadel’s approach, the opposite: he is making a name for his brother, because he is making a name for his brother—which was what he wanted. But he didn’t want it. What do you mean? But he didn’t want it. He is looking for someone most similar, he is looking for all that. But he doesn’t want that. What do you mean? He doesn’t want that because it won’t be his; because that brother will be walking around his house, not the child he wants, his own child. Exactly. So what’s the problem? So that’s why he didn’t want it. So why does that contradict what he writes? I don’t understand. Because what he says is that they’re looking for someone to continue the brother’s enterprise. Not necessarily the enterprise; someone who will be similar, who will build a similar house, who will be like him. Yes. Then Onan says, I don’t want someone like him in order to establish his name. What? Then Onan says, I don’t want someone like him, in some fantastic way that it isn’t. I don’t see the contradiction to his interpretation. Basically, at least with that first child, it would be as if the child belongs to his brother, not to him. Right. So why does that contradict Nadel? I don’t get it. It fits just fine with him too. I didn’t say it wasn’t fine. He says it will be your child; you will have no connection. Fine, he doesn’t want to continue his brother; he doesn’t want to—that’s exactly the point. Maybe he cared that the home… He cared; that’s exactly what he cared about. I don’t see any contradiction to his words in that. That’s what bothered him. He didn’t want it, and therefore he was punished with death. He got the death penalty, yes, because that whole way of thinking was twisted. No, but the question is what exactly was the twisted thought. That there was a twisted thought is written; the question is what the twisted thought was. That was the debate.

Anyway, that is his suggestion. “But if he was born only after his brother died, then levirate marriage does not apply.” “One could extend this idea further,” he says, “and say, for example, that only brothers who literally lived together”—now we enter the question of where you draw the line. Right?—“only brothers who literally lived together would be obligated in levirate marriage, or only if both were adults at the time one of them died, and so on. Any idea can be extended and expanded, and it can be narrowed and shortened. From the precision of the verse we learn the formal binding form of the law: that they had one dwelling in the world.” Right? “When brothers dwell together”—that they had one dwelling in the world. So from this he argues that from the Torah’s formulation you can derive where to draw the line. Once they lived together in the world, that’s enough.

“Thus we have a language which on the one hand conveys an idea in literary language, and on the other hand enfolds within it a precise law.” Now here too there is room for some hesitation. That same language—I don’t see how from within this language you must insert specifically that they overlapped for one second. “Dwell together”—on the contrary, I could insert into that same language exactly that “dwell together” means they lived together for a significant time, I don’t know. You can say: what is significant time? Like “enough.” Meaning, you have to draw the line somewhere. If you say formally I draw the line where they had one second together, that’s it, because there’s no choice, Jewish law has to be cut sharply—that I could hear. But he wants to say more than that. He wants to claim that even the line itself, even that, comes from the wording of the verse. In other words, “when brothers dwell together” itself also gives me the line of where to cut: once they dwelled together, that’s enough. Here I’m not… there is a little less logic here. What? A little less logic. Exactly. That’s why I say that here I think he already—meaning he doesn’t quite manage to go all the way with his method.

And by the way, this is true in almost all the cases I know from him. Meaning, the idea is a very beautiful idea, and I think at least a very beautiful one, original, I wouldn’t have thought of it, and all in all I think it does fit—that’s what I think, it fits. But when you get to the details—and by the way this is related to Maimonides’ reasons for the commandments. In Guide for the Perplexed Maimonides already says that the reason explains the main commandment; the details many times you won’t succeed in explaining. Where you draw the line, until when, what yes and what no—you won’t succeed in explaining with that reason. Maimonides’ reasons in Guide for the Perplexed, by the way, are very similar to Nadel’s reasons. Not reasons of exactly this kind, but what…

Okay, fine, there you can say it’s esoteric writing, esoteric writing. Fine. But with Nadel it’s not esoteric writing. So that’s why I’m saying that with Maimonides maybe yes. With Maimonides… yes, yes, fine, Maimonides says incense is because of deodorant, bad smell in the Temple, so it sounds ridiculous. Because whoever takes that literally, it sounds ridiculous. Yes, fine, maybe yes, maybe no. I’m not sure Maimonides didn’t mean it. But the steaks in the Temple bothered things so much that they needed incense? Not only steaks, there was more than steaks there, there was… the priests walked around and trod in blood with their robes; I assume there was more there… it didn’t smell like steaks. What? Fine, never mind—that’s another discussion.

I’m only saying that Nadel’s move has in it—and I’m saying for today this is a novelty. The medieval authorities (Rishonim) did this quite a bit, and Torah commentators do this a lot. Maimonides in Guide for the Perplexed did it. But somehow in the yeshiva world we lost it. Meaning, we stop thinking in simple human terms—what is this thing trying to achieve?—and we move to definitions, to these legal-halakhic constructions. And therefore what Nadel does suddenly sounds like a real novelty. But when you think about it, in the end this is what Torah commentators did. It feels dangerous; that’s what scares us in Torah. No, fine, maybe. It may also have sociological reasons. But the fact is that it is considered a major novelty, when in comparison this is simply what biblical commentators did. Many of them. Even Rashi. Yes, all biblical commentators. A great many. You can find many ideas of this kind in Rashbam, in Nachmanides, in Sforno, in all of them. Meaning, among biblical commentators this is standard; this is how they worked.

But in yeshivot they also don’t like learning biblical commentators, because it really seems not yeshivish. It’s not… “You’re giving homeowner explanations; you need to explain legal constructions.” And Rabbi Gedaliah somehow restored, in that sense, the crown of earlier biblical interpretation. He restored it just as it was. I don’t think, by the way, that he has greater or essentially different innovations from what the early commentators did. It’s only a novelty because he comes within our world—yes, already after Volozhin and all the yeshivot—and suddenly someone comes and interprets like Rashbam and Sforno, so it sounds terribly innovative.

On the other hand, one of the things that always bothers me in biblical commentators—and therefore I also don’t really love the genre—is that in the end it really doesn’t fit the details. Meaning, there are details you ultimately can’t explain on the basis of that move. So Maimonides tells us: look, the idea only needs to give us the general direction; the details have to be cut somewhere. So you have to cut them somewhere. For example, here: suppose I accept Rabbi Gedaliah’s interpretive idea. I’d say: the idea is indeed that. Now I ask the question: okay, but where do you cut? That they overlapped for a year? overlapped until bar mitzvah? age 13? I don’t know—something. You can cut it in many different places. It has to be a formal cut. The sages say: cut at birth. The moment there is overlap between them, there is levirate marriage. That’s perfectly fine. This too, by the way, is Maimonides’ way. Maimonides says: take the principal direction; the cutoffs are arbitrary. Meaning, you won’t find an explanation for them in themselves. And that’s fine; somewhere you have to cut.

And if they had cut at age two, then would you have had an explanation? Meaning, you have to cut somewhere. And it’s semi-logical: cut where the logic ends. No, okay, but where is the logic here? I don’t know where the logic is—how would you cut? He says where the brother learned a little from his brother, or learned from him—or no, it’s not exactly like that. You know, it’s like structuralism in… there are approaches in hermeneutics, the theory of interpretation. It’s part of the system. I wouldn’t cut there. No, not necessarily at all. If there’s some overlap with his brother, it’s not exactly like that, because to establish a home means—they did not “dwell together” in the sense of sitting together, but he came out of the womb and already they had dwelled together. No, so that’s what Yossi is saying. Yossi says: but if you went with Rabbi Gedaliah’s mindset, you’d expect the cutoff to be at age 10, I don’t know, or age 13, age 20.

But I think that’s not necessarily exact, because you know, in hermeneutics, in the theory of interpretation, there are several approaches. One of them is called structuralism. Structuralism is basically a view that says… let’s divide them schematically into three approaches—either the author, or the text, or the interpreter. Broadly speaking. The naïve approach says that interpretation of a text is an attempt to discover what the author intended. That’s what people usually understand by interpretation. What did structuralists say? No, interpretation is not necessarily what the author intended; sometimes even the author himself was not aware. Interpretation is what the text says. There is something in the text itself beyond the author’s intention. In a moment I’ll come back to that. And the third thing—yes, Derrida and the other nihilists—speak about the fact that basically the interpreter is what matters. In other words, what it does to me—that is the interpretation, not the text and not the author. “The death of the author.” Yes, exactly. The death of the author, and all sorts of pompous words they like to use. The author is dead, and so on.

In any case, structuralism—and this matters for us here—says: what do you mean, the meaning of the text detached from the author’s intention? The author wrote the text. What could be in the text that the author didn’t intend? If you find other things there, that just goes back to the interpreter. After all, the text is the product of the author. If the author saw the interpretation made of him—that’s Kurzweil and Agnon, yes, ask Kurzweil. So I’m saying structuralism, at least broad parts of it, claims that there is something that affects the author and passes through him into the text. Something in the environment, something in the culture, something in the world in which he lives, that passes through the author into the text without the author necessarily being conscious of it. His subconscious. Without his consciousness. Meaning, if you had asked him, he would not have understood that this is what he had invested in the text, but it is really there. Since the one composing the text is not just a person, but a person who is a pattern of the landscape of his birthplace—that is, all his environment, the whole atmosphere in which he acts—that too is part of the text. Obviously connotations are things that are a function of the environment. The same words themselves, or the same intention of the author, can be interpreted in different ways depending on different contexts.

So clearly there is some influence of the environment. And for our purposes—I’m not going to get into hermeneutic issues now—but I want to return to Yossi’s question. The fact that the law is cut at the point where you were together in the world, even if you were together in the world for one second—what did you learn from your brother? You were a one-second-old infant when he died. What, you learned nothing. But that isn’t exact, because you still live within the same world, you are within the same cultural atmosphere, and in some sense you will resemble him. Quite often there are people—or not quite often, but I saw some—who explain like this, and this is also true if you were born a month after him. Right. That’s why I’m saying: somewhere you have to cut. But that formal cutoff has behind it something not completely detached from the idea. Since resemblance to my brother need not stem directly from contact with him. Rather, I lived in the same house in which he lived, and so in some sense I came out similar.

And I was in the middle of something… yes, there are people who explain this way, for example, the period divisions in the history of Jewish law. Why do Amoraim not disagree with Tannaim? Why do Geonim not disagree with Amoraim? Why do later authorities (Acharonim) not disagree with medieval authorities (Rishonim)? Let’s say it’s a cutoff; it doesn’t matter—suppose for the sake of discussion. What is the idea behind it? The idea behind it—there are those who explain, I think I heard it once from Rabbi משה שפירא, I don’t remember; there are several who go in this direction—that once you live in a world significantly different, you no longer can really understand what he truly meant and argue with him. This is regardless of whether he is greater than you or smaller than you. Meaning, “decline of the generations” here is not only hierarchical—that he was greater and I am lesser. Rather, I simply already live in another world. Once I live in another world… So it’s not decline of the generations, it’s change of the generations. Right, exactly.

So you can’t really understand what he meant. In some sense, say, you see the process of decline of the generations as a process of mediation from this perspective. Meaning that I, for example, am very far from the Talmud. Historically speaking, we are far from the Talmud. So who knows what the Talmud really connoted when it writes something? So for that I need mediation from people who lived closer. Meaning, the Geonim, after all, lived in the same place; they were in Babylonia. The cut between the Amoraim and the Geonim is not sharp. Fine? After all, Tosafot writes in several places that every “Rav Aḥa” in the Talmud is Rav Aḥai Gaon. Rav Aḥai Gaon is from the later generations of the Geonim, centuries after Rav Ashi and Ravina. And that enters into the text of the Talmud. And the Savoraim certainly entered. There are various parts of the Talmud, later parts. Meaning, these are still people who are within the same cultural atmosphere, so it is very reasonable that they interpret the Talmud more correctly than I do. Therefore the authority of the Geonim or the medieval authorities (Rishonim) is not merely formal. They have some advantage. They really can understand the Talmud better than I can, simply because of the distance. And the same goes for the Mishnah, right? It’s the same idea. Or later authorities versus medieval authorities, and things like that. Meaning, there is something in living within the same cultural world. Today the transitions are so rapid that if you live twenty years later, you may already not understand at all what was twenty years before. But once upon a time the whole business moved more slowly. If you lived in the same century, it was more or less still the same thing—or the same two hundred years, or the same three hundred. And therefore as long as you belong to the same world, you are a dialogue partner. You can argue, disagree, dispute, because you understand where he’s coming from, you understand his considerations, and you disagree. You may be smaller, you may be greater, but you still belong to that same milieu, that same world. But when you are in a different stage, it is a completely different world. You don’t understand the connotations, the context. Maybe they meant… You don’t know when you read a passage in the Talmud whether they meant it ironically or seriously. With a contemporary author too you can’t always know, but the feeling is that we have more ability to know, because all in all we understand. But he isn’t so far from you that—who knows.

He tells you to accept it as truth just because it’s another generation. Who says they were right? Maybe I’m right? No, no—who says? You can’t understand deeply what it means. Your logic says the opposite of a Tanna whose ruling was accepted as Jewish law. So just because he was in an earlier period, he’s certainly right? Because again—let’s talk about an Amora, because with a Tanna the question is what he is interpreting. The Amora interprets the Tanna. The Amora understood the Tanna better. Assuming the Tanna holds something true, and both of us are trying to interpret the Tanna, it is more likely that the Amora interprets him correctly than I do. You can ask: but why interpret the Tanna at all? Then why can’t an Amora disagree with a Tanna? What? Obviously, relative to me. Now the Amora too is from a different generation than the Tanna. Right. So we say he cannot disagree with the Tanna because he doesn’t enter the same conceptual framework. Right, but that still doesn’t mean the Tanna is right. No, it does, because if I… Therefore it’s more convenient for me to talk about the Tanna, because the Tanna already relates to Scripture. The question is what advantage the Tannaim have over the Amoraim regarding Scripture.

But let’s speak—more convenient for me to speak about the Mishnah, okay? So I have a dispute with the Amora about the meaning of the Mishnah. We have no such dispute today. Right. So now it is more likely that the Amora is right, because he studied with them. After all, Shmuel instructed; ben aḥi went down to Babylonia; Rav was still in Rabbi’s court. Meaning, he studied with them. So you are arguing with him about what Rabbi said? He knows better than you what Rabbi said. He understands the language, the context, and so forth. So if you assume that the truth lies with Rabbi, not with Rav—Rav is something else—if the truth is with Rabbi and you are basically searching for what Rabbi meant, then Rav has an inherent advantage over you. Therefore the Amora has authority over me. You can ask: but why assume in the first place that Rabbi was right? Maybe I’ll disagree also with… Rav understands Rabbi better, true. But I’ll disagree with both of them. I think the Torah means something else—not what Rabbi said and not what Rav said. That is already a different discussion.

Once an Amora raises something that disputes a Tanna, then they immediately say to him… Fine, so I’m saying that belongs to the second question. The question is: why accept this whole matter at all, his authority? You assume that accepting that authority is because it is true. I’m not at all sure you’re right. It is definitely possible that accepting that authority is not because it is true. Because otherwise there would be chaos. Yes, because otherwise there would be chaos, exactly. Or because there are rules, certain rules, without which the framework falls apart. And it does not necessarily have to be because it is true. But that really is a different discussion. In science it’s the opposite, exactly the opposite. Fine, okay. The newer the period, the more… that’s true. But that is because in science we really have more means of doing experiments. Because in science you do an experiment. Exactly. You have sources of information. How can you do an experiment and dispute a Tanna? It won’t help. No, but you can’t do an experiment. You can’t do… how will you do an experiment in interpretation? No, you can’t. Why not? He tells you an eagle flapped three times with its wings and then you learned… you gave some example… No—if you’re talking about that, you can dispute him. On that you can dispute him. And I immediately change the version. On that, dispute him. On facts… right, because that is subject to experiment. But on things that are not… interpretations are not subject to experiment. Fine, never mind, I’m exaggerating. But I’m saying…

But his interpretation of a verse in the Torah—that… you cannot experiment on the Mishnah. The Mishnah is given; it is the source of information. And what you call an eagle and what he calls an eagle may not be the same thing. Fine, that also could be. Never mind. But in the end you chose a random detail… what experiment is there? No, there are things where there is experiment. One doctor says this and one doctor says that; you check… No, no. What do you check? If you mean facts in the Talmud, no problem. Facts… But facts have no authority. He has no authority over facts; to the best of my knowledge he has no authority over facts. Precisely because of that. With regard to facts I can be better than he is. His authority is exactly what I said before: interpretive authority, traditional authority. Yes, or tradition, or proximity to the source, or his judgment. Again, that’s already not… Also judgment, because judgment is like, you know—even in science. Before you send someone who finished a doctorate out into life, into research, he goes through a kind of internship, right? A post-doc. He works with someone more experienced. You need to get seasoned. Now there is something in that transition beyond the material you learned. You need to understand the mindset, the context. “Serving Torah scholars” they call it. In the East it’s even more developed, the relationship between teacher and student. But that post-doc has the option, in twenty years, of being the teacher… Obviously, obviously. But still, you see he wasn’t… he was in the lab, he was present there. He was in their generation. He can say, “You surpassed me,” because he does experiment. But that’s exactly the point. He receives the method from his teacher. Meaning, you need this continuity even in the scientific world, not only in the… and all the more so when we are speaking about an interpretive world. Because in an interpretive world, if I take the Upanishads and start interpreting them, what do I understand about them? I know nothing about the context in which they were written, about the life in which they were meant to be applied—nothing. What I interpret there may be very creative, very beautiful, and appeal to many people, but it has no connection whatsoever to what the thing actually means.

Still, a Gaon who lived 50 years after the last Amora is still closer to the last Amora than the Amora who lived 300 years before the first Amora. Yet the later Amora of 300 years can disagree, and the later one of 50 years can’t. Again, we have come back to the question of the cutoff. Exactly the same as what we did here. The question of the cutoff arises in this context too. Where do we decide that a period has been cut off? Why, when the Tannaim ended—within the Tannaim, the Kesef Mishneh asks at the beginning of the laws of rebels—why could the Tannaim of the last generation disagree with Tannaim of the first generation, while the first Amoraim, who were basically in the same place, already cannot disagree? There is “Rav is a Tanna and may dispute,” so there is some… What is the explanation? The explanation is completely different. No, the explanation is not different. It is a line of division and agreement. Exactly. Just like saying after 8:45 they don’t let people in. A cutoff line. Meaning, at some point you need… to set a line where the difference is already significant enough that we no longer belong to the same world.

Now clearly one can argue about where that line passes, so they set it. By the way, that line really isn’t sharp either. “Rav is a Tanna and may dispute,” Rabbi Yehoshua ben Levi—there is a seam generation there that did belong to both places. This sort of division is usually done retrospectively. In other words, many years pass, and then we say in retrospect: okay, up to that generation is called the medieval authorities (Rishonim), or is called Tannaim, or Amoraim, or Geonim. Why do they always challenge Rav when he disputes a Tanna? After all, Rav is a Tanna and may dispute. No, because the ones who challenge him are already after the divisions were established. Rav was not bothered by that; he didn’t say to himself, “I’m a Tanna and may dispute.” But those who made the divisions say: okay, the division has been made—what do we do now? Okay, but Rav is fine. In other words, the cutoff too should not be made too Orthodox. But with a text like this, after so much time has passed, maybe this interpretation too has no connection to what really exists in reality or what the truth was. Meaning, of course. Here too, with this interpretation, exactly as if you interpret some text by someone and you don’t know at all where he lived or what he was. If I had, say, an interpretation from Tannaim, then I’d say okay, apparently the Tannaim interpret more correctly than Gedaliah Nadel. But if I don’t have an interpretation from Tannaim, what can I do? I’m left only with Gedaliah. Right, but this is a kind of interpretation of levirate marriage—why after the son? No, fine, but that is exactly the point. Who supposedly fixed the problem? Fine, but in this area there are no authorized interpretations like the laws of the Tannaim. Here and there some suggested ideas, and he too suggested ideas. If an authorized interpretation had been accepted, they would have also determined that one may not dispute even that interpretation. They didn’t establish such a canon. There is no… What do you mean? In principle there could have been such a thing. You could have established that it is forbidden to interpret differently; this is the correct interpretation. Whoever interprets otherwise is wasting Torah study, I don’t know. Fine. Or wrong, excluding himself…

Who said that only on Jewish law it is forbidden to dispute? Maimonides says that in matters not touching Jewish law there is no ruling or no authority. But one could have said there is. By the way, some think there is. That even in matters that are not halakhic there is authority and one may not dispute. In the Talmud itself, when something non-halakhic appears, very few people today would say: okay, it appears in the Talmud but I don’t accept it. It’s not Jewish law; it’s an idea, it’s aggadic literature, it’s… But here Rabbi Gedaliah Nadel comes and innovates, and this is an enormous innovation. He says: look, there is no such thing as a decree of Scripture. Every decree of Scripture contains logic. For example, the explanation of levirate marriage—which perhaps he really took as something almost certainly a decree of Scripture in terms of the scale of the thing—he says: here, I have a logical explanation. This explanation falls immediately—you’ve got a one-day-old baby, what questions they’re asking on him before he even managed to finish a word! I haven’t yet heard even one objection. Here, a one-day-old baby—what does that have to do with… No, so I say again: a one-day-old baby is a cutoff. What’s the problem? No objection, nothing falls here. You can argue whether the interpretation seems plausible to you or not, but so far I haven’t heard anything that collapses this interpretation. But if he made the cutoff at age zero, what’s the problem? And if he’d made it at age 10, then you’d ask why. And at age 10 if he did? “A decree of Scripture”? But at age 10 it’s because the brother saw the woman… But that’s not a decree of Scripture, it’s a cutoff by the sages. It’s not a decree of… no, it’s a cutoff. You have to cut somewhere. Just as Maimonides writes. What’s the problem with that? Every legal system cuts.

Why is adulthood in Israeli law from—I don’t know, doesn’t matter—18? 16? I don’t know how much. Why there? And what if there’s a wise 17-year-old? And what if there’s a clever child of 17? He has legal responsibility. Are we talking about 18 or nine? No, 18 or 17 I’m speaking now. Why don’t you accept the wise 17-year-old? Even there there is a difference between age 13 or age zero. No, what difference does it make? I’m showing you that even systems that are not religious at all and not authority-based draw lines. You can’t avoid drawing lines. You have to put boundaries. So what’s the problem? So he cut at age zero—what’s the problem? That is within the logic. The logic I brought earlier says age zero is very logical. Very logical. Very logical. And that’s why I said the final point about structuralism—exactly for this reason—to show that he was born and lived in the same house, in the same atmosphere, there is absolutely no problem with it. Really no problem at all. Now one can argue whether you agree with the interpretation or not, but I haven’t heard objections yet. No, I think it’s perfectly fine. He just has to be of a certain age, right? The levir, from a certain age he can perform levirate marriage, but the question is the obligation of levirate marriage begins the moment he already exists in the world. From when can he actually perform it? From age nine, when he is fit for intercourse. So until age nine they wait for him? Yes, until age nine they wait for him. They wait for him until age nine? Yes. Nine years is not a lot. No, the question with Rabbi Gedaliah Nadel is that from now on say the normal thing—for this we started waiting? For your soul yes, she does need to wait. You understand your soul better? What’s logical about that? Why do I care about the soul? I want to get married. What soul? You come and say to him, sir, there is some kind of—like what they said to Job—you tell him it’s a decree of Scripture, souls, and they need to be waited for. It’s really the same thing. What happened happened; people died. Right, they didn’t see bacteria, but in principle you can see them. Just wash your hands and you’ll see it improves. What do you mean? So they didn’t see. But he washed his hands. And who says that in principle one can’t see souls? Ask the gynecologists of then what they said. What did the gynecologists of then say? But this is a stage in the process. Moses was there, received the Torah, okay? They saw the first levirate case, said he has a brother age six, they said yes, end of story. Then it rolled onward. And when it gets to today, you try to find interpretations for it. Look, from the outset, if the interpretations were enough, I wouldn’t tell you I accept it. I understand, I agree it can be a reason. I’m not saying that’s the reason. I don’t know if it’s not the reason—who says it’s not the reason? You know Gedaliah? I agree that this can be the reason, certainly it can be. But between that and “I’m sure”… I don’t know, I have this feeling, and it’s true in almost every law I learn, that Moses was there and told them: here like this and here like that and here like this, and from there everything starts getting complicated. Maybe. Maybe yes, and maybe they were right and maybe not. But there is a discomfort one feels with interpretations like these—not only these, with interpretations in general. Never mind. Okay.

Fine, let’s move on. The point that really I think I want to end this chapter with is that in the end, the cutoff—he tries to derive the cutoff too from the verse. Right? He basically says “when brothers dwell together”—from here it emerges that they need to dwell together in the world; that’s the definition. In other words, even the cutoff at age zero comes from the verse. Here I’m no longer with him. Because that’s not necessary. That doesn’t have to be. It’s Torah-level reasoning, fine. But you can’t extract that from the verse. If you said, look, this is a beautiful idea, I accept it as a reason—Yossi doesn’t accept it, fine, not the souls, I’m talking now about Gedaliah’s idea. But now, Gedaliah, we accepted your souls, leave it, we accepted that. In all my learning I’ll say the same thing. What? That you don’t derive it from the verse? Certainly. Meaning, in the end you draw the line, and that line is drawn by the sages. Not by the verse. The verse gives you the direction, tells you they need to be together. He tries to derive even the detail, even the line of division—that this is the meaning of “brothers dwell together.” In other words, the Torah also says the exact line. Here I’m not sure I agree. That I could have cut in a thousand other ways. But you can go with him without going all the way. Meaning, this is the idea, and the cutoff is age zero, fine, because that is the line the sages saw fit to draw. And that does not mean it is rabbinic law. When sages draw a cutoff, that determines the definition of the Torah law; in many things it works that way.

And therefore I don’t think one needed to… Is there any discussion above? No discussion above? Gedaliah starts as if he’s alone in the world, nobody thought of this before. When did… who says there’s nothing above? He doesn’t have to… What do you mean? Did someone in the Talmud discuss this? What is the reason for “when brothers dwell together”? I don’t know of any. Don’t know. But how do they know it starts from age zero? The Talmud, yes—that’s the law. Law without explanation? Law. “When brothers dwell together”—it learns it from the verse, and the Talmud says age zero, no disagreement: “the wife of his brother who was not in his world.” If he was in his world, then there is levirate marriage; if not, then not. Yes, and that is ruled as Jewish law. It is a simple law; everyone rules this way. It’s Talmud. But that is the law. The question is what stands behind it; that is his discussion. Again, maybe there were earlier discussions among medieval and later authorities, fine. He doesn’t have to bring them all. He doesn’t have to provide a survey. He suggests his own path. In the Talmud itself there is no determination—certainly no binding determination—of the idea standing behind these halakhic details. So what is binding? Then we’ve returned to the previous discussion. I’m not sure there is one. Even Sefer HaChinukh doesn’t write a reason here? I don’t remember right now. Maybe. I don’t remember. Not sure that it explains the details. The reason for levirate marriage in general many people write about, but whether you then also claim, on that basis, to explain the details—that “the wife of his brother who was not in his world,” and so on—that’s already a more specific passage… So here Yossi says Abarbanel also explains matters…

“Viewing the Torah as a collection of ideas that do not bind in a precise way—this is a Christian conception. The faith of Israel sees the Torah as precise and binding Jewish law, instruction. This conception of the essence of Torah is taught to us by the Oral Torah.” And again, it seems to me there is here a bit of exaggeration, or a description that is too black-and-white, too dichotomous. Because if I went with him not all the way, but said: your idea is a nice one, but the cutoff at age zero does not come from the verse “when brothers dwell together,” from the wording of the verse. Rather, “when brothers dwell together” requires some kind of sharing between the brothers. Now what kind of sharing? Where do you move the line? The sages set the line: if you were in the same world, if you lived in the same world, then yes. So what is that? Is that less precise? Is that already Christian? That’s exaggerated. Meaning, I think he takes his correct idea too far. In other words, it is true that one should seek the idea behind things. On the other hand, to derive everything from the wording of the verse—I think that will be difficult. Again, if they convince me, fine. But if it’s not convincing, then one shouldn’t panic over it—you haven’t become a Christian because of that. I don’t think it has to go all the way for the correction to happen. Fine. But this is an interesting acquaintance with Rabbi Gedaliah’s mode of thought.

And did the Torah mean a certain definition, or did it hand it over to the text? The Torah meant that the brothers should belong to the same world. Did the Torah—the Holy One, blessed be He—think that we have to cut specifically at age zero? I don’t know. What difference does it make? Cut wherever you want; that’s the idea. You decide where to cut. Or perhaps He did think so—I have no way to answer that. How should I know? The problem is that age zero leaves the woman chained for 13 years. Well, nine. Nine. What nine? Nine. How much? Nine. Yes. Until he matures. Fine. Right. And in any case it’s like that. What can you do. But it’s hard. What? The truth is that nine—it’s not hard to cut at such a… Yes, yes, nine for levirate marriage. For levirate marriage, and for halitzah it’s age 13, maybe—I don’t remember anymore. But that’s what Shlomo Ibn Gabirol’s “Judgment of Solomon” brings. What? What was Solomon’s judgment? Well? About what did they quarrel? Supposedly there was a rabbi and all that; there was a case involving a woman and her daughter-in-law and her mother-in-law. That is written. Yes. And now if the baby belonged to the mother-in-law’s husband, it could be that my mother-in-law… she requires halitzah. He says her husband has… It’s a woman and her mother-in-law that… so the daughter-in-law requires levirate marriage, because the husband, the son, died between the birth and this. So here it needs to be… so the daughter-in-law… the question is whether the daughter-in-law requires levirate marriage or not… she doesn’t want to wait. Okay. That clarifies it, but in exactly the opposite way on the same idea.

Fine, okay. I said—I don’t learn biblical commentators, as I said earlier. The Torah? Huh? Rashi isn’t Bible? Maybe he also meant that the Written Torah is shared by us and the Christians, and the Oral Torah is what makes us… No, that’s true. Because I’m saying he tries to—and he argues that I need to derive even the details of Jewish law from the written text. As if now what does he mean? “When brothers dwell together” is part of the narrative. I accept his claim that from this one can derive the idea of the law that “the wife of his brother who was not in his world.” But he takes it all the way down even to the detail of where you draw the line—what does it mean to have been “in his world”? That he was not born. Not age 10, age zero. That is the sharp cutoff. Now that does not have to come specifically from the verse. One need not go all the way with this thing. Yes, it is true that from the Torah’s formulation we can learn various laws. In the Christian world there is no such thing as Jewish law; it isn’t relevant. It’s not only a matter of a different way of looking at the Torah. They also claim that even the parts of the Torah that explicitly state laws they interpret differently. They simply say it’s no longer relevant. They are in a new phase now. Yes—so now there is a New Covenant. So the Christian perspective is not just another interpretation of the Torah. There are also parts of the Torah that are clearly halakhic sections, and no one disputes them, and you can’t explain them otherwise. “You shall not plow with an ox and a donkey together.” So what—the Christian interprets that differently? No. He says: we don’t do that. I think the sharp distinction he draws here is too sharp. It doesn’t need to go that far.

Okay. Chapter 3—I thought I’d finish this in fifteen minutes. Chapter 3 begins with reasoning. And he defines reasoning here as the part… he claims that “reasoning” in the language of the sages is not what we usually call first principles. First principles are something… And “reasoning” is something one could also have said otherwise, and still, since the sages thought this was right, that is what is called reasoning. In other words, first principles, from his perspective, are something beyond reasoning. Meaning, if it were obvious, that wouldn’t even be called reasoning. When they say, “Why do I need a verse? It is reasoning”—if it were at the level of first principles, they wouldn’t even say that. They would simply say: there is no such thing; it doesn’t need a verse at all. Meaning, when you talk about what? One plus one equals two. Yes, exactly. So when you speak about reasoning, you’re speaking about something that could have been said otherwise. It isn’t necessary, but still, the sages think this way.

Now the first part of this chapter deals with what are called first principles. Fine, let’s read and see how much I manage to connect to… We said that the two principal sources of Jewish law are Scripture and reasoning. “When we say reasoning, we do not mean what philosophers call first principles. A first principle is something whose truth is completely clear to a person without need of proof. Something a person recognizes and cannot think otherwise. Nowadays, however, in science they argue whether the first principles, the axioms, are a system of arbitrary assumptions that man posited, and in the same measure he could posit other assumptions and derive from them results, and these have no superiority over those; or whether in first principles there really is an initial and unshakable truth.”

Meaning, the debate he has in mind is whether these things that seem self-evident to us are statements about the world or statements about us. Yes—one could connect this, for example, to the question of Platonism in mathematics. Is a mathematical principle necessarily true simply because the world is built that way, or simply because our thinking is built that way? Is it a statement about us, not about the world? Okay. So there is a debate here whether the first principles reflect some truth about the world, or are merely patterns of thought with which we were born and from which we cannot deviate. And therefore they are necessarily true. They are necessarily true because we cannot step outside them or think otherwise. Fine. Now where exactly this belongs, what dispute there is here—it’s not a dispute in science; it’s a dispute among philosophers. And also with the “first principles” he mentions here, the question is what he means. Does he mean that between two points there passes one straight line? Or does he mean the law of causality, which is a scientific assumption? This is an assumption in mathematics, so there is room here to distinguish among different kinds of first principles. But there is some such debate here, and there are these two ways of looking at it. And indeed there are quite a few philosophers who claim that the first principles are a statement about us.

And all these discussions we argued over not a little in previous years—yes, all kinds of claims that the Holy One, blessed be He, is beyond contradictions, or that one can believe in logical contradictions, and things like that, which I said are meaningless pilpulim—basically are grounded in some assumption that contradictions are really part of our structure. They are not some real constraint on reality. Meaning, it’s not that there cannot be a triangular circle, or a square whose diagonal is shorter than its side. It can be—only in our thinking it doesn’t work. In other words, our thought-patterns are bound to these assumptions. But someone could come who is, I don’t know, above that matter, or without those limitations, and he’ll make triangular circles, I don’t know. Riemann? Yes, Riemann is something else; he’ll get to Riemann in a moment. But then all those who speak about living with contradictions, or that God need not be disturbed by contradictions in faith or contradictions in a religious worldview, basically somewhere assume this claim—that contradictions are a statement about us, or that logic is our structure. It is not a constraint on the real world, the objective world outside us.

Now he says: “But this debate has no meaning. Clearly, as a thought experiment one may also posit as axioms just two arbitrary assumptions, even ridiculous ones, and if they are independent of one another—meaning one cannot prove one from the other, and not from somewhere else, that’s already not independence, never mind—one can build from them, by means of the law of contradiction and a few other logical laws, a system of propositions. But that is only an exercise in logic. In truth, the first principles are the truths that the Holy One, blessed be He, implanted in man, truths whose veracity every person is convinced of.”

Here he is already really speaking, yes, about Riemann. Meaning, he says that when I assume that between two points there passes one straight line, some will say this is a statement about me, or not even about me—it’s just arbitrary. I posit that assumption and try to see whether it is fruitful. Meaning, whether I can derive enough interesting theorems from it. Then I’ll posit the opposite assumption and see whether I can derive interesting theorems from that. And then, in this mathematical perspective, following Riemann who dealt with non-Euclidean geometry—in which between two points more than one straight line can pass—basically a feeling developed, especially among mathematicians but not only among them, that these assumptions really are arbitrary. There is nothing there beyond our habits of thought. And Rabbi Gedaliah argues that the first principles are “the truths that the Holy One, blessed be He, implanted in man, truths whose veracity every person is convinced of.”

It is not entirely clear what he means here. What does it mean that every person is convinced of their truth? Wait, fine, that’s an axiom; he’s explaining what an axiom is. An axiom is something every person is convinced is true. What does that mean? That we are compelled by it? He still hasn’t explained. Or that it is true? No—that once I as a person think this way, then the world too is this way. Ah, so here the question is what he means, because he says: “the first principles are the truths that the Holy One, blessed be He, implanted in man.” What does “implanted in man” mean? That this is how the world is? He doesn’t say that. “That the Holy One, blessed be He, implanted in man, truths whose veracity every person is convinced of.” That fits perfectly with the subjective view. No—if that were the formulation, he wouldn’t say “the truths He implanted in man.” It would be things He implanted in man that man is convinced are true, not truths He implanted in man. “Truths” means the truths of the world that He implanted in man. Could be. It’s quite clear to me that that’s what he means. I’m saying that in the formulation, otherwise they aren’t “truths”; they’re things He implanted in man. Could be. He calls them truths even before He implanted them in man. Yes, yes. It may be that his intention is that this is truth. I’m saying, yes, of course he means to argue against the subjective view. That is his intent. It could be that in the wording this too slips in. Okay.

“For example, Euclid’s famous axiom, according to which from any straight line and a point outside it one can create two parallel lines that will never meet. This is a first principle stemming from the very perception of space that the Holy One, blessed be He, implanted in man. Man cannot think otherwise.” Notice that he keeps using subjective wording. “It stems from the very perception of space that the Holy One implanted in man”—not, it stems from the nature of space itself. He keeps somehow returning to man. Again, I don’t know; this is also Rabbi Shilat’s wording, so I don’t know exactly what’s going on here. But I’m sure he really means the objective claim. Yet the formulations are all subjective formulations. “Man cannot think otherwise.” It isn’t that he cannot think otherwise; he simply sees that this is the truth. “Cannot think otherwise” is the statement pointing in the subjective direction. No—he doesn’t see that it’s true. Why? Since it is an axiom, he doesn’t see it’s true. Why does he see it? How does he know it’s true? He doesn’t “see.” It’s an axiom; you don’t see an axiom. What do you mean, you don’t see? You see with the mind’s eye. Ah—if you see with the mind’s eye, then that is because there are truths in the world, truths in the world that you don’t see with your eyes. There are truths in the world. It’s not “implanted in man”—ask a person about various laws of physics, he won’t tell you until he studies and they prove it to him. So that’s still not implanted in man. The ability to see was implanted in us. If we didn’t see, then even the fact that there is a wall here would for me be something subjective. So the ability to understand the axioms was implanted in us too, but once it was implanted, through it we grasp something about the world. It isn’t only something embedded in us. Again, clearly that’s what he means, so there’s no point getting hung up on the wording. It reaches the floor even if you don’t understand the law of gravity. No, fine, we’re talking about the law. The phenomenon is a phenomenon—we see it—but the law of gravitation, that we do not see. “This is a first principle stemming from…” yes. “Man cannot think otherwise. Whoever says that he will posit a different assumption and that it too can be valid is speaking about something else, not about space.”

Here he already says it. Meaning, whoever speaks of a non-Euclidean assumption, an assumption of Riemann, simply isn’t speaking about our space. So this isn’t subjectivity but simply talking about a different reality. What? About the plane or about space? It doesn’t matter; it can be space too. Why? What is Riemann? Space. He talks about space, even three-dimensional space. Three-dimensional. What’s the problem? Yes. There are non-Euclidean geometries in three dimensions too. What’s the problem? No, Euclid is geometry of the plane. We’re talking about Euclid. Fine, but there is Euclidean geometry in three dimensions too, what’s called stereometry. So here he simply claims that it’s misleading to talk about non-Euclidean geometry as if it were relevant to Euclidean geometry. It is not another way of seeing the same thing; it is simply seeing something different. Yes, exactly. And in that sense he is completely right. Many times, by the way, mathematicians can miss such a point—specifically mathematicians—because for mathematicians, mathematical thinking leads them to grasp these assumptions in exactly that subjective way. Subjective, meaning that for them it’s a set of assumptions and let’s see if it is fruitful. Actually the physicist’s viewpoint says: wait, what does this set of assumptions mean? This set of assumptions means that you are speaking about a certain type of space, and now you are already speaking about the world. In another sort of world there will be another set of assumptions. Once you speak about the world, you are already a physicist.

Meaning, the mathematician does not see, does not conceive his work as dealing with the world, but as dealing with some abstract construct, some object. We are now defining a space whose axioms are Euclid’s axioms, from which we begin, and let’s see whether that is consistent, what it gives. Then we’ll change one of the assumptions and see where that leads us. And I think historically that’s even how it was, by the way. Once they found that one can change one of Euclid’s assumptions and still remain consistent—we don’t reach contradiction in the mathematical sense—it doesn’t describe our world, but we don’t reach contradiction; it’s consistent. For the mathematician that is enough. There we stop: there are two geometries. The physicist asks himself: wait, what do you mean? Either in our world this geometry is correct or that one is. Then it becomes a kind of physical statement saying there are two different kinds of spaces involved. Now there is a lot of mathematical work to define these spaces and what is called the metric of these spaces, but the idea here is a physicist’s idea, not a mathematician’s. Again, I’m not expert in the history of exactly how it arose, but I’m saying categorically: the mathematician, from his perspective, it is a set of assumptions and an opposite set of assumptions, and let’s see what comes from this and what comes from that. The amazing discovery for the mathematician was that a non-Euclidean system too is consistent—you don’t arrive at contradiction. People had been sure that if you changed one of the assumptions you would reach contradiction. For the physicist, what was discovered here is simply that there are other kinds of spaces. It’s not at all a question of contradiction or no contradiction; you are describing a different kind of space, a curved space. And in that space the sum of the angles won’t be 180 degrees, and all sorts of things won’t hold there that do hold here, and there is no problem. You can define it, you can understand it, even intuitively you can understand it. There’s no…

Like a ball. Exactly. The surface of a ball is the standard example. You immediately see that the sum of the angles is not 180, and that all sorts of things do not hold there. That is, parallels—there is no such thing as parallels; parallels do meet. Exactly. In basketball there are lines. Yes, exactly. For example, he can talk about circles on the sphere whose radius is the radius of the sphere, and say that any two such lines must meet, that there is no possibility of creating two parallel lines. “This is non-Euclidean geometry, which cannot come in place of ordinary geometry, but one can find an application for it in a certain place where it will indeed accord with the first principles.” Basically what he argues is that the subjective view and the objective view are what I called earlier the mathematician and the physicist. The mathematician sees these two systems as something subjective, something that says nothing about the world. This set of assumptions isn’t necessarily—it leaves it to the physicist to determine something about the world. For him it’s not… as long as the system is consistent, has no internal contradiction, I examine what follows from it. What difference does it make? If it is consistent, fine. The other system too is consistent, to everyone’s amazement, and interesting things come from it too, so he works on such systems. Then you immediately slide into a kind of outlook that sees these things as subjective, meaning just our structures, and they really are not true in any sense. At most they can be non-contradictory.

Meaning, a mathematician or logician can also toss out a system of assumptions. If it contains an internal contradiction—not because it doesn’t fit some reality, that doesn’t interest him. What interests him is that it not contain internal contradiction. So when they discovered it did not contain internal contradiction, that was an amazing discovery—that there are other geometries that don’t lead to contradiction. But he still remains in the subjective outlook that says: fine, but that doesn’t say anything about the world. Therefore the conclusion indeed was that there is nothing especially true in Euclidean geometry, because the second geometry is just as consistent. But here that is already a mistake. There is something true in Euclidean geometry, and that is what Gedaliah Nadel says, because we are talking about our world. Our world is more or less a straight world. Yes, except Einstein with gravitation claims it isn’t, but broadly speaking it’s a straight world. And since that is so, Euclidean geometry really is true in the world.

But now the interesting question is: how do you know? Suppose the world is a straight world. The mathematician, even after the physicist reveals to him that Euclidean geometry speaks about a certain kind of reality, isn’t interested and isn’t bothered, because from his point of view there is no need to justify the axioms of Euclidean geometry. Whether they fit a certain space or not—that’s the physicist’s problem, not his. As long as it’s consistent, fine, and he’ll examine what follows from it and what doesn’t. He doesn’t relate to axioms as something requiring justification, as something true or false. Why should he care? Assume it and let’s see what follows; assume that and let’s see what follows. But the physicist, when he says that the Euclidean system fits Euclidean space or straight space, is basically claiming that these are true statements about a certain kind of physics. Geometry turns from a branch of mathematics into a branch of physics. And now you are making a claim about the world. In our world, the sum of the angles in a triangle is 180 degrees.

Okay, that’s a very… What? There are no points in the world. What? There is no point in the world. The concept of a point. Never mind; it’s an abstraction. But there is a point in the world—why not? You can call it… then it’s called “there is no point.” It occupies no volume and has no mass, but who says it doesn’t exist? No, space is made up of points. There are points in the world—why not? True, this is a kind of abstraction process, but it is an abstraction that brings me to… But Euclidean geometry too is a process of idealization. No, no, I don’t agree. Not idealization in the sense of going beyond the world, but idealization in the sense of creating concepts that may not be exposed to direct sight. But you still understand that space is made of points, a line is made of points, there are points on the line. A point is not something nonexistent—it exists; it has no length. Like the number line is made of numbers, yes, including irrational numbers. You can’t define rational… I can say there are irrational numbers in the world, definitely. Why not? Pi is an irrational number. There are irrational numbers in the world exactly as there are rational numbers. The square root of two is an irrational number; you use it every day for… No, use is something else; the question is whether it exists. I’m saying, numbers—if you decide that numbers in general exist in the world, if you’re a Pythagorean, then there is no difference between rational and irrational numbers. If you decide there are no numbers in the world, then there are no rational numbers either. Then you’ll claim a number is a mental abstraction; there are no numbers in the world. There are numbers of books, numbers of legs on a table; the number, the idea itself, is not in the world. One can argue about that, and I accept that, but it still isn’t connected to rational or irrational. It would be true of all numbers. If you assume numbers exist in the world, the irrational ones exist too, because on that line if you put a dart, it will sometimes land on—usually it will land on an irrational, of course. There are many more irrationals than rationals. There are more infinities of irrationals. Yes, the infinity there is aleph-one, that is, the continuum. Is there infinity in the world? Are there infinitely many points in the interval zero to one? You can assume there are points, right? And if there are points, then there is also infinity. Clearly. I’m presenting the thesis that there is; I didn’t say I must hold that way. But I’m saying you can view it that way, and then there’s no difference between rational and irrational numbers.

In any case, the point is that when the physicist looks at this as a proposition in physics, a very difficult question arises that doesn’t trouble the mathematician at all. And the question is: how do you know that between two points there passes one straight line? Even in Euclidean space, how do you know? It is not the result of observation. In observation you can see that one straight line passes; you cannot see that no other passes. Or that two… If it were something from which you could know, it wouldn’t be an axiom. Right. Maybe if it were the result of observation, in a mathematical sense it could serve as an axiom. That could be. But I’m saying, for example, two parallels—how do you know they never meet? Have you ever followed them to infinity? Seen it? How do you know they don’t meet? These are logical inferences we make. But those logical inferences—how can it be that our logic, which is something embedded in us—why do we believe it really describes what happens in reality itself? And it isn’t even logic; it’s intuition. Yes, intuition. So the question now is what are called first principles. This intuition is implanted in us, and the question is why we really think it also describes what happens in the world.

Forget it—it’s Euclidean space, fine, all okay. Even in Euclidean space you cannot tell me that two parallels never meet. No one has tried it to the end, but it is clear to us logically that this is so, and I’m willing to stake my head that if you go as far as you like—one can’t go to infinity, but go as far as you wish—they will never meet. Really? In a closed universe, no… In a closed universe… in Euclidean space… We live in a universe, but… Never mind, in Euclidean space, not a closed universe. Take this little segment and extend it infinitely—not our universe. This little segment, extend it like a flat map of the earth, yes? In that picture, as a local approximation. That perspective is perfectly clear to us, but nobody actually tried it. It is built into us. On the other hand, we think this is a claim about the world. It is not only because this is how we are accustomed to think and can’t think otherwise. Meaning, the move from mathematics to physics is not only that I found a physical meaning for the set of mathematical assumptions, but that I also claim that in that physical reality the mathematical claims are true factual claims. And that is something that would make a mathematician tear his hair out. There is no such thing. Even a proper physicist should tear his hair out sometimes, because this is not the result of observation. So how can you say such a thing? And from here these subjective conceptions emerge. It starts with the mathematician.

But really the mathematician isn’t the beginning of the path, he’s the end of the path, because move from the mathematician to the physicist, who tells you there is some space with respect to which these assumptions are factual claims—Euclidean space. Then suddenly the physicist asks himself: ah, for this space these are factual claims—how do I know that, actually? He has no way to answer, because it isn’t a result of observation, and the fact that I’m built in a certain way doesn’t obligate the world to anything, as Mark Twain says: it was here before me. Meaning, why should the fact that I’m built a certain way mean that the world must also behave that way? But I’m sure the world does behave that way. How do I know? So this difficulty brings us back, at the end of the process, to the mathematician. Fine, then this is just my way of thinking. It isn’t really a claim about the world. The mathematician is the end of the process. I began with him because he is already familiar to us; we are already after him. But when mathematics suddenly began to understand itself as an abstraction not touching the world, that is modern mathematics. Mathematics did not begin there. It began as geometry for measuring areas. At some stage they suddenly grasped that there was an abstraction here about the world. Why did they grasp there was an abstraction about the world? Because of these problems. Because as claims about the world, you cannot bring observations to ground them. So who says it’s true? It’s just our habit of thought. And by a wonderful irony, this outlook, which in my eyes is not correct, proved very fruitful. Meaning, all of modern mathematics basically created all kinds of utterly bizarre theories. Why? Because you stopped being bound by what you observe, what you see in the world. You define for yourself something opposite—because later David showed that it is very useful for physics. Exactly. Like what happened to Maimonides with the book that no one was supposed to need any other book, and on that book there are the most books. Yes. So there really is a very interesting process here. What is called mathematics today began as physics. It underwent abstraction because of these problems and became pure mathematics. Pure mathematics gave rise to a subjective approach. But then physicists suddenly come and take this mathematics as factual claims about the world. After all, there are Euclidean and non-Euclidean spaces in the world itself. Physics talks about this. Relativity talks about this. Right? Then one asks: okay, now I understand that I have really returned to the situation of the Greeks or Assyrians, all those who took geometry as a measuring tool, meaning as claims about the world. But how do you know this, actually? And then you arrive at a kind of subjective statement—you become a mathematician again after the physical stage. Meaning, you have to give up, because if you cling to observation, observation does not produce this.

And what he claims is no, you must not go back. True, it doesn’t come from observation, but it is true. It is true because the Holy One, blessed be He, implanted this thought in us, and it is a true thought—not only that we are compelled to it and cannot step outside it, but that it is a true claim about the world. If you extend those two lines to the end in Euclidean space, they will never meet. They really will never meet. How does he know? He knows it as we know it. He believes it. Yes. It is a very strong intuition. Right. But there is a very interesting move here around geometry—how geometry serves as the clearest example of this game between mathematics and physics. In the end he reaches a position I agree with very much. The view that these intuitions, although they have no observational basis, are what Kant calls synthetic a priori judgments. Meaning, they are a priori judgments, not the result of observation, but they make claims about the world. And all the dilemmas and skepticism and David Hume and all the problems the philosophers wrestled with before Kant—basically he mapped them onto this one problem: are judgments possible that originate in our thinking rather than in observation, and yet are claims of fact about the world? Our ordinary assumption is no. If you know something about the world, it’s because you saw it, observed it. But one can see that many of the propositions we think are claims about the world are actually a priori propositions.

And then that leads people to think: well then, if so, they aren’t synthetic claims, they aren’t claims that say something about the world, but something about us. And Kant too, in a certain sense, retreated there. He wanted to argue that these claims are really about us and not about the world, and that is how he explained their existence. But what he really wants to claim here is that that is not true. It is a claim about the world, not about us, even though it is born from us. The great philosophical difficulty is: how do you know? Isn’t Euclidean geometry a priori? It is a priori, but synthetic. Why synthetic? Because it makes claims about the world. It is not a purely a priori claim just about the fact that… It is purely a priori—that’s exactly what Kant said. There can be synthetic a priori judgments; not every a priori judgment is analytic. That’s exactly what he said. It is a priori, but also synthetic at one and the same time. Wait a second—isn’t it like two plus two? It is like two plus two. Why not? Two plus two is also a claim about the world. What do you mean it’s a claim about the world? A claim about the world. Take two apples plus three apples—you can predict a priori, without observation, that the result will be five, even though that’s a claim about the world. Ah—it is an a priori proposition that doesn’t come from… But it will work. Count apples and see that it works. Of course. So that means it is synthetic. It is a priori and synthetic—that’s exactly the point. Every a priori is like that; it is a priori. Not true. There is analytic a priori and synthetic a priori. What does analytic a priori mean? Well, that’s a question. Seven plus five equals twelve—no, that is a proposition that says nothing beyond what is contained in its definitions. That is analytic. A synthetic a priori proposition is a proposition that says something beyond what is contained in its definitions, but still it is a priori, not the result of observation. Now, if it does not follow from its definitions and it is not the result of observation, then how do you know it? That is the big question. Because a priori I know. How do you know? A priori is your own thought—how do you know it about the world? That is exactly the point. So what do you say—it’s a claim about me, not about the world. Fine. That’s the debate we’re discussing here. Okay?

So basically there is here—wow, we’re already… In short, that is his claim. What he calls here “first principles” seems to me more or less to be what philosophy calls synthetic a priori judgments. Let’s see how this connects to Yom Kippur. Yes, I saw that I’m already not getting there. I saw that I’m already not getting there.