Tractate Sotah – Chapter 5 – Lesson 13 – Rabbi Michael Avraham

Table of Contents

• Background of the topic: a third degree of impurity in creeping-creature impurity and the refutation from a stricter side
• Types of common-denominator arguments and the learning mechanism
• The example of blessings over enjoyment and the formal structure of a common denominator
• Refutation as proof of non-necessity and the asymmetry between the learner and the refuter
• Occam’s razor as the foundation that saves the common denominator
• The common denominator as scientific generalization, elimination, and diversity in evidence
• Two verses that come as one, why both are needed, and the constructive role of refutations
• An ordinary refutation of a common denominator: the altar-side in blessings
• Ketubot, Makkot, and Ulla: a common denominator regarding monetary payment and lashes, and regarding a prohibition with no action
• Tosafot’s question on the refutation from a stricter side and the Ritva in the name of medieval authorities (Rishonim)
• The distinction between factual refutation and halakhic / of Jewish law refutation as an explanation of the refutation from a stricter side
• A meta-halakhic implication: laws arise from properties, not from an arbitrary royal decree
• Conclusion

Summary

General overview

The lecture concludes the semester by clarifying the logic of learning from a common denominator and of the refutation from a stricter side, against the background of the topic of a third degree of impurity in creeping-creature impurity learned from one who immersed that day due to creeping-creature impurity, and the dispute over whether one can refute with a stricter side. It presents two models for understanding the common denominator, analyzes the role of refutations both as obstacles and as builders, and compares the common denominator to scientific generalization that relies on preferring the simpler explanation. Starting from Tosafot’s question about the refutation from a stricter side, it builds an explanation that distinguishes between “factual” refutations and “halakhic / of Jewish law” refutations, and suggests that behind laws stand factual properties. From there it draws a meta-halakhic implication against the view that the commandments are arbitrary and without reasons.

Background of the topic: a third degree of impurity in creeping-creature impurity and the refutation from a stricter side

The previous summary reached the dispute over whether there is a third degree of impurity in creeping-creature impurity, learned from one who immersed that day due to creeping-creature impurity by way of a common denominator according to Rabbi Yohanan ben Zakkai. Rabbi Yohanan ben Zakkai is concerned that the derivation will be refuted by a refutation from a stricter side, and he himself does not use such a refutation. The lecture continues from there to clarify what the refutation from a stricter side says about the logic of the common denominator.

Types of common-denominator arguments and the learning mechanism

The common denominator can be built from two a fortiori arguments, from two paradigm constructions, or from a combination, and there is a dispute whether a common denominator built from two a fortiori arguments remains an a fortiori argument or becomes an independent common denominator. Understanding the mechanism determines the ruling: if the common denominator “reveals” a shared property from which one learns about the target case, that is a paradigm construction; if the second source only removes a refutation from the first a fortiori argument and leaves it otherwise intact, then it remains an a fortiori argument. The example in Bava Kamma is presented as an arena in which a similar phenomenon appears in the dispute between the Rosh and other major authorities.

The example of blessings over enjoyment and the formal structure of a common denominator

The Talmud in Berakhot learns the blessing over enjoyment from a vineyard and standing grain: “Just as a vineyard is something from which one benefits and it requires a blessing, so too anything from which one benefits requires a blessing,” and this is refuted with, “What about a vineyard, for it is subject to gleanings,” then “standing grain proves it,” and that is refuted with, “What about standing grain, for it is subject to challah,” and finally, “the law returns… the common denominator between them is that they are something from which one benefits and that requires a blessing, so too anything from which one benefits requires a blessing.” The lecture narrows the structure down to A and B as the source cases and C as the target case, with a shared property Z and separate stricter properties X and Y. The analysis moves from comparing C to A and B to comparing A and B to each other, and then determining that Z is the relevant parameter.

Refutation as proof of non-necessity and the asymmetry between the learner and the refuter

The derivational argument has to be necessary, whereas a refutation is satisfied with showing an alternative possibility that cancels the necessity without proving that the conclusion is wrong. Presenting an alternative “theory” that attributes the law to X or to Y rather than to Z knocks out the derivation because there are now two possibilities. The asymmetry is described this way: the learner bears the burden of necessity, while the refuter bears the burden of generating a possible alternative.

Occam’s razor as the foundation that saves the common denominator

The common denominator is presented as a case in which there are two competing theories, but one is simpler and therefore preferable: a single Z-based explanation is preferable to an “either X or Y” explanation, which is more complex. An ordinary refutation of a common denominator happens when an additional shared property W is discovered in both source cases but not in the target case, because then a simple alternative theory is proposed at the same level of simplicity, a single-parameter theory competing with Z. The lecture presents Occam’s razor as a principle operating in science, in law, and in methodological conduct, and also mentions a personal claim that it is a logical rule and not merely a methodological one, though it does not go into the proof and suggests sending a link to anyone interested.

The common denominator as scientific generalization, elimination, and diversity in evidence

The common denominator is described as scientific generalization: a phone falls, a key falls, therefore the shared property, “mass,” is the relevant cause, and elimination removes incidental parameters such as rectangular shape or being “a piece of metal.” A refutation of a common denominator is presented as the discovery of a property shared by the two source cases, such as “black,” which is absent from the target case, requiring the addition of another example that does not carry that property, similar to building a common denominator from three or four source cases in the Talmud. In the world of science, the rule of “diversity in evidence” is emphasized, in which varied examples strengthen induction, and this parallels the fact that in Jewish law, differences between the source cases strengthen the generalization beyond their role as solutions to refutations.

Two verses that come as one, why both are needed, and the constructive role of refutations

The question is raised how a common denominator can teach anything when “two verses that come as one do not teach,” since there are two sources for the law. The answer is tied to the idea of why both are needed: specifically the refutations show that it would not have been possible to write only one of the source cases, because each one on its own cannot teach the other, and therefore there is no true redundancy and the two verses are “like one verse.” Here the refutations receive a constructive role, not just a disruptive one, and they explain why it is permitted to learn from the common denominator and why it does not fall under the rule of two verses that come as one.

An ordinary refutation of a common denominator: the altar-side in blessings

The Talmud in Berakhot adds a refutation to the common denominator: “What about the common denominator between them, for they have an altar-side,” because vineyard and standing grain are connected to the altar, through meal-offerings and libations. This is a refutation of the type in which the two source cases share a property that is absent from the target case, and it sets up a simple alternative theory at the same level of simplicity, competing with the “benefit” generalization.

Ketubot, Makkot, and Ulla: a common denominator regarding monetary payment and lashes, and regarding a prohibition with no action

In Ketubot 32b, Ulla learns that whenever there is monetary liability and lashes, “he pays money and does not receive lashes,” from one who injures another person, and that is refuted with, “for he is liable for the five payments.” He then learns it from conspiring witnesses, and that is refuted with, “for they do not require prior warning,” and then he learns it from the common denominator of the two. In Makkot, a parallel derivation is brought regarding “one receives lashes for a prohibition with no action,” from one who brings out a bad name and from conspiring witnesses, with the same refutations, receiving lashes and paying, and not requiring prior warning, and a common denominator is then built. In both places the surprising line appears: “What about the common denominator between them, for they have a stricter side,” and a dispute of tannaim is established over whether one may refute with a stricter side, where “Rabbi Yehuda does not refute with a stricter side.”

Tosafot’s question on the refutation from a stricter side and the Ritva in the name of medieval authorities (Rishonim)

Tosafot asks that if one can refute with “a stricter side,” then “we will never again learn from a common denominator anywhere,” because in every common denominator each of the source cases has a different stringency. The Ritva brings an answer that one refutes with a stricter side only when the stringencies are “very unusual, with nothing else like them in the entire Torah,” and connects this to examples such as conspiring witnesses and one who brings out a bad name, one who injures another person and conspiring witnesses, and an earthenware vessel and one who immersed that day, and also to “a prince and a deaf-mute, for both are unusual.” The Ritva also brings in the name of Nachmanides an explanation that interprets a stricter side only when the two source cases have stringencies absent from the target case, and the target case has no stringency absent from the source cases. He also brings an explanation in the name of the Ra’ah that limits the refutation from a stricter side to stringencies that pertain mainly to the very law being learned, such as stringencies in the area of lashes when one is trying to learn something regarding lashes.

The distinction between factual refutation and halakhic / of Jewish law refutation as an explanation of the refutation from a stricter side

The lecture proposes a different solution: the refutation from a stricter side appears when the stringencies are laws rather than factual properties, because a stricter law serves as an indication of an underlying microscopic factual stringency standing behind it. When the two stringencies differ halakhically, such as “liable for the five payments” as opposed to “do not require prior warning,” they may still express the same underlying factual stringency that does not exist in the target case, and that mere “possibility” is enough for a refutation. It is argued that the refutation from a stricter side does not appear when the two refutations are factual, as in Bava Kamma, “its initial formation was for damage,” “common wind,” “its intent is to damage,” and therefore there one does not refute with a stricter side, whereas in topics of laws such as impurity and purity there is room for concern about a refutation from a stricter side.

A meta-halakhic implication: laws arise from properties, not from an arbitrary royal decree

A claim is presented that this distinction assumes that behind the laws there are factual or policy-based properties that justify them, and therefore Jewish law is not “detached from the properties.” From here a “halakhic proof” is proposed for Maimonides’ claim in Guide for the Perplexed, Part III, that the commandments cannot be arbitrary and without reasons, because if the laws were a royal decree with no connection to facts, then factual and halakhic refutations would have no meaning and there would be no basis for the logic of derivations. The lecture suggests that stronger meta-halakhic evidence comes from the mechanisms of Jewish law itself more than from general philosophical arguments, and it concludes with the example of personal injury as opposed to property damage as a distinction dependent on the identity of the damager, a person versus property, and on the stringency attributed to a person’s responsibility for his own actions.

Conclusion

The lecture ends by clarifying that there is no exam on these lectures and by wishing success to anyone who does have exams.

Okay, last time we went through the topic that deals with deriving by means of the common denominator, and in the end we got to the dispute about the refutation called “a stricter side.” Right? About whether there is a third degree of impurity in the impurity of a creeping thing there. Is there a third degree? They learn it from one who immersed that day, from one who immersed that day after contact with a creeping thing. We saw that in the end they derive it from the common denominator, and Rabbi Yohanan ben Zakkai is—meaning, he derives it from the common denominator—and he is concerned that they will refute it with the refutation of “a stricter side,” while he himself does not refute with “a stricter side.” That’s where we stopped.

What I want to do now is talk a bit about the common denominator and about the refutation of “a stricter side,” and what this whole thing means, and with that we’ll finish the semester. When we talk about the common denominator, we also saw examples of this and I mentioned that there are two kinds of common denominator: from an a fortiori argument and from an archetypal source, or three kinds, or two archetypal sources or two a fortiori arguments. We discussed the dispute over whether, when we make a common denominator from two a fortiori arguments, in the final analysis it remains an a fortiori argument or it remains a common denominator. And I tied that to the question of how we understand the mechanism of the common denominator. If we understand the mechanism of the common denominator as exposing a shared aspect of the two source cases, from which we derive the target case, then it really is an archetypal source. But if we understand that the common denominator really leaves the first a fortiori argument in place—the refutation raised some problem with that a fortiori argument, and the second source case basically shows that the refutation is irrelevant, so the first a fortiori argument remains—then it stays an a fortiori argument. I mentioned that you can see this phenomenon in tractate Bava Kamma, in the dispute of the Rosh and other major authorities. So all that is what we discussed last time.

I want now to get a little more into the logic of the common denominator, and as a result also of the refutation of “a stricter side.” So I’ll start maybe with an example from the Talmud in Berakhot. The Talmud in Berakhot brings the following derivation regarding blessings over benefit, because it deals with the question of where we know that one must recite a blessing over food before eating it. “We have found it regarding a vineyard; from where do we know it לגבי other kinds?” Where do we learn that one must bless over all foods before eating? “Let it be derived from a vineyard: just as a vineyard is something from which one derives benefit and it requires a blessing, so too anything from which one derives benefit requires a blessing.” “It can be refuted: what is unique about a vineyard? It is obligated in gleanings.” It has a special obligation unique to a vineyard, and therefore you can’t learn from it to the other things, that they too require a blessing. So the Talmud says: “Standing grain will prove it.” “What is unique about standing grain? It is obligated in dough-separation.” “A vineyard will prove it.” “And the argument returns: this is not like that and that is not like this; the common denominator between them is that it is something from which one derives benefit and it requires a blessing; so too anything from which one derives benefit requires a blessing.” Okay? So that is, for example, a case of a common denominator. We also saw an example in the previous class from our own topic.

Now, whoever brings this example at home—in any case, how does such a derivation actually work? So let me remind you of what we saw last time too. Look at this scheme. Do you see? Say we have a vineyard and standing grain; A and B are vineyard and standing grain, and C is all the other foods that we need to bless over before eating. Now the structure is always like this: I learn C from A, either by an a fortiori argument or by an archetypal source, whether it’s equal or more stringent. Okay? And then they say to me: no, A has a stricter characteristic, X. You see? Here. X is here. And here there is no X—you see, X with a roof? So there is no X here. Since A is stricter in terms of characteristic X—it has gleanings, say, if it’s a vineyard—then you can’t derive from it. That’s a refutation. So then they say to me: standing grain will prove it. Why will standing grain prove it? Because standing grain has X-roof, not X. Meaning, it doesn’t have the advantage that A has. Okay? In that sense it’s like C, right? In both of them X is absent. Okay? So they say yes, but here there is another refutation, Y. It has characteristic Y, which the other source case doesn’t have, right? Namely, it is obligated in dough-separation. That’s regarding the standing grain, so that is Y. Then the Talmud says: if so, we can’t. We tried to derive from A, and we rejected it because of the refutation on the X-axis. We tried to derive from B, and we rejected it because of the refutation on the Y-axis. Seemingly, that’s it, hopeless—you can’t derive. Done, you have to look for our bread elsewhere. And not bless over it either. Okay, so how does the Talmud do it anyway? Suddenly, abracadabra. What does that mean? It takes—okay, each one separately can’t teach, but both together can. Right? “And the argument returns: this is not like that and that is not like this.” By the way, who is “this” and “that”? That’s A and B. Not A and C and not B and C. Suddenly we shifted to a comparison between A and B. Right? Each derivation separately deals with the relation between C and A, and the refutation also says the relation between C and A is not as you thought. After that, the derivation from B says what the relations are between B and C, and the refutation says not as you thought. But in the summary we’re not even dealing with the relation to C. “This is not like that and that is not like this” means the relations between A and B. What is it? Look here. A is not like B, because A has X and B does not. B is not like A, because B has Y and A does not have Y. Therefore this is not like that. Their common denominator, right, is that both involve benefit—that in both of them there is benefit, Z. There is benefit both in eating the vineyard produce and in eating grain. But Z also exists in the other foods. We derive benefit; these are blessings over benefit. We derive benefit from all foods. Right? Since that is so, we can derive from both of them to here.

What does this actually mean? I talked about it last time. It basically means that we are learning that wherever there is Z—there is benefit—one must bless. And A and B are simply examples of the matter. Now why can I actually do such a thing? On the simplest level it seems like this. We see that each of the two source cases has three characteristics. Right? The first two differ from each other, they are opposites, and the third is shared—Z is shared. Okay? Now the first derivation of C from A basically wanted to derive C from A, say by an a fortiori argument or by an archetypal source. Then we refute. What does it mean that we refute? Does it just totally collapse? We’ll see in a moment. What does it mean when we refute? That A has the characteristic X and C does not. So what? So maybe the obligation to bless comes from characteristic X. And characteristic X, after all, does not exist in C. Therefore you cannot derive from A to C. Right? Then we move to B. B also has a refutation because it has the stringency Y—it is obligated in dough-separation. Maybe the obligation to bless in B stems from the fact that it is obligated in dough-separation, and other foods are not obligated in dough-separation. Therefore you cannot derive from A and you cannot derive from B. But now, if that’s really so, then why can you derive from both together? You tell me because both of them have Z. But on the other hand, both of them also each have some stricter side. You can already see the refutation of “a stricter side.” In each of them there is some stricter side. In A there is X, and in B there is Y. Therefore, in effect, I can still claim that the obligation to bless over the vineyard is because it has gleanings, and the obligation to bless over the grain is because it has dough-separation, and therefore you cannot derive from both of them to other foods, to C. Why do you decide that the obligation to bless depends on Z? Maybe it depends on X or on Y.

So it turns out that the refutation—or rather, the derivation of a common denominator—has something unclear in its logic. Because understand, the basic idea is that when you come to derive something, it has to be necessary. And if there is a possibility that it is not true, that is enough to knock it down. I do not need to prove that it is false. It is enough for me to show that it might be false. Right? How does a refutation work? I basically say: look, C is more stringent than A, so let’s derive by an a fortiori argument. No, there is a refutation: in terms of X, A is more stringent than C. Fine—but who says it depends on X? Maybe it depends on W, where C is more stringent than A. No. The moment there is a possibility of attributing it that way… Here too there is an asymmetry between the one making the derivation and the one refuting it. The one making the derivation has to show that it is necessary. The one refuting it does not have to show that it is false; he has to show that it is not necessary. Once I have an alternative explanation, that’s enough. All refutation in the whole Torah is built that way. Right—from archetypal sources, from a fortiori arguments, from verbal analogy, from everything. A refutation is never like the argument itself. The argument itself comes to show that something is necessary. The refutation comes to show not that it is false, but that it is not necessary. And once it is not necessary, we have no derivation, and therefore we cannot derive the law. To derive the law we need a valid derivation. Okay?

So this basically means that in the end too—after you now see the whole scheme—we actually have two alternatives. We know that in A and B there is an obligation of blessing. In a vineyard and in standing grain there is an obligation of blessing. Right? That we know. We just do not know why there is an obligation of blessing, and the conclusion will depend very much on that. Because one theory says: the obligation of blessing depends on Z. Anyone who has benefit must bless. Right? Z exists in both A and B, so that explains why in A and B one must bless. Right? Now if that is the theory, then in C too one must bless, because there too there is benefit, and in the other foods that are neither grain nor vineyard produce. Okay? That is one theory. And there is a second theory. The second theory says: maybe the obligation of blessing stems from X. You’ll tell me that in B we see there is no X and still one must bless. Fine, but it has Y. So what does that mean? That there is an alternative theory. It may be that the obligation of blessing stems either from the fact that there are gleanings or from the fact that there is an obligation of dough-separation. If that is the theory, then in the other foods there will be no obligation of blessing, because they have neither gleanings nor dough-separation, right? That’s X-roof and Y-roof. An unequal side. Exactly.

Now we have two possible theories. Both are possible, right? What happens when there are two possible theories? It’s not necessary, and that’s enough. Exactly. Then are we in a situation of proof or of refutation? Refutation. I spoke about asymmetry, right? It is enough to show that it is not necessary for this to count as a refutation. Well then, it’s not necessary. You have one theory that it comes from Z, and another theory that it comes from X or Y. Right? Two theories. Where is the practical difference between them? What will the law be in C? If it comes from X or Y, then in C there will be no obligation of blessing. If it comes from Z, then yes. Now I don’t know. I have two alternatives. The moment I have two alternatives, the derivation falls, since it is not necessary. Let’s say, since there is no necessity, then it should still stand unless you prove otherwise. No—what are you talking about? It’s also not necessary that fairies exist in the world, so should we then say there are fairies unless it’s proven that there aren’t? Right, but… Right, but what is a refutation? A refutation is not to show that it’s false; it’s to show that it is not necessary. Well then I showed it is not necessary. You have two theories; according to one theory you do not bless in C, according to the other you do bless in C. So you have two theories—there is a refutation here. You cannot prove that one blesses in C because maybe yes and maybe no. And I said that “maybe yes and maybe no” means refutation.

But here there is Y and Z, there’s an a fortiori argument—what? I no longer remember exactly what A versus C was, what the a fortiori argument was. No, here in this case it is not an a fortiori argument but an archetypal source. The archetypal source is actually based on Z. The hypothesis. Meaning, the fact that in both of them one derives benefit—you derive benefit from this and from that—so if one blesses here, one blesses there. Then the rejection says: no, but there there is an obligation of gleanings. Maybe because of that, and not simply because of the benefit. So Z is really—the whole thing starts from Z. Z does not appear only at the end; it starts from Z and also ends at Z. That’s the point. Okay? So not an a fortiori argument; an a fortiori argument would require adding another parameter here. And what would the stringency be? Because there’s an a fortiori argument with problems—the problem is solved by the fact that Z is actually… No, no, not yet. Even in an a fortiori argument the same problem exists. You just add another parameter, but you still have two alternatives. More lenient and more stringent, and then you say yes, but there is a stringency on the other side. But there is a stringency on the other side too, so it isn’t simply lenient and stringent, because the refutation says there is a stringency in the source case too. So there are no simple relations of leniency and stringency. That’s exactly—again—two possibilities, and therefore it is a refutation. The moment there are two possibilities, that is a refutation. Okay?

Maybe there is some hidden assumption saying that if there is an a fortiori argument, and I show with a second example that the a fortiori argument is irrelevant, then it doesn’t become relevant again for our topic. That’s how one proves it. And then says— That’s how I explained it, that’s how I explained it—but in the end it doesn’t hold. Because I have another theory, that either X or Y is what determines it, and that theory has not fallen. Okay? So what do we do? Why does the common denominator work at all? How can it? It makes no sense. The moment there are two options, that is a situation of refutation, not of derivation.

The answer is probably Occam’s razor. I have two theories, but one of them is simpler. The theory that attributes it to one parameter is simpler than the theory that attributes it to X or Y. So yes, I have two alternative theories, but if one of them is simpler, I prefer it. Right? Occam’s razor says that I prefer the simpler explanation. So the explanation that says there is one factor for the obligation of blessing—Z. Benefit is always what causes it, not specific factors like obligation of dough-separation or obligation of gleanings or something like that. I prefer the simpler explanation, and therefore even if I have an alternative explanation, if this explanation is simpler than the alternative, the inference still stands. In order to refute it, you need to bring an alternative explanation that is not more complex. Okay?

In a single a fortiori argument, say I derived C from A and now I said: no, there is a refutation, A has X. Here indeed the alternative is no less simple than the derivation itself. Either that is more stringent or this is more stringent; there is no hierarchy between them, so that is a refutation. But when I’m dealing with two source cases, now I have two theories. Either everything depends on Z, which is seemingly the simplest, or the matters depend either on X or on Y and have nothing to do with benefit. You don’t bless over benefit; you bless over anything that has gleanings or anything that has an obligation of dough-separation. Fine, that’s a theory—but it’s a more complex theory. I prefer one explanation over two different explanations. Okay?

Does Occam’s razor work in logic and mathematics? Meaning, I want to get here to a situation where logically it can’t be otherwise. What do you mean, logically? These are not entailments; it’s not “logically” in that sense. Occam’s razor works everywhere. Occam’s razor works in science; you build airplanes on the basis of Occam’s razor. But in logic you can define it simply. What is logic? It’s like science—what do you mean? A tree fell in the forest: did demons make it fall, or did it fall because of the wind? Okay, it’s clear there what counts as complex and simple, right? But here can you define what is complex and simple? Why not? I think two different explanations—Occam’s razor basically says: the fewer parameters you have in a theory, the simpler it is. And here you have a one-parameter theory versus a two-parameter theory. In all options in logic… It’s always like that. What… That’s all Occam’s razor is. Occam’s razor basically says: the fewer entities or the fewer principles you have in a theory, the simpler and preferable it is.

And is that only as a rule of conduct? Like when you get to law, you have probability considerations, so you go with what is simplest as a practical guideline; it does not establish the truth for you. Why? Ah—that’s another question. But it’s true everywhere, in science and in law and in every field. There are views that say Occam’s razor is a guideline and not a determination. What does that mean? If I have two theories, one complex and one simple, why assume the simple one is more correct? But on the other hand, if both work, why adopt the complicated one? The simple one is simpler, so I adopt it. I don’t know which is correct, but as a general guideline, as methodology, I prefer the simpler explanation. Okay? On that I once wrote an article, and in several places I wrote about it—I can prove that this is not correct. Occam’s razor is a logical rule, not a methodological rule. And the simpler one is actually more correct—not just a methodological preference for the simpler explanation. Anyway, let me not get into that now; whoever wants, I’ll send a link, because it would require going into another topic. Maybe at the end, if there’s time, we’ll see.

In any case, I assume it’s clear that Occam’s razor is a rule. By the way, in Jewish law too it can be a methodological rule, fine, and then we work with the methodological rule. I’m just claiming that that’s not right—not in science and not in Jewish law. It’s a logical rule, not a methodological rule. The simple one is actually more correct—that’s the claim. In physics that is certainly true, because there are many disputes in physics where to say this is the physics… Right, that is basically part of the foundation of my proof, but it needs to be refined more. I assume that in Jewish law and law and all these areas I’m willing to take the privilege that maybe I’m wrong by ten or twenty percent… Maybe you’re wrong is always true. Occam’s razor doesn’t tell you that you are certainly right; it only says the simple theory has preference. But in logic, if we attach it to mathematics, I don’t have the privilege of saying one plus one is three. Again: in mathematics you don’t need Occam’s razor. There are not two possibilities. In mathematics, if you have premises, they have one conclusion. You cannot derive from the same premises both a conclusion and its opposite; if you can, that means there is a contradiction in your premises. Obviously. Logic and mathematics do not belong to this whole discussion at all. The fact that I’m using symbols here doesn’t make it mathematics; this is a legal inference, not a logical entailment. I’m only formalizing it—it doesn’t matter—but that is only notation. Okay? By the way, this connects to the formalization we did of the a fortiori argument a few classes ago—I don’t even remember anymore. It’s an extension of that, but I won’t get into it here, I don’t have time.

In any case, that is basically the claim. I’ll give you an illustration so you can see. What we are doing here is basically a scientific generalization. The common denominator is nothing more than a scientific generalization. Look: for example, I take, say, a phone. I let go of it and I see that it falls to the table. I say, okay, then apparently objects with mass fall to the table. Fine? No—what is unique about the phone? It’s square, rectangular. Fine? So I say okay, let’s take a key, let go of it, and it also falls to the table. It’s not rectangular. Right? So all is well. But yes— it has a metal extension, fine, and the phone doesn’t, just say. Okay? “And the argument returns: this is not like that and that is not like this; the common denominator between them is that they have mass,” right? Therefore anything that has mass falls to the earth. You see that this is exactly a scientific generalization. The common denominator is just doing elimination. It says: the parameter of squareness is apparently irrelevant, because it falls even without being square. The parameter that it has a metal extension is also irrelevant, because it falls even though it has no metal extension. So apparently those are not the relevant parameters. So what is shared by these two? They have mass. Right? So apparently that Z is what determines the falling to the earth, and therefore everything that has mass falls to the earth. Okay? That is basically the common denominator.

In other words, the common denominator basically says: I see all the examples—and the more varied they are, the better. Fine? And now I say: if they are varied and yet the same thing happens in all of them, that means they have one shared feature that is what causes that result, and that is the relevant parameter for the result I am talking about. Okay? Now here too one could say: maybe the things that fall to earth are either rectangular or have a metal extension. That’s also a theory, right? And then I cannot infer conclusions regarding, say, this piece of plastic, okay? It is not rectangular and it has no metal extension. Fine? I cannot infer, because maybe that really is the theory. But you see, in science we do make such a generalization. Why? Because the generalization that there is a common denominator responsible for the falling to earth—namely mass—is simpler. Fine?

Now what would a refutation of the common denominator look like, for example? A refutation of the common denominator would be if another W appears, in A and B; both have characteristic W, okay? And in C there will be W-roof. It won’t have W. That will refute the common denominator. A refutation that is a stringency in A does not refute the common denominator. A refutation that is a stringency in B also does not refute the common denominator, because that is where we started. But a refutation that exists in both of them as against the target case does refute the common denominator. Refutations of the common denominator in the Talmud are always a shared characteristic of A and B, a stringency, that does not exist in C for our purposes. What is unique about these two? They are black. So maybe only black things fall to the earth, and not this green plastic thing I showed you before. Okay? That’s an example of a refutation. Then what would we have to do? We’d have to bring something else that is not black, right? That’s how science works. We take something not black and see whether it also falls to the earth; if it does, that means this common denominator too is irrelevant. Of course, if we then find in it some special characteristic, once again there will be—and the Talmud has this too—a common denominator from three, from four source cases, where it keeps going. Then there is a refutation against both, and another source case will come that doesn’t have that refutation, but it will have its own refutation that the other two don’t have, and then there will be a common denominator where one branch will be a common denominator from two, and one branch will be a derivation by a fortiori argument or archetypal source from one side, and of course it can continue as long as you want. After that, the whole thing is a common denominator, and now suddenly another common denominator will come from the other side, whether from two or from ten or from seventeen. In principle it could continue infinitely. Okay? But that is the logic, and that logic is exactly the logic of science. No difference. It is simply scientific generalization. Every scientific generalization and elimination that we do—the scientific elimination always rests on Occam’s razor. What does the scientific elimination we did here actually say? That the theory that it depends on a metal extension or a rectangular shape is less simple than the theory that it depends only on mass, because here there is no either-or; there is only one parameter. So I prefer to adopt the theory that mass is the factor. But if I bring a refutation saying, what is unique about both? They have a stricter side—what did the refutation do? It showed an alternative theory that is no less simple, also one parameter, and still explains why both fall to the earth, and from it it would follow that the plastic will not fall to the earth. Now once the two competing theories are at the same level of simplicity, that is a refutation. Therefore this really does fit. It really is a refutation of the common denominator. The moment I find a special characteristic present in both source cases. Okay?

Now one more important point to look at. Don’t we need elimination here? We need elimination, right? We need elimination, because otherwise it will never end. Yes. Which parameters are relevant? Obviously. Completely. It could indeed also be the green wall. Completely. Yes.

I want to look at this from a slightly different angle. Let’s look—ah yes. Let’s look. There is a rule in the Talmud that two verses that come as one do not teach. There is a dispute—some say only three—but for our purposes, simply speaking, in practice we hold that two verses that come as one do not teach. How does that fit with the common denominator? Here, in the common denominator, we have two verses and yet they do teach. Doesn’t that contradict the rule? What do you mean? It comes only to say that and not beyond. It contradicts the rule. Say that in standing grain and in a vineyard there are two verses, and you have only its specific novelty—only those two and not other foods. The question is whether they come as one or not come as one. They do—they come as one. They don’t have to be written together. “Two verses that come as one” means that we have two verses. They come as one, they say the same thing, right? They say the same law—yes, here one must bless and here one must bless. They don’t have to be written together. If there were a source that a vineyard requires a blessing, and I have a source that standing grain requires a blessing, that is called two verses that come as one. If there were a general rule, there would be no need for two verses; one verse would suffice. Right—so why in the common denominator do we learn from them? There too, two verses do not teach. You have two verses—they do not teach. If there were a rule we would write one verse; why not? Maybe there is no Z, no common denominator, between the two examples; is that why they are not “two verses”? In two verses that come as one it’s true there is no Z—but there is also no X and Y. You don’t need refutations on each of them in order for two verses not to teach. Even without refutations they do not teach. Just the fact that there are two source cases here. For example: agency to commit a transgression. It is learned from misuse of consecrated property and, I think, from misappropriation—or something like that—that there is no agency for a transgression, right? Why? Because in both places it is written that there is agency for a transgression, and they do not teach because they are two verses that come as one. You won’t find a refutation there, not because from one of them you can’t learn to the rest and from the second one too, but simply because there are two source cases here. What you said—that Z is a priori, meaning it doesn’t come only at the end but also at the beginning. What do you mean? On the contrary—look at the beginning, before we got to X and Y. In both of these there is Z, and in both of them one blesses. So why are there two verses? Why do we need two? Write one. Two verses that come as one do not teach. Why don’t they teach? Because why write it twice? If they would teach, write one and I would learn already to all of them. Precisely because there is a refutation, there is reason to say… Exactly. Here the refutations work in favor of the matter. And the refutations are not just something disruptive that we solved through the common denominator. The refutations build the ability to derive. Precisely the refutations. The refutations create the need, because due to the refutations there is no redundancy. Exactly, and that is the idea.

So in fact the refutations also have a positive role, not only a negative one. Here the refutations look like they play a negative role and Z solves the problem, but no. In this perspective the refutations have a positive role. What is the positive role? They are basically saying: you could not have written only A, because if you had written only A, then I could not have learned B, for example. Why? Because X would have been a refutation against it, right? And if you had written only B alone, you still couldn’t, because I could not have learned A, because there is Y, right? So I have no option of writing only A or only B. So there is no question why you wrote both, because I could not have written only one of them. If there is no question why I wrote both, then when I write both of them it is like one verse; it is not like two. Okay? That’s another way of looking at it. In other words, in the way I described it until now, the refutations interfered and we solved the interference. Here the refutations have positive value: they are what prevents this from being two verses that come as one.

Okay, now seemingly this does not exist in scientific generalization. There is no Z maybe between this and that; rather it is like… It’s a comparison between A and B, not between A and C and B and C. It creates for me a comparison between A and B. That there is non-dependence between A and B—you really can’t derive one from the other. There is mutual necessity here between A and B. Now whenever there is such mutual necessity between two source cases, the rule that two verses that come as one do not teach does not apply. In many places in the Talmud, once you say two verses that come as one do not teach, but then you show that there is mutual necessity, the rule falls away. It is already like one verse, since you have no question why the second verse was written. There is mutual necessity—you could not have learned from there, and you also could not have learned the first from the second. Once that is so, it is like one verse; it is not like two, and therefore they do teach.

Now understand that in the context of scientific generalization this is not built that way, because in scientific generalization there is no question of redundancy. I am not asking why nature makes this fall to the earth and that too fall to the earth. It falls because both of them fall. There are no verses here. That aspect does not exist in scientific generalization. The first aspect I described does exist in scientific generalization; the second does not. And now I’ll show you that in a certain sense it does exist there too. Why? In philosophy of science there is a rule that when you generalize from examples, it is better that they be varied. Meaning, say I see a raven and it is black, and I want to infer that all ravens are black—to make a generalization. Okay. Now the more black ravens I see—and this is really my topic next Sunday—the more black ravens I see, the stronger the conclusion becomes that all ravens are black; it is corroborated. Okay? But if, say, all the ravens I saw were Israeli ravens, that’s not so good, because maybe only Israeli ravens are black. Maybe ravens from Indonesia are not black. Therefore it is better to take ravens from Israel and ravens from Indonesia. And even that isn’t enough; maybe in Britain it’s not so. So the more varied it is, the more grounded the generalization is considered to be.

Now what does “varied” mean? Varied means there is a difference between A and B. There is a parameter that appears in A and not in B. One is from Israel and the other is not, or this one is from Indonesia and that one is not. So you see that even in the scientific world, the difference between A and B has a role. The role is not because of redundancy—there is no redundancy because there are no verses in the scientific world. That is not the point. But the mutual refutations, the differences, do have a constructive role. Because when the examples are varied, the generalization built on them is more grounded. So variety in the evidence—that’s what it’s called in philosophy of science—is very important. And in that sense it really does remain similar to halakhic generalization. Regarding Jewish law—meaning, with two verses, where is the limit to almost infinite proliferation? You can find tons of parameters that differ from one another. So therefore we talked about relevance. So I say: therefore we need to talk about relevance. We are speaking about variety in parameters that seem relevant to us; otherwise there is no end to variety. You can always attribute it to things. But there too there is relevance. You’re talking about a minimum. But there too—the relevant parameters. There’s a difference because “vineyard” is written with one letter and “bread” with another. Nobody raises that as a parameter—why? Because it is irrelevant. Okay? We still assume relevance in parameters. You can’t escape that. Judgment enters here; this isn’t mathematics. Okay.

Now notice—this is an interesting point, because many people don’t notice it. Now look at the other side. It’s complicated, but I hope you’re following. Look at the other side. In the halakhic world we understand why you need the mutual necessity or the reciprocity: in order to neutralize the issue that two verses that come as one do not teach. Once there is mutual necessity, then it is like one verse, not like two, because you could not have written one and learned the other from it. Right? Now we discover something else in the halakhic world. What exists in the scientific world certainly also exists in the halakhic world; only the reverse is not true. Variety in the evidence is important in Jewish law too. If you see that one blesses both over a vineyard and over bread, okay, that is more significant than if you saw it only with a vineyard. Because that really gives corroboration to the claim that anything from which one derives benefit requires a blessing. And the more varied your evidence is, the more grounded the generalization. Meaning that in the halakhic world, this whole game—the differences between the two source cases—has three roles, not two. In the scientific world there are two, and in the halakhic world three. One role is a disruptive role. You can’t derive from A; you can’t derive from B; okay, but the common denominator solves that. Okay? The other two roles are constructive. When I create differences between the two source cases, that neutralizes the problem of “two verses that come as one do not teach,” because they become effectively like one verse. That exists only in Jewish law, because in science there is no such thing as two verses. But there is a third role that constructs in this area, and it exists both in Jewish law and in the scientific world, and that is variety in the evidence. The more I see the obligation to bless appearing in more and more contexts, the easier it is for me to generalize that anything from which one derives benefit requires a blessing. Look—you see two totally different things, a vineyard and bread, and both require a blessing. Why? That is very varied, they are different from one another. Apparently it’s because whenever there is benefit one blesses. What they have in common is that it is benefit. Okay?

So the variety in the evidence that we see in the scientific context teaches us that even in the halakhic world, the difference between the two source cases is not only there to neutralize the issue that two verses that come as one do not teach. It has a positive role in the logic itself, not only a negative interpretive role at the interpretive level of whether two verses that come as one teach or do not teach. Here I am speaking on the level of the inference itself, the logic of the inference—it has a role. Because the more varied the examples, the more grounded the inference at the logical level, not at the interpretive level. At the logical level. That is similar to laws in the Torah, just as in physics, for example, there is a big question: are there laws of physics, or do we invent them so that it will be easier for us to understand? In the Torah too? In the Torah too. No, in the Torah there are laws. Who told you? The same question you ask about physics can be asked about Torah to exactly the same degree. On the contrary—in the laws of physics we know of no exceptions. In the laws of Torah there are tons of exceptions to every rule, and that raises even stronger questions: are there really laws in Torah at all, or are we just constructing laws because that is how we arrange the phenomena? It is our way of thinking. We play with laws, we work with laws, but that is methodology, not truth. Exactly the earlier comment.

Yes, but Torah—from the school of thought that says Torah has rules—it follows, as it were, that the Holy One established rules, and we are trying to figure out the rules that the Holy One established, and that is how He built the Torah and what we are trying to uncover. But why do you assume there are rules? Why do you assume there are rules? Because the fact that there is… We work with such a methodology, but that doesn’t mean there really are rules here. If we were working according to—I don’t know—as in nature we don’t work with two verses that come as one… we wouldn’t do it here either. What? I didn’t understand. If it is not that the Holy One established rules but that we invented these rules, then these rules should be rational like those of nature. No—the Holy One established, for the sake of argument, these inferential rules of midrash, the hermeneutic principles. Yes, but that doesn’t mean there is a rule that anything from which one derives benefit requires a blessing. It’s not some such rule. Rather, practically, de facto, things from which one derives benefit are blessed over. How does that come out? That’s how we organize the phenomena for ourselves, because simply that is the most convenient organization for our way of thinking. Maybe the Torah could have… But in science too there is the same evidence: in fact everything with mass falls. Do you want to say that exists only in my mind? Have you ever seen something with mass that didn’t fall? So that too is a law in reality itself. The question, even in the scientific world, is not that simple. The claim is that basically we make such generalizations, but who knows—maybe it isn’t true. For example, if I found a case in which there is benefit and nevertheless one does not bless, for some other reason—say, a prohibition. Okay? When I eat something prohibited there is benefit and I don’t bless. So there you see: even though there is benefit, one does not bless. It is not true that there is a sweeping rule saying that anything you derive benefit from you must bless over. “For I the Lord love justice, I hate robbery with a burnt offering.” “One who blesses over theft blasphemes the Lord.” Let’s put aside those exceptional cases that are connected… In intuitive matters, for example the issue of variety—the variety in Jewish law with which you make this inference—it is intuitive, because I see that researchers in other fields also work that way. That is the intuition behind it. But again, “two verses that come as one” does not appear as a rule in the world. Right, that is an interpretive rule only. It is not part of human intuition. It is a novelty. That is why I defined it earlier—I said it is an interpretive rule, not a logical rule. Obviously. “Two verses that come as one” is an interpretive rule, and therefore it appears only in Jewish law and not in the world. And why is there this interpretive rule? I don’t know—we received from Sinai this interpretive rule from the Holy One, that there is no redundancy in the Torah. Yes—no, obviously He wants us to work with that. Because there is no redundancy in the Torah—that is the assumption. The simple assumption is that there is no redundancy in the Torah. So if two things are written, clearly they are intended to teach only about themselves, because otherwise only one would have been written.

Obviously there is such an assumption, but that is a methodological assumption. It says nothing about whether there is such a rule that anything involving benefit requires a blessing. I am now talking about the halakhic rules themselves, not halakhic methodology. The halakhic rule that I uncovered is that over anything from which one derives benefit one blesses. Is there such a rule? Or is that only the most convenient way for us to organize the phenomena, to group them into categories and think about them by means of schemas or general headings, groups, all kinds of things like that? There are such claims in philosophy of science—that laws there are only a taxonomy of phenomena, meaning they are only a way to organize and collect the phenomena, to group them and divide them; it is simply more convenient for us to think that way because that is how our minds are built. In Jewish law you could make the same claim.

And yet still think that there is a rule—two rules? In our methodology there are not only logical rules but also interpretive rules, because Torah deals not only with logical inference but also with interpretive inference from the text. In contrast, when you study physics and you do— It wasn’t simply someone over the generations—no, not the Sages. A law given to Moses at Sinai. Why the Sages? So then it really comes from the Holy One? Certainly. I mean that the Holy One gave us interpretive rules. Okay? No, but there is a difference between scientific-philosophical research, which is our way of organizing things, and saying that the Holy One established it. It’s either to say that the Holy One established rules and we must from there… I’m not talking about the methodological rules; I’m talking about the product. The rule is not “every two verses will teach if there are differences between them.” You are looking at that as the rule. I am not talking about that rule. I am talking about the rule that anything from which one derives benefit requires a blessing. The result of the inference, not the method of inference itself. The method of inference itself certainly is a rule, but in science too it is a rule. No one disputes that in science there is a rule that conclusions are inferred by induction—until there is a refutation, never mind, but in principle. He says that this is a way of arranging? The product of this matter says: all bodies with mass fall to the earth. I don’t know whether all bodies fall—everything I’ve seen so far. So it is convenient for me to think of it as if it were a rule. But there really is no such rule. That is the claim of those who challenge it there. They are not talking about the methodology of the discussion; they are talking about the product—that is, about the scientific law itself.

So this analogy to scientific inference is interesting, because it basically says that the differences between the two source cases have a destructive role, and that exists both in science and in Jewish law, but the common denominator solves the problem or neutralizes it, okay? And they also have two constructive roles. One constructive role is variety in the evidence, which exists both in science and in Jewish law, and the second constructive role is that it comes to neutralize the principle that there is no redundancy in the Torah. That is an interpretive rule, not a logical rule. It is an interpretive rule. A text could have been written without the assumption that there is no redundancy in that text. The Holy One could have written the Torah even without the assumption that there is nothing superfluous in the Torah. Fine? Like “something derivable by an a fortiori argument, yet Scripture took the trouble to write it,” or “something derivable by reasoning, yet Scripture took the trouble to write it.” That means the text is not really so exacting. There are superfluous things in the text. But that’s a difference between Talmudic passages and other things. I didn’t understand. The Torah is a completely finite text. We have the Five Books. What is infinite there? In the Torah there are Five Books. That is the text. I’m talking about the Written Torah. The hermeneutic principles are not applied to Talmudic passages. The hermeneutic principles are applied to the Written Torah. Okay.

There is even—this is interesting—in Menahem Elon’s book he brought, I saw several examples of someone expounding general-and-particular rules in the words of medieval authorities. Maharam of Rothenburg does a general-and-particular, I don’t remember where—there are several examples. Later I collected and found quite a few such examples. Because behind it there is some kind of logic. That was my claim, and therefore I collected those examples. It is not merely some arbitrary decree that we received from Sinai. There is also some kind of logic behind it; it comes to solve a problem. We talked about this in the Sunday classes at some point. It comes to solve Hart’s problem in legal theory, if anyone knows it, with the prohibition against bringing vehicles into a public park. Yes, that’s the example they always bring. What counts as a vehicle? Is a toddler ride-on toy a vehicle? How do you define what a vehicle is? So in the legal world there is a dilemma as to how you do it. From the context you try to understand, but it is always a question; you can never know. The Torah gives you rules for learning which “vehicle” is meant, through examples and the way the examples are written. If it is general and particular, particular and general, general and particular and general. Each of those is a different instruction for how to generalize the examples. In other words, there is a very precise logic that comes to solve Hart’s problem. That is exactly what it is doing. That is the difference between the three rules of general and particular, particular and general, and general and particular and general. And there is a fourth: particular and general and particular. That also exists, although it does not appear among Rabbi Ishmael’s principles, but there is a Talmudic passage in Nazir where there is such an exposition too.

Anyway, for our purposes. It’s like how many properties to take in order to generalize the thing? Right. Or how many properties to take. Meaning, you invent the properties yourself, but the question is how far: the more properties you take, the narrower the generalization will be, right? Because you require similarity in all the properties. So only what is fully similar enters the category. The more similarity you require, the smaller the extension. Now the writing form of general and particular, particular and general, and general and particular and general determines how many parameters of similarity need to be taken—one, two, or three, essentially. And that determines the radius of the generalization. Now which are the relevant parameters? That is the interpreter’s judgment. Obviously. You have to reach that yourself. But from that point onward, once you have made a map of the relevant parameters, the Torah tells you how many of them to take—that is, what the radius of expansion is. So as not to fall into confusing metaphors, like all these spaces and so on—what’s it called? Pokémon, where part is here and part is there. That is exactly the example he brought to illustrate this point.

In any case, now I want to move on. After we’ve understood this idea of the common denominator as scientific generalization, I want to get to a surprising phenomenon, and that is the refutation of “a stricter side.” Okay? Now the Talmud in Berakhot that I brought earlier, which derives blessings over benefit from vineyard and grain—we said there are refutations on both sides, and the common denominator is that there is benefit, therefore anything involving benefit requires a blessing. The Talmud continues to the next stage: “What is unique about the common denominator between them? They both have an altar aspect.” The two source cases, vineyard and grain, both have an altar aspect. Both come to the altar—meal-offerings and libations. Both are brought to the altar, okay? So they have an altar aspect. What is that refutation? That refutation is of the kind of “black,” right? Both source cases have a characteristic on which the obligation of blessing can be attributed. Everything that has an altar aspect, one blesses over it, because it is connected to the Holy One, something like that, therefore one blesses over it. Things that have no altar aspect, perhaps one does not bless over them. So you have presented an alternative that is no less simple than the inference you want, therefore it is a refutation. Okay? Now yes, here you see the added W—both source cases have W, here and here, and here there is no W. Fine? We already discussed this before; it is the black color.

Now I want to show you a Talmudic passage in Ketubot 32b, which is basically parallel to our passage, but there there is an interesting addition. “Apparently Ulla holds that whenever there is money liability and lashes, one pays the money and does not receive lashes.” In every case where one is liable to pay money and also liable to lashes, one pays the money and is not lashed—so claims Ulla. This comes exactly from the verse that says… wait, in a moment we’ll see where it comes from. In a moment we’ll see where it comes from. No, it’s not so simple; in a moment we’ll see where it comes from. So it is like “he incurs the greater penalty,” but here it’s not the greater penalty in the usual sense; specifically, one pays and does not receive lashes. Fine? So the Talmud says that.

The Talmud says: from where does Ulla know this? He learns it from one who wounds his fellow. Just as one who wounds his fellow—where there is money liability and lashes—you have to pay me if you injured me, and you are also liable to lashes—there, one pays the money and does not receive lashes. So too, wherever there is money liability and lashes, one pays the money and does not receive lashes. So it is learned from one who wounds his fellow. “What is unique about one who wounds his fellow? He is liable for five payments.” We have a refutation, okay? He is liable for five things. One who wounds, as distinct from one who merely causes damage, is liable for loss of livelihood, medical expenses, pain, humiliation—not only damage. Okay? Therefore you cannot learn regarding ordinary damage, for example, a case where there is only monetary liability without the additional four things, that he too is exempt from lashes. There is also logic to this, because if you are liable for five things, that means that the money payment for the damage is paid, and you also have a financial penalty, because all these are penalties or things of that sort, so you have already received the punishment and not only the compensation obligation. But in a place where there are no additional four things, only damage liability, there perhaps you would also be liable to punishment, namely lashes. Okay?

So the Talmud says: rather, he learns it from conspiring witnesses. Just as conspiring witnesses, where there is money liability and lashes, one pays the money and does not receive lashes, so too wherever there is money liability and lashes, one pays the money and does not receive lashes. Right? With conspiring witnesses, if they were exposed in false testimony regarding money, then we do to them as they conspired to do, right? They pay the money. Besides that, they transgressed “Do not bear false witness against your fellow”—they lied—so they deserve lashes. So conspiring witnesses are liable for both money and lashes. Again, I don’t remember where it is learned from, but the rule is that they only pay and are not lashed. Fine.

Then the Talmud says: but conspiring witnesses also have a refutation. “What is unique about conspiring witnesses? They do not require prior warning.” In the case of conspiring witnesses, we punish them even without warning. Okay? So they have a unique stringency. Therefore there too there is a stringency. “Rather, he learns from both of them,” says the Talmud. “What is the common denominator between them? Where there is money liability and lashes, one pays the money and does not receive lashes. So too wherever there is money liability and lashes, one pays the money and does not receive lashes.” Exactly like our structure, right? You see this diagram. One who wounds his fellow is A, conspiring witnesses is B, and all the other cases of money-and-lashes are C. Z is that there is liability for money and lashes. X is… that no warning is required—or Y is that they are punished without warning, and X is that there are the four additional payments. Fine, this is exactly the same structure, the standard structure of a common denominator.

Okay, simple enough—but here there is a surprise. The Talmud says: “What is unique about the common denominator between them?” For us this is no longer a surprise because we already saw it in our own passage too: “They both have a stricter side.” Now this is strange. Let’s go back for a moment to the diagram. Notice that the refutation of the common denominator—you remember we saw this diagram where there is W, a property that exists both in A and in B and does not exist in C—that is the refutation of the common denominator, right? That is clear, and we explained why. There is an alternative theory here whose result is opposite and it is no less simple. That is, the question whether it depends on Z or depends on W gives two competing theories, and in both cases it depends on only one parameter, so that is a refutation—you can’t know. Okay, that is the refutation we know of the common denominator.

But notice that the refutation of “a stricter side” is a refutation of this structure: there is no W. This is the structure. And what are we refuting? A and B have a stricter side. Look—A has X and B has Y. So that means both have a stricter side, while this one does not have a stricter side, because it has neither X nor Y. So this is the refutation of “a stricter side.” Okay, so really we did not need W at all in order to refute the common denominator. The structure of the common denominator is refuted from within itself; there is no need to bring a different refutation. “What is unique about the common denominator? Both have a stricter side.” What do you say about that refutation?

Tosafot in Ketubot asks: “That both have a stricter side? Difficult—for if so, then we will never derive by common denominator anywhere, because in every case one can refute either with a stricter side or with a more lenient side.” If we want to derive a leniency then it will be leniency and stringency, it doesn’t matter—it’s not specifically “a stricter side” for our discussion. Okay? Every common denominator falls, because in every common denominator the two source cases do have a stricter side—we saw that. So if you refute with the refutation of “a stricter side,” then in effect every common denominator collapses. No common denominator remains in the Torah. Because every derivation by common denominator means that in both of them—if there weren’t in each of them a stricter side, we wouldn’t derive, because of the rule that two verses that come as one do not teach. Only because each one separately has a stricter side can we derive from both of them to this. But then they say no: if both have a stricter side, then there is a refutation against the derivation. So it comes out that you cannot derive from two source cases. If there is no stricter side, then it’s two verses that come as one. If there is a stricter side, then both source cases have a stricter side, so again you cannot derive. So in practical terms you can’t derive anything from two source cases. Then how can there be those who refute with the refutation of “a stricter side”? The Talmud later says there are those who do not refute that way. It is basically a tannaitic dispute whether one does or does not refute with “a stricter side.” In our case too it is a dispute: Rabbi Yohanan ben Zakkai does not refute with “a stricter side,” while the later generation—the future one he was worried about, if you remember—they would refute with “a stricter side.” Okay? So there is a dispute whether one refutes with “a stricter side.” But according to the view that does refute with “a stricter side,” there is simply no common denominator in the world at all. You cannot derive from two source cases anything.

Now I want to translate Tosafot’s question into the terms of the description I gave earlier. Not for nothing did I give it. In fact, what I said earlier explained what the logic of deriving by common denominator is built on. Let’s return for a moment to the scheme. I said that basically I have two ways of explaining why one must bless—or why in a case of money and lashes one only pays and is not lashed. This is a formal scheme that can describe either this derivation or that derivation; it doesn’t matter. Let’s talk about blessings, okay? How can I explain what one blesses over? I have two theories. Theory one: anything that has gleanings or that has an obligation of dough-separation is something over which one blesses—or X or Y. Right? According to this theory, over other things, C, which have neither gleanings nor dough-separation, one does not bless. Right? Alternative theory: what determines the blessing is Z, namely the fact that there is benefit. That exists both in A and in B, so that explains why in A and in B one blesses, but the implication now is that we will bless in C as well, because in C too there is Z, there is benefit. Right? I have two competing theories whose results regarding C are opposite. According to the first theory, in C one does not bless. According to the second theory, in C one does bless. And the question is: which of the two theories is correct? Right? That is really the question.

So we explained that the common denominator is based on the idea that the simpler theory is the correct one. The theory that attributes everything to Z is the simpler one. Therefore it is the correct one, because the theory that attributes it either to X or to Y is more complex. It is possible, but it is less simple. The assumption is that it is not correct. Okay, that is how we explained it. And that is basically what Tosafot is asking. Tosafot is really saying: what do you mean—if you tell me that there is a refutation saying that both have a stricter side, what are you actually saying? You are basically saying: maybe the reason one blesses is either because there are gleanings or because there is dough-separation, right? “What is unique about both? They have a stricter side.” But we already rejected that because of Occam’s razor. We said that the simpler theory is preferable to that theory. Someone who says there is a refutation of “a stricter side” is basically telling me: since there is an alternative theory, I do not derive. Right? But that isn’t true, because the alternative theory is less simple. When I have an alternative theory that is less simple, it does not compete with the other theory. It doesn’t knock it down. It doesn’t constitute a real alternative. That is what Tosafot is asking.

Okay? Now the question is how to resolve this. So look, there is another place where this appears—also in our own topic, but there is another place. I didn’t bring it here. Tosafot surely resolves it also without Occam’s razor—that is, what is he proving to us? That there is a view in the Talmud that you simply can’t derive by common denominator. So it doesn’t use Occam’s razor, as it were? Because it doesn’t derive by common denominator. There is no common denominator in the world according to that view. You can never derive by common denominator, in any case. Tosafot is asking a question, after all. Yes. Okay.

Now, in tractate Makkot there is the stronger side—I’m not sure how to define it—but maybe the other side is somehow more stringent than the second side. What do you mean, more stringent? In what sense more stringent? But it’s like Z is also stringent. Z is also a stringency, only that this stringency also exists in C, not only in A and B. But on the face of it there is no relation of stringency between X and Y on the one hand and Z on the other. Do you want to argue that it depends on whether X and Y are as stringent as Z? Maybe, but on the face of it that doesn’t seem to matter. What matters here is the logic, not the degree of stringency. And the number of parameters favors the theory of Z. In a moment we’ll see, because there may be medieval authorities who say something like that.

The Talmud brings here in Makkot… wait… yes. “Rabbi Meir holds one is liable to two authorities.” Someone who receives punishment is liable to two authorities. It says: rather, what is Rabbi Meir’s reason? Why is he liable to two authorities? Ulla said: he learns it from the case of one who defames his wife. Notice again, it’s Ulla. He learns it from one who defames his wife. Just as one who defames his wife receives lashes and pays, so too all cases receive lashes and pay. The Talmud says: what is unique about one who defames his wife? It is a fine. Defamation is a fine. Where the payment is not a fine, you cannot know. He holds like Rabbi Akiva, who says conspiring witnesses are a fine. Wait… here, it starts here. There is an earlier discussion, but let’s start here. This is what matters for us. Okay? Ulla said: he learns it from one who defames his wife. Just as in the case of one who defames his wife, for a prohibition with no action one receives lashes, so too every prohibition with no action receives lashes. Okay? I am not talking about lashes and payment, I am talking about a prohibition with no action. Fine? A prohibition with no action receives lashes. So says Ulla. Why? It is learned from one who defames his wife. That case is a prohibition without an action—he only spoke, okay?—and he receives lashes. They say: what is unique about one who defames his wife? He both receives lashes and pays. We saw that above. One who defames his wife receives lashes and pays, so he has a stringency. You cannot learn from him. Rather, says Resh Lakish: he learns it from conspiring witnesses. Just as conspiring witnesses, for a prohibition with no action one receives lashes, so too every prohibition with no action receives lashes. There is a refutation: what is unique about conspiring witnesses? They do not require warning. What we saw in our passage in Ketubot. “One who defames his wife will prove it, and the argument returns, this is not like that,” etc. The common denominator: for a prohibition with no action one receives lashes, so too every prohibition with no action receives lashes. This is C, yes, that is C, right? The same ordinary structure of a common denominator.

Then the Talmud comes and says: “What is unique about the common denominator between them? They both have a stricter side.” Again, a refutation of “a stricter side.” Fine? “And Rabbi Yehuda does not refute with ‘a stricter side.’” This is the tannaitic dispute I mentioned earlier. Here too we see there are tannaim who do refute with “a stricter side”—that is the one who disagrees with Rabbi Yehuda. So he actually predicted well, even though he told him in the Mishnah that Rabbi Akiva brought a verse—whatever.

In any case, here I open the Ritva. The Ritva elaborates a lot on this. “What is unique about the common denominator between them? They both have a stricter side.” See? Tosafot objected: if we refute with “a stricter side” even though the stringencies are not similar to one another—if the two stringencies are similar, that is W, then certainly we refute. But if the stringencies are not similar to one another and still we refute with ‘a stricter side,’ then you have abolished every common denominator in the world. And they answered that we do not refute this way except when the stringencies are highly unusual, with nothing else like them in the whole Torah. Conspiring witnesses are lashed without warning, and one who defames his wife is lashed and pays. What special anomalies—then yes. In both cases there is some special anomaly. Not every anomaly, but a very special anomaly—then yes. And in the chapter ‘These Young Women,’ where we raise this refutation—what is unique about one who wounds his fellow and conspiring witnesses? One who wounds his fellow is liable for five payments. In tractate Sotah, regarding one who immersed that day—our own Talmudic passage—even earthenware vessels where one who immersed that day is a primary source of impurity and the vessel imparts impurity through its airspace, and it is somewhat similar to what we say in Sanhedrin: what is unique about the prince and the deaf-mute? They are both unusual. ‘They are both unusual’—what does that mean? They are unusual from different angles, but both are unusual. So the claim that both have a stricter side means a highly unusual stricter side—not merely the fact that it is a stricter side, but that there is something very, very exceptional there.”

He doesn’t really explain so much why these things are so exceptional. Why are they so exceptional? “A stricter side” is something we find in all sorts of places. What is so special about this refutation? So it’s like a characteristic that only you have and nowhere else? I don’t know exactly. In what subject? About conspiring witnesses? About lashes-and-payment? About one who wounds his fellow, conspiring witnesses? What? The prince and the deaf-mute. Right. How many princes are there? Fine, but how many conspiring witnesses are there, or how many cases of one wounding his fellow? Not common. Exactly. Right—but he says it there too. He learns from here to there: here too it is special, and therefore there too one refutes with “a stricter side.” So what is not special? I don’t entirely understand the criterion.

Then he says: “And our teacher Nachmanides explained that we do not refute with ‘a stricter side’ except where the two source cases have stringencies, neither of which exists in the target case, and the target case has no stringency absent from the source cases, as in the case here. And so it is. But generally, where we do not refute with ‘a stricter side,’ the target case has some stringency not found in the source cases.” So there has to be, in the target case, some stringency that the source cases do not have. He adds another parameter, so that this basically leaves an a fortiori relation between the source cases and the target case. But that is against the accepted logic, because it means that in each of them there is a stricter side, and also in the target case there is a stricter side. But when there is a stricter side in both directions, that is a refutation; we do not derive. Since when do we find that stringencies cancel each other out? If stringencies canceled out, there would be no refutations in the world. We make an a fortiori argument from A to B; you say no, what is unique about A? It has a stringency, right? What are you saying? In A there is a stringency relative to B, and in B there is a stringency relative to A. Nachmanides says no problem: let’s cancel them and derive. No—stringencies do not cancel. If one is stringent in one respect and the other is stringent in another respect, then there are no simple lenient-stringent relations and you cannot derive. So here Nachmanides says that because the target case has some kind of stringency—he doesn’t say what stringency—but if it has some special stringency then… very strange, in short.

And my teacher the Ra’ah explained that we do not refute with ‘a stricter side’ except when the stringencies concern essentially the same thing we are trying to learn from them. For example, here we are trying to learn regarding lashes, so if he is lashed and pays, then that is a stringency within the very law of lashes itself. So if I have two stringencies within the law of lashes itself, that indeed will be a refutation. But if I have two other stringencies that the source cases possess in other areas, not related to the law of lashes that I want to learn, then no. Fine—that too. Why and what more is here? But maybe this at least sounds more plausible.

“And I saw that Rabbi Meir Ashkenazi wrote that ‘a major stricter side’ means that sometimes with conspiring witnesses there is the stringency of one who defames his wife, namely receiving lashes and paying.” You can in some situations find the same stringency. None of these explanations, in my opinion…

We saw this already regarding the a fortiori argument. In all the cases where they use the refutation of “a stricter side,” there is a dispute, but those who use the refutation of “a stricter side” do so always—as far as I checked—in cases where the refutations are legal rulings and not factual characteristics. Think about it. I could say: what is unique about conspiring witnesses? They do not require warning. That is a legal refutation, right? Or I could say: what is unique about conspiring witnesses? They are especially wicked. Not a refutation of the same type. A refutation speaking about the nature of their act, not about the legal rules that apply to their act.

Think, for example, in tractate Bava Kamma, where we derive regarding an ox, a pit, fire, and the like. All the characteristics brought there, which serve as refutations and a fortiori arguments and so on, are factual characteristics. What is unique about a pit? Its creation was originally for damage. What is unique about fire? Another force, the wind, is mixed into it. Fine? What is unique about horn-damage? Its intention is to damage. All the characteristics there are not halakhic characteristics. They do not say: what is unique about horn-damage? It is also liable in the public domain. That is the legal result. Rather they say: what is unique about horn-damage? Its intention is to damage. Meaning, the properties under discussion are factual properties.

In our case of the common denominator, there can be situations where the refutations are factual refutations—that is, there is some stringency in the source case because it is stricter in some factual sense. And there can be a halakhic refutation—it has some law that shows, say, there are four additional payments in the case of one who wounds. So he says it is more stringent because it has some law that is stricter than in the target case. What’s the difference? The rule in Jewish law, generally, is always a mapping of a law onto a factual situation. Right? Jewish law is always built this way: there is a factual situation and a law sits on top of it. Right? In this factual situation the law is such-and-such. In that factual situation the law is such-and-such. In other words, Jewish law is always a mapping between factual situations and laws—which laws apply to each factual situation. That is how halakhah is built, right? Now the factual situation is not just some random place where laws apply. They apply there because there are certain characteristics of that situation due to which the Torah says that this is its law. Right? Always something. Why are there five payments in the case of one who wounds? That is a law. Why? Apparently there is some kind of stringency there because of which the Torah says he must pay five payments and not one. I don’t know what that stringency is, but in the background there is some stringency because of which the laws are more severe.

Which means that when I say its law is more severe, that is not the refutation itself at all. A legal refutation is not really the refutation. The refutation is not because its law is more severe. The fact that its law is more severe means that it itself is more severe. Meaning, it has some factual characteristic that is more severe. Ah—if so, then perhaps also regarding the law I want to derive, it cannot be derived, because maybe the factual characteristic present in the source case is also what causes the law that I want to derive, and that characteristic is absent from the target case. That is how a halakhic refutation is built.

If I were to say: what is unique about a pit? Its creation was originally for damage—that is a factual refutation. Then I say: if I found some stringency in a pit, maybe it is because its creation was originally for damage; therefore the stringency is there. But in the target case, where its creation was not originally for damage, that stringency will not exist. If I say: what is unique about a pit? It is exempt regarding vessels—or, conversely, what is unique about a pit? It is liable regarding concealed items, unlike fire, say. So what does that actually mean? The fact that it is liable regarding concealed items is a law. That is not the stringency itself. The stringency is presumably that there is something in a pit that is more severe than in fire, factually more severe—for example, that its creation was originally for damage—and because of that it is liable regarding concealed items. Fine? In other words, I am really using legal rulings as an indication of factual characteristics. The legal rulings are not the refutation in themselves. The legal rulings are a sign that there is a refutation here.

If I have source case A and I derive from it to C—what is unique about A? It is liable for five payments, while C is not liable for five payments. The point is not that it is liable for five payments. The fact that it is liable for five payments and C is not tells us that there is probably some kind of factual stringency in A that does not exist in C, and that is what causes the liability for five payments. If so, then perhaps regarding blessing too, that stringency is what determines it. It’s here? It could be that regarding blessing too, that is the determining stringency. Okay? There is a big difference between a halakhic refutation and a factual refutation.

So where is the… where is the point? Look what happens in the refutation of “a stricter side.” In the refutation of “a stricter side,” if both sides—or even if only one side—is a legal refutation, it may be that the same factual stringency in both source cases comes to legal expression differently in each of them, but it is the same factual stringency. Its legal expression depends on the circumstances: here the legal expression is that he is liable for five things, and there that he is punished even without warning. Fine? But it may be that it is the same factual stringency in both, and therefore it is a refutation. Of the very possibility, even if here it is not known? It is enough to show a possibility. A refutation—I said—a refutation only needs to show a possibility in order to refute. An inference has to be certain. A refutation only has to show another possibility. And I say: although these are two different stricter sides in the two source cases, since the stricter sides are legal ones, it may be that underlying them is the same factual stringency, a shared factual stringency, which is absent from the target case, because in the target case these two stringencies are absent. Okay? Since that is a possibility—not certain, but a possibility—it is refuted.

That is the correct explanation. And throughout the Talmud you will find that the refutation of “a stricter side” never appears when the refutations of the two source cases are factual refutations. Only when the refutations are halakhic refutations. It should be straightforward, because most cases are like that, so it’s not such a great novelty that only such cases are found—but still, there are also other cases. For example in Bava Kamma. In Bava Kamma, right, they derive from pit and fire together regarding one’s stone, knife, and burden. On page 6 there are several common denominators there, right? Three or four examples where they derive by common denominator. No one there refutes with “a stricter side,” because there the refutations are factual refutations. In factual refutations, no one refutes with “a stricter side.” And regarding Tosafot’s question and the questions of the other medieval authorities, the Ritva and all those authorities—so what remains of the common denominator? The answer is: every common denominator where the refutations are factual and not halakhic—no one will refute with “a stricter side.” That is the kind of common denominator the Torah is speaking about. In every place where it is about law? Yes. My claim is that in every place where the refutations are halakhic refutations, there is a view—not always stated explicitly—but the one who refutes with “a stricter side” would refute there. It is not always brought there; never mind. And where it is not brought, it is simply because they are following the view that does not refute with “a stricter side.” That’s all. But in places where the refutation is factual, there is no one who refutes with the refutation of “a stricter side.” There is no such thing, because otherwise you have destroyed every common denominator in the Torah. Okay? In our case too, in Sotah, it is like that. It is all laws—laws of impurity and purity—so all the refutations are halakhic refutations. Therefore Rabbi Yohanan ben Zakkai was concerned that the later generation would refute here with “a stricter side.” Okay? Because the refutations are halakhic.

Now, as an aside, even if you find an example where there is a halakhic refutation and they do not refute with “a stricter side”—and I said there are places in the Talmud where common denominators are brought and the view that refutes with “a stricter side” is not brought— it could be because, by reasoning, I can understand that the two legal rulings in those two situations do not have a shared factual basis. Somehow I understand by reasoning that the factual basis that causes those two laws is not shared. There is nothing common there in the two source cases. In such a case, even the one who refutes with “a stricter side” would not refute. That too can be a solution. But it could also simply be that he was not cited there. That’s all. In other words, there is such a view. It is brought in some passages. In passages where it is not brought, they simply did not bring it. That’s all.

Okay? Now if that is so, then this really rounds out the picture a bit. If you remember when I discussed the analysis of the a fortiori argument, then in the analysis of the a fortiori argument the whole idea was—you remember the rotation of the a fortiori argument? I tried to show why one does not reverse an a fortiori argument when someone raises a refutation. And the answer lay in the fact that underlying the legal rulings written in the table of the a fortiori argument are microscopic characteristics—I called them factual—the alpha and the beta, right? Factual stringencies that generate those legal rulings. And that solved the problem there. And I’m saying that with the common denominator too, in order to solve the logical problems that exist in the common denominator and in the refutation of “a stricter side,” it is because behind the legal rulings sit factual properties, and one must understand that.

Jewish law is always built that way. Everyone understands that—just not necessarily in these contexts. Everyone understands that why do I say that in one act one is liable for forty lashes and in another act not? Because there is some kind of stringency there because of which one is liable for forty lashes, right? Meaning, obviously there is some factual characteristic there because of which we obligate forty lashes, and elsewhere, where we do not obligate them, apparently that characteristic is absent. Before that—is it a stringency, or maybe, say, legal policy? For example, “the burden of proof is on the one who seeks to extract money from another”… Never mind. That is a stringency of the sort called legal policy. It doesn’t matter. But there has to be something in the situation that causes the law here to be more severe. It is not just that law is some random thing dropped from above.

Oh, we are liable for forty lashes, whereas elsewhere we are not. Apparently there the characteristic is absent. Before that—is it a stringency, maybe of legal policy? Say, “the burden of proof is on the claimant.” Never mind. It’s a stringency of legal policy. It doesn’t matter. But there has to be something in the situation that causes the law here to be more severe. It’s not just random. Jewish law is not just some detached thing unrelated to properties.

Now this is a very interesting point, because when people study reasons for the commandments, for example—so today’s class has a bit of philosophical orientation—but when people study reasons for the commandments, they always bring this view that says the commandments are all the king’s decree. Arbitrary, yes, arbitrary—they have no reasons. And Maimonides in Part III of Guide of the Perplexed says that cannot be. Obviously the commandments have underlying reasons. Because they want to make the Holy One seem grander than His creatures, as someone who does things that are not understandable, unlike human beings who just do things in a rational way. But in fact they turn the Holy One into something worse than His creatures, Maimonides says there. They turn Him into one who does things for no reason, someone who does things without reasons.

I’m saying here: I have a halakhic proof that Maimonides is right. Because if I say that the commandments are merely the king’s decree, then that means that the fact that here we obligate lashes is not because there is some factual property on account of which we obligate lashes. It is simply a scriptural decree; the Torah decided that here there will be lashes. If so, then there is no difference between halakhic refutations and factual refutations. What difference does it make? I would say even more than that: all factual refutations—who says there is a refutation at all? After all, according to that conception, Jewish law has no connection to facts. So what do I care if there is a factual stringency in the source case or in the source cases? What does that say about the law? It’s completely absurd.

And one of the interesting things—this is another methodological point—is that many times there are meta-halakhic discussions about philosophy of Jewish law, all kinds of things like that, which are discussions I would call journalistic. That is, “it can’t be” and “it can be,” like Maimonides writes there. A priori philosophical discussions of that sort. I’m saying that if I can show, and bring evidence from within Jewish law itself, for these meta-halakhic discussions, that is much stronger. Right? I brought—I’ve mentioned this more than once—for example the question whether Jewish law is pluralistic. Right? Is there one halakhic truth or are there multiple halakhic truths? There are discussions about this. Avi Sagi wrote a whole book about it; it’s not worth much. Only the conceptual analysis—he has impressive analytical ability—the conceptual analysis is good. The sources aren’t worth much; some are, in my opinion, not analyzed correctly, and others are journalistic sources, books of thought and the like. Show me from within Jewish law itself. I have proof from within Jewish law itself, from all sorts of halakhic passages, that Jewish law is not pluralistic. And in my eyes that is much stronger—to show it from within Jewish law itself—than to talk in general arguments about what it makes of the Holy One and what is or isn’t logical.

Take, for example, a prohibition repaired by a positive commandment, for which one does not receive lashes. There is logic in that; it is not arbitrary. That is the question. According to those views there need not be any logic in it. One does not receive lashes because the Torah decided one does not receive lashes. Again, in my opinion that is not logical. I agree with Maimonides that it is not logical. And I think it is much stronger to argue against the second position if you simply bring evidence from Jewish law itself that it does not work that way.

Where is the connection between fact and law and reason? Meaning, where is the reason? Why do you call it reasons for commandments? Why does the fact of this… For example, why is there liability for five payments in one who wounds, while in one who damages there is not? Only damage. Apparently one who wounds involves some act that is more severe than when one’s property causes damage. More complex—it doesn’t have to be more severe. Someone who thinks there are no reasons for commandments doesn’t need this, because he’ll tell you: the Torah decided that he pays five payments because that’s what it wanted; it gave its coinage. So if there is a connection between facts… Yes—that is what I am claiming, that there is a connection. And if you see this thing, then what? Then apparently there is a reason, no? Correlation is not causation. Fine, you can say correlation is not causation, but I think they deny the correlation itself. Otherwise why should there be a correlation? The simple assumption is that if there is correlation, then yes, it is causal. It doesn’t have to be, but if there is correlation, the simple assumption is that it is causal. No one says that all these bodies fall to earth just because they feel like it; it just happens by chance that there is a correlation that it happens to all bodies with mass, but they do it just because they feel like it. That is basically the analogy to that claim.

But that is not a definition of the reason for the commandment. They are making meta-claims, not claims about the reason itself—they’re just in another discussion. After there is—they assume there is a connection between law and fact. So why is that not enough? Why nevertheless did the Holy One want that… So why? What is this connection between law and fact? Why does this law apply to that fact? Apparently because something in that fact generates that law or suits that law. Therefore the Torah said it specifically on that fact… Otherwise why didn’t it just make a lottery? Just make a lottery. Say that damage caused by property should incur five payments, while a human being who wounds should pay only one damage payment. What difference would it make? Why not say that? But there are difficult legal cases, truly, because it really is… But in things like sukkah and such, that comes to expression there too. There too. Why? There too, perhaps the Torah wants a temporary dwelling, and that’s what a temporary dwelling looks like. That is a reason too. Then think about it: why did the Holy One want sukkah at all? Fine, that is always the question of reasons for commandments. That is a question. But still I can explain why He wants a temporary dwelling altogether. In that case the Torah actually says so: “that your generations may know that I caused the children of Israel to dwell in booths,” and so on. “So that your generations may know.”

But if those principles themselves are clear to me, then for me that is already the reason. There will never be an infinite chain of justification. I can’t make an infinite chain. The question is where it stops. If it stops at a place that is self-understood, then for me that is indeed a reason. Here another reasonableness, here another reasonableness—I understand that they are needed. But these things in sukkah, these extra normative additions that you added, from which to build a proof that the Holy One expects from us things beyond morality and beyond law and beyond things where one needs to ask—so is it really necessary to explain why this extra layer of sukkah, tefillin, and all those things beyond morality is expected of us? Nothing needs to be explained. He wants us to be moral. He wants us to be moral—what do you mean? What is the problem? Not sukkah—are you speaking about pious conduct or things of that kind? Are you talking about going beyond the letter of the law in sukkah? No, simply—why sukkah? Why did the Holy One command us regarding sukkah at all? “So that your generations may know.” “So that your generations may know that I caused the children of Israel to dwell in booths,” and that is a memorial to what happened there. Why did you go further into why all those commandments beyond law are needed? What do you mean, why needed? I don’t know if “why needed,” but they exist. The question is whether they exist or not; I don’t know why they are needed. That is a factual question. And I think that from here there is strong support for the claim that they do exist.

You’re telling me: fine, maybe this is only in the legal realm. Could be, I don’t know. But at least in the legal realm it is so. But why say that one who wounds has a greater payment rather than saying that the damage of the one who wounds is more complex and therefore requires payments? That’s all. What? But also an ox that gores a person causes him loss of livelihood, medical expenses, pain, humiliation, everything. Why don’t you pay? You are distinguishing between damage caused by a person and damage caused by property. But the difference between one who wounds and one who damages is in the damager, not in the injured party. Whether the damager is a human being or whether the damager is property. You are distinguishing between whether the injured party is a person or whether the injured party is property. That is not the difference between one who wounds and one who damages. The laws of one who wounds and one who damages in Maimonides are distinct from the laws of property damages. The laws of one who wounds and one who damages concern a human being who caused damage, whether to a person or to property. And in the laws of property damage, the issue is that my property damaged a person or property. “Property damage” means the property is what caused the damage, not that the damage was done to property. Damage to a person by an ox. Obviously—you are absolutely right. But that is not the difference between one who wounds and one who damages. Because the difference between one who wounds and one who damages is a difference in who the damager is, not who the injured party is. Liability for five payments exists only when the damager is a person. But if the damager is property, even if the injured party is a person, there will not be five payments. Why? The damage to the person is the same damage. Why can’t he? His owner can—what do you mean? The owner pays. If the ox gored you, I have to pay. Why do I pay only damage and not medical expenses, pain, loss of livelihood, and humiliation? Because you’re a human being and you do things—watch everything you do. Good—so now you explained what the stringency is in a human damager compared to an ox that causes damage. That’s all. So it’s not connected to the question what happened in the damage, what happened in the damage. That is the stringency exactly—a human damager as opposed to a property damager. Exactly.

Okay, we’ll stop here. If people have exams, then good luck to you. Exempt from an exam on these classes? Exempt from an exam on these classes. Yes.