Another Look at “the Common Denominator” (Column 346)
With God’s help
Disclaimer: This post was translated from Hebrew using AI (ChatGPT 5 Thinking), so there may be inaccuracies or nuances lost. If something seems unclear, please refer to the Hebrew original or contact us for clarification.
To my daughter Rivka, may she live and be well
In the previous column I discussed the relationship between avos and toldos (primary and derivative categories) in Shabbat, and I mentioned the difference between damages (nezikin) and Shabbat (see there around notes 6–7). In damages there are derivatives that cannot be learned from a single primary and are learned from two primaries, whereas in Shabbat we do not find such derivatives (I noted this there in note 7). In contrast, in the derivation called the “common denominator” (ha-tzad ha-shaveh), the matter depends on the question of the logic of that derivation. From its very name it would seem that such a derivation is based on a shared similarity between the two teaching cases (the melamdim). In Misharin, Article B (and in more detail in the eighth book of Sun and Shield: Talmudic Logic), I showed that there is another similar kind of derivation that I called “conceptual construction,” and it is not based on a shared tzad shaveh between the two teachers.
In recent days, while learning the sugya of “the owners attend to the carcass” (ba’alim metaplim b’neveilah) in Bava Kamma 10a—a question that has bothered me for over twenty years—the answer crystallized for me together with my daughter Rivka, may she live and be well, regarding this sugya.
The tzad ha-shaveh is a very fundamental inference in Talmudic logic—far beyond what people ordinarily imagine—and I have written quite a bit about it. It contains not a few challenging riddles, and varieties of similar inferences that, when solved, expose foundational layers in lomdus and in thinking more generally.
Here I wanted to present the logic of tzad ha-shaveh in general, and afterwards to point to a sugya about “the owners attend to the carcass” that challenges the usual conception of the tzad ha-shaveh. Finally I will return again to the question of the logic of the tzad ha-shaveh in the labors of Shabbat. Following this discussion requires some concentration to keep track of the differences between the cases and the various states.
The basic scheme: the common denominator
At the beginning of the Sifra a baraita is brought listing Rabbi Yishmael’s thirteen hermeneutic rules. Among them are “a paradigm (bin’yan av) from one text” and “a paradigm from two texts” (some count these as one measure). According to the common understanding, the first rule is nothing but analogy: we analogize one law (the derivative) from another (the primary). The second rule is based on two primaries (avos) that, each by itself, is insufficient to teach the law. This is the logic of the “common denominator.” Note that some commentators explain that even “a paradigm from one text” is based on the logic of the common denominator; the difference between the two rules is only whether the two teaching cases appear in the same passage or in two different passages (see Encyclopedia Talmudit, entry “Bin’yan Av”).
For our needs here, I will bring an example of this logic from Berakhot 35a, which deals with blessings over benefit before eating:
We have found kerem (vineyard/grapes). From where do we derive for other species? We learn by comparison: Just as the vineyard is something from which one benefits and therefore requires a blessing, so too everything from which one benefits requires a blessing. One can refute: what of the vineyard—that it is obligated in gleanings (olelot)? Let standing grain (kammah) prove otherwise. And what of standing grain—that it is obligated in challah? Let the vineyard prove otherwise. And the matter returns: This is not like that, and that is not like this. The common denominator between them is that in them there is benefit and a requirement of blessing—so too everything from which one benefits requires a blessing.
Here we have two primaries—vineyard (grapes) and grain—and we want to learn for other items (like other fruits and vegetables) that just as we bless over grapes and grain, so we should bless before eating anything else as well. Why do we need two primaries? Because each one has a unique feature that prevents us from learning from it alone: the vineyard is special in that it is obligated in gleanings for the poor, and grain is obligated in challah. The combination of the two together can teach us about everything from which we derive benefit, namely that there is an obligation to bless before enjoying them.
The general structure of such a derivation is as follows: We have two primaries (A = vineyard; B = grain), and there is a property P that exists in both of them (the obligation to bless), which we wish to extend to the derivative (C). Each primary also has its own unique property that the other lacks: A has x (obligated in gleanings) but not y, while B has y (obligated in challah) but not x. (We assume C—the derivative—has neither x nor y.)
- We first attempt to learn P for the derivative C from the primary A (by bin’yan av or by kal va-chomer).
- We reject this due to the stringency unique to A (because A has x, perhaps precisely due to that stringency P applies in A).
- We attempt to learn P for C from the primary B.
- We reject this due to the stringency unique to B (because B has y).
- We therefore learn P from the common denominator of A and B together, and the inference returns (v’chazar ha-din): what they share (call it z)—the aspect of benefit—is what determines P. Since that aspect exists also in the derivative, P applies to C as well.
Schematically: each of the unique features of A and B (x, y) is eliminated as the determinant, leaving the shared aspect z as the relevant determinant of P.
The problem with the common denominator
On its face there is here a logical wonder. Each primary alone cannot teach the derivative—but their combination, without any further addition, manages to do so. Why exactly does the combination succeed where each fails? We can formulate the difficulty thus: Perhaps the rejection (pircha) of learning from A or B is not valid, for one could also refute the combined inference by pointing out that the derivative C lacks both unique properties (x and y). If so, why do two primaries help?
A refutation: a shared feature
The Gemara there in Berakhot indeed refutes with: “What of their common denominator—that they have an aspect related to the altar?” That is, the two primaries share some other unique feature w (a link to the altar) that is absent in the derivative, and therefore the inference collapses. In general: if the primaries have a shared feature that the derivative lacks, one cannot learn from them.
This sharpens our earlier question: When there is no such shared feature w, why doesn’t the inference collapse similarly in the ordinary case?
The logic of the tzad ha-shaveh
It is commonly thought that the justification of the inference is an elimination: Primary B shows that P does not depend on x (since B lacks x yet has P), and primary A shows that P does not depend on y (since A lacks y yet has P). We are compelled to conclude that P depends on the shared feature z. Thus P will also apply to the derivative C, which also possesses z.
But this does not completely solve the problem, for why can’t P be determined by the presence of at least one of x or y? In other words, there are two competing theories:
- Theory A: P holds whenever at least one of the features is present: (x ∪ y) → P. According to this, P will not apply to the derivative C, which has neither.
- Theory B: P does not depend on x or y at all, but on some other feature z shared by the primaries: z → P. According to this, P will also apply to C (since C has z).
The claim underlying the tzad ha-shaveh is that Theory B is simpler—it relies on one parameter rather than a disjunction of two—and by Occam’s razor the simpler theory is preferred; hence the result is that P applies to the derivative as well. By contrast, when there is a unique shared feature w that is absent from the derivative, a third theory arises—P depends on w—which is also simple (one parameter) and therefore cannot be dismissed; in that case the inference fails.
The refutation of “a more stringent side” (tzad chamur)
In several sugyot we encounter a phenomenon that seems to challenge this entire scheme. For example, in Ketubot 32a the Gemara attempts (following Ulla) to learn that one cannot receive both lashes and payment for the same act. The structure is just as described: the Gemara tries to derive from one primary (injurer), then from another (false witnesses), and then from their common denominator. Suddenly a surprising refutation appears: “What of their common denominator—that it has a more stringent aspect (tzad chamur)!” At first glance the Gemara is raising Theory A as an alternative and rejecting the logic of the tzad ha-shaveh. Where did Occam’s razor in favor of Theory B disappear?
Tosafot there (“she’ken”) ask: If so, we would never be able to learn by tzad ha-shaveh anywhere, since there will always be some more stringent or more lenient side to refute with. In other words, every primary has, by definition, some stringency not present in the derivative, so such a refutation would undermine all tzad ha-shaveh inferences. Tosafot and the Ritva (see also Makkot 4a) offer answers, but they are strained.
The logic behind refuting with a “stringent side”
In my view this can be easily resolved if we return to the logic of the tzad ha-shaveh. We must distinguish between two kinds of unique features that appear in hermeneutic inferences (bin’yan av and kal va-chomer): halakhic features and factual features. In the cases we brought earlier, {x, y, z} were halakhic features (e.g., obligation of gleanings or of challah, or a link to the altar). But in other cases the features are factual. For example, at the beginning of Bava Kamma the defining traits of the heads of damages are factual: pit—its beginning is to cause damage; fire—another force is involved; horn—intent to damage, etc. Every halakhah rests on some factual feature. The reason that, say, false witnesses do not require prior warning, or that vineyards have gleanings, derives from some underlying factual features of the situations. Thus the halakhic features conceal factual drivers.
Now, when I have two primaries each with a different factual feature, I can perform the elimination described earlier and show that neither factual feature is the determinant of P, leaving Theory B (the simpler theory) as superior. But if the primaries share the same factual feature w, then—even if their halakhic manifestations differ (x here, y there)—the inference by tzad ha-shaveh collapses, because there is a simple theory tying P to that shared factual feature w. As far as I can tell, whenever the Gemara raises a refutation of tzad chamur, it is speaking of halakhic (not factual) features.
The sugya of “the owners attend to the carcass”
Bava Kamma 10a rules that if Reuven’s ox damaged Shimon’s ox, the carcass belongs to the injured party (ha-meit yihyeh lo). If something happened to it—say it rotted on its own or crumbled—the loss is on the injured party. This means that the injured party should immediately deal with the carcass (e.g., sell it at its higher value right after the damage), thereby preventing subsequent depreciation. The Gemara brings three sources for this rule:
- Rabbi Ami: “He who strikes the life of an animal shall make it whole (yeshalemena)”—read not yeshalmena (“pay it”) but yashlimena (“complete it”), meaning the owner (injured party) completes the payment by handling the carcass.
- Rav Kahana: “If it be torn, he shall bring evidence; he shall not make good that which was torn”—until the point of tereifah he pays, but not for the tereifah itself.
- Chizkiyah: “And the carcass shall be his [=the injured party’s].”
The first source speaks of a person who damaged an animal; the second from the laws of a guardian who was negligent; the third from damages of a pit in the public domain. The Gemara assumes a tzrikhuta—that all three verses are needed. Such a tzrikhuta effectively says that none of the sources alone could have taught the law, because each would have faced a refutation due to its unique feature; hence we need all three. This means we have three primaries, and by their common denominator we wish to learn for all other cases. Of course, the logic of the common denominator can also operate with three or four primaries; two is just the simplest case.
Two difficulties
(1) When the Gemara examines the possibility of deriving from the first two sources (without the pit), it rejects this by refutations based on each source’s unique feature (tzad chamur). This seems to contradict the logic of tzad ha-shaveh (the situation of our Figure 1 rather than Figure 2), for here the features are factual, not halakhic; thus the earlier explanation of refuting via halakhic stringencies shouldn’t apply. In which case, the inference from two primaries should have been valid (no need for a third source).
(2) The tzrikhuta is incomplete: the Gemara only considers (and rejects) derivations from the first alone, the second alone, both together, and the third alone. But it does not examine the remaining pairs (first+third, or second+third). Why doesn’t the Gemara complete the analysis?
An inference from several primaries—without a common denominator
In light of what I explained above, we can suggest a resolution to both difficulties. The Gemara shows that each of the three sources has its unique feature. The question is whether they share a common denominator. For the sake of the argument let us assume they have none. Then the scheme of the inference is as follows: each primary has its unique feature, and no pair shares a common denominator. In such a triangular inference without a common denominator, the only remaining theory is Theory A: P holds whenever one of the unique features obtains: (x ∪ y ∪ z) → P. There is no simple Theory B (no single shared feature across all three). Thus there is no need to continue the tzrikhuta beyond showing that no pair yields a valid tzad ha-shaveh. And it is obvious that one cannot learn from any pair to other cases if those two share no common denominator.
Note the halakhic upshot: In the ordinary tzad ha-shaveh (Figure 1), the result applies to all derivatives regardless of their properties—more precisely, to anyone who has the shared feature z of the primaries. Here, by contrast, I claim that the law that “the owners attend to the carcass” applies only where one of the three unique features holds (an uncommon kind of damage; damage occurring on its own; damage via one’s property rather than via one’s person). If there is a case in which none of these holds, then the rule would be that the damager must attend to the carcass (and any depreciation would be on him).
Indeed, perhaps this explains why the Gemara later determines that the rule does not apply to a thief or robber: in theft/robbery none of the three unique features is present. There it is a person causing damage directly and intentionally; it does not occur on its own (unlike pit), and it is common (unlike ordinary accidental human damages). Thus the rule is confined to the union of the three sets taught by the three primaries, not to their intersection.
A difficulty with this explanation
I assumed that the three primaries have no common denominator, and that indeed resolves the questions. But perhaps one will say: after we eliminate the unique features of the three sources, we remain with the fact that there is damage and a carcass. From this, perhaps, we should conclude that in all cases where there is damage and a carcass, the injured party must attend to it. One might object that this cannot count as a “common denominator,” since that is precisely the subject under discussion. The features we seek should be ancillary (like “it occurs on its own,” “it is via one’s property,” or “it is uncommon”), not the very subject (damage with a carcass).
But that is not precise. Even in the earlier cases, the “common denominator” is not ancillary: in Ketubot the common denominator is that in both primaries the person is flogged or pays, and that is precisely the subject of discussion. And in Berakhot, too, the common denominator is that in both there is benefit—again, that is the very subject.
The answer is as follows. We see later that the rule does not apply to a thief and robber—even though there too there is damage and a carcass. Since explicit verses teach that in theft/robbery the injured party does not attend to the carcass, the Gemara evidently understood that “damage with a carcass” cannot serve as the relevant common denominator; were it so, it would have applied to theft/robbery as well. Therefore the Gemara concluded that there is no common denominator of that sort, and we return to the logic explained above; the two difficulties remain resolved.
Summary
We have seen three kinds of inferences that look similar but, upon further examination, are entirely different:
- Figure 1: There is a common denominator among the primaries and the derivative. In this case one can derive all derivatives that share the primaries’ common feature—even those not otherwise similar to either primary.
- Figure 2: There is a common denominator between the primaries but it does not exist in the derivative. In such a case the inference collapses; one cannot learn to any derivative that lacks the primaries’ common feature.
- Figure 3: There is no common denominator even among the primaries. This, as we have seen, is really a sum of three separate “paradigms from one text,” and it has no connection to the tzad ha-shaveh.
In the next column I will try to discuss a fourth kind of derivation from two primaries, in which there is no common denominator between the primaries and yet one can still derive broad conclusions for the derivatives. I call this “conceptual construction.”
Related article: Two Kinds of “Common Denominator”: Conceptual Construction
It came out as a file. Is that intentional? Because it's a little less convenient to read.
Because there are diagrams
Regarding the issue in the inscription, it is possible that the difference lies between a “unique side” and a “serious side”. A unique side is not a rebuttal, because it is not a true common feature.
Charging minors or challah are unique features (but they are not a serious side), on the other hand, an exceptional punishment (in the case of conspirators or a perpetrator, even if the exceptionality of the punishment is expressed in different ways) is a true common feature that indicates that this is a high-level crime and that it is impossible to learn from it about minor crimes (and according to Rivaz in Sota and Rivaz in Yehuda in Beatings that Do Not Rebut a Serious Side, perhaps they believe that the severity of the punishment does not reflect the severity of the act, but rather is a unique feature).
1. I liked the excuse of a serious side that is said only in halakhic terms. I think it can also be based on the fact that what is not halakhic serious but rather a division of material from the explanation is not really treated as something more serious than halakhic serious.
You can see this in a matter of light and matter - in a situation where there is material from the explanation that is said as a pirkha to light and matter, you can say “I will put all this into light and matter”, especially since sometimes the rejections of learning stem from explanations that are more correct to define them as a realistic difference and not as something serious in the reality of the teacher on the student. (It is enough to pirkha every dehu in the construction of the father)
2. But I did not understand what injustice you found in the Ramban”s commentary, saying that it is urgent (I understand why it is urgent, that every subject is needed for a new explanation). According to the Ramban, if we are talking about an equal side, which is essentially a rejection of the falsification of the simple (that there is a falsification in the learned that is not in the taught, as he defined it) - it is very logical that it is impossible to say a severe side - because it is possible, as I said before, to introduce the severe side into the falsification. But if we are talking about a fundamental construction - any falsification is sufficient (even just a division that is not clear that it is a falsification) and therefore even a theory that there is another severe side in any place that causes the law is sufficient to reject the teaching. After all, the burden of proof is always on the “inventor” of the teaching, and even if he claims a theory that is superior, his words are still unproven, since the simpler is not always the correct one.
And in the matter of Pesachim Az. They take a hard line from the fact that it is always tadir and kalil - and indeed it can be said that this is a halakhic definition, but even if this is true - it turns out that the Gemara does not claim that it is tadir and therefore it has a virtue that is perhaps indirectly related to the virtue of Pesach, which has Keret, but it is also the realistic severity in it that causes it to be said that Shabbat is rejected.
In other words - even if you say that kalil and tadir are halakhic, it is unlikely that they are a sign of severity, but rather they represent the severity itself. Therefore, the Ramban's explanation is better on the issues of Shas (although the idea of the excuse is really nice and thank you very much for this article!)
The problem is that according to the Ramban, we need ad hoc justifications. There is no criterion for when the materiality of the learned differs from the two materialities of the learned. Furthermore, when there is materiality in the learned, it does not change the logic, since the materiality in both directions is enough to unravel the inference. It is not necessary to prove that it is not true, but it is enough to show that it is not necessary for it to be true.
I do not see why an equal side based on a line is the conceptual construction. I really do not think so.
I will add and say in explaining the Ramban method that when it comes to an equal side based on a light and a medium, the equal side is nothing more than a conceptual construction as you define it, which aims to prove the irrelevance of the serious aspects in the melamid. The source of the serious aspect in the melamid does not stem from its equality with the melamid but from its original material, and this also explains why the analysis of the serious side is irrelevant here (apart from the fact that it is possible to insert that same common serious side into the light and a medium).
Explaining the difference between a regular equal side - which is based on learning from the sources and an equal side that is actually a minor and aggravating circumstance
I am trying to argue this way:
We say that
A has the severity X and does not have Y and Z and the law is unknown
B has the severity Y and does not have the rest and the law that is forbidden
C has the severity Z and does not have the rest and the law that is forbidden
D has the severity Y and does not have the others and the law that is permitted
We want to learn a minor and aggravating circumstance for A that is forbidden because of the severity X
Of course, we are rejected by the fact that B has Y and maybe that is the reason why it is forbidden
Now there are two options - if we bring D - we will actually prove that the severity Y is not the one that causes the prohibition - after all, in D it is permitted despite the severity Y - and then it is clear that the minor and aggravating circumstance is valid despite the severity on both sides
But even in the absence of D, it is possible to confirm the minor and aggravating circumstance by C: The argument of the jurist is that the severity Y causes the prohibition. The converse theorem is that when there is no material Y, it is permissible. By C we prove that this is not true because there is a situation where Y is not present and it is still prohibited. Hence, it is proven that Y is not relevant to the prohibition and we can go back to making aggravation (because we have no proof that X is not relevant - but if the material X is in one of the teaching - we can no longer make aggravation).
If so, the proof from C is only that the characteristic Y is not the cause of the prohibition - apparently a conceptual construction and not a study on the basis of the common that may not exist at all
Then the source of the law in A is not B, but the material X that is in it, and therefore it is even possible to learn that in A there will be a greater materiality than in B, of course within the limits of the law of sufficient (but as is known, sometimes sufficient is said only partially, on one subject and not on another, and it is also not said where the material and the material are refuted)
You have built a construction here that is not a regular equilateral triangle based on a line. Adding unnecessary elements. A regular equilateral triangle based on a line is much simpler and is not a conceptual construction.
I entered the party late and I am writing on the side that on your Sabbath as a soloist of the Torah Kadisha you have not yet packed the microphone. I was attacked by a recitation binge and we were saying that women should not recite after recitation, unless they are written. The discussion is rich in power and charm, but the conclusions do not sit well with me without further explanation, and this is why I came to ask for it. [If I need too many fasts per week and have exceeded my limits, then please also write them down with a marker and I will accept the judgment with love].
First, a few corrections to the text so that I can at least bring some benefit.
1. Page 4. It is written “The Gemara in the Ketuvot tries to teach that it is possible to be flogged and pay for the same offense”. A tsal that is not given. It is known that one is not afflicted and pays, the only question is whether one pays and is not afflicted (ula) or is afflicted and does not pay (R’ Yochanan). This text is also repeated at the end of the column in the chapter ‘Difficult with this explanation’ (The equal side is that there is in principle a financial obligation and beatings and concludes that according to Ulla the obligation chosen for realization is financial). It is possible that I did not understand correctly.
2. There note 5. ‘The Gemara says’. It is better to say ‘The Gemara says 4: beatings’ (it is mentioned only after the note).
3. Page 6. “And the third source from the damages of a fool”. Ch”Sh. And also on Lakman and on page 7 (a total of 3 times). This is how Rashi interpreted it, and the dead man will be with him (and in this he explained that it is not in any way. And see the gloss by Rashi), because the Gemara says, “Let us write a bull under the bull and be silent.” As for the substance of the matter, perhaps he will understand this.
4. Page 6. In the second difficulty in the structure of the need, it is written, “Learn from the first and second sources.” The explanation is on the serious side.
My soul is alive, it looks sparkling like crystal, and it is beautiful to you, it is beautiful to you. But when you rub the pearl, it is not certain that more than a pearl remains in the mind. And in three parts, we will gather:
A. There is no logic in such a serious side interpretation (according to the sages of Dr. Yehuda). Because it is clear that the “burden of proof that both have a common factual characteristic” lies with the interpreter, as you wrote in note 6. If he has an idea for such a factual characteristic, he should honor it and present it (with relevance in the explanation, of course, and not just any one).
B. If we have come to such speculations, then every equal party in the world has a serious side. Perhaps even in the fathers of torts there is a common factual characteristic that is hidden and hidden for exactly all four of them and there is no learning from it for anything else? Surely you will tell me that only if there is a serious side according to halakhic law is there room for speculation that there is a common factual characteristic. But then please explain why the thing being studied itself cannot function as the serious side that would establish the hypothesis that they have a common characteristic. What about the fathers of torts, since we know that they owe payments, and therefore we can assume that they have a common factual characteristic, and from now on, who will argue that it also exists in a rooster that pecks and breaks dishes? The same applies to every equal side in the world (and please be careful. And don't ask me about your discussion at the end of the column about the difficulty in this explanation).
C. To explain why the Gemara does not always interpret a severe side (which is true according to the narrow explanation of the Tosafot that a severe side is strange), you said in note 6 that the Talmud according to Rabbi Yehuda does not interpret a severe side. So sometimes the Gemara feels like arranging for the sages as well and sometimes not? And how does it know that Ulla arranges for himself as well as the sages, and not according to Rabbi Yehuda until it comes up with a gazâsh for him? And so, and the gezâsh is addressed (otherwise, they would certainly respond and it would not have been of any use), then the Gemara should have continued and said that R’ Yehuda, according to Eliyahu, does not need the gezâsh (and then perhaps they will run the trouble and cut it equal to her reading). It is difficult for me to check now, since I am devoid of books other than Google, and therefore I will ask with your permission as a matter of hearing, whether it is clear that the disagreement between R’ Yehuda and Rabbanan is on equal terms in every world or perhaps they only disagreed in the case where it is relevant (while in other cases, when relevant, then the law interprets the severe side).
The issue of owners treating the filth.
D. The need for owners treating the filth above is easy to explain. Factual and logical reasons for making it more severe can accumulate. Very simple (and this is different from your explanation). In Hell, there is an accumulation of reasons to make it more severe (both common and not necessarily so) and therefore perhaps the Torah did not make it less severe. Only in the three meldems together do we see that each pair of reasons to make it more severe does not add up to make it more severe (and the accumulation of three reasons does not seem sufficiently different from three reasons to the Gemara. If this is the problem, I have explanations). In my opinion, it is simple and clear. Therefore, it is also understandable that the requirement does not need to be completed. On Shabbat, I will get to the place of the book, the fig, and the pomegranate and try to check.
E. You wrote that because these three are studies in building a father, then at least one of the characteristics is always required to make it less severe. Maybe I simply do not know famous laws – what is the ruling on a person who is a normal harmer who broke a table and the trees are worth money. This is common damage, both to the hands and to the body. In your opinion, is the reduction of trees to the harmer? (I understand that only killing a fellow ox is not common, but damaging a fellow's property is common and common).
F. Your explanation is simply strange to me. It is clear as day that the equal side among them who is liable for damages and owners who treat carrion is also liable for anything that is liable for damages. Owners treat carrion. This is the equal side of the three fathers, and the assumption ‘for the sake of the discussion’ that they do not have an equal side is simply not true. The question of why we learn that owners treat carrion from the above trio and do not learn the opposite from a thief and a robber is a question in itself that I am convinced that the commentators have addressed. And probably the simple answer is that they learn damages from damages and not from something that involves taking away one's possession. Is this Naomi? I am beginning to suspect myself that I simply did not understand what you are claiming and that this is the case.
It is difficult for me, in my sins, to go into the details of the party again (especially on the issue of owners dealing with the waste). I will try briefly and from the top.
A. Absolutely not. Note that the interpreter here is in the position of a defender and not an attacker. After all, the equal party is trying to prove something, and the interpreter claims against him that he has no proof.
B. Not true. When both teachers have a serious halakhic side, it is clear that at its core there is a serious factual side. The question is whether it is the same serious side or not. In an ordinary equal party, there is no basis for suspecting that there is a common serious factual side that the learner does not have, since we have no halakhic indication of its existence. This is exactly what I argued here.
C. This is very typical in Talmudic issues. Sometimes a tserikuta is made and sometimes not. Sometimes the disputant is brought in on the same issue and sometimes not (this is what happens in any situation where some leader speaks about the dispute over the issues).
Owners dealing with the waste:
E. This is the best law that can be paid from movable property as money.
F. This equal side is not a side but the learned law itself. Although we sometimes find in the Talmud that it is referred to as an equal side (even any command from time immemorial and for generations), on the surface this is a different matter. Father, this is a halachic, not a factual, equal side, and therefore it is open to the interpretation of a serious side.
A, B I need to reflect and still no confessional silence. F I don't understand but that's what it is.
E. I didn't understand and it's probably a famous law that I probably don't know. I'll write at length so you can answer briefly. The Gemara asks, after all, the damage can always be paid with dead wood and answers that it's about dead wood (from the time of damage until the time of payment). That's why I'm asking about dead wood. You write that if none of the three voices are present (not common, anyway, from Mono), then it's impossible to learn because there's no equal side here at all, but only three individual studies. So ostensibly, a person who damages a table has no law in it, the owners take care of the dead wood, meaning the owners take care of the trees and the trees belong to the harmer from the time of the damage and if they are dead, they are dead wood to the harmer.
E. True. And this is in good agreement with the law that the harmer pays from the best (=money or the equivalent of portable money). Therefore, he can take his trees and pay with them for the damage. In any case, it is clear that if the trees have decreased, they have decreased for the harmer (because the determining time is the time of payment). As for who takes care of the trees, I don't know.
Incidentally, all of this assumes that a person who damages a table is really common. It is possible that not every person who damages is common.
I suppose that the harmful person is the most common one. If there is no equal side but rather separate studies, then a person who damages trees is less trees than a harmful person (and a person who kills an ox is less carrion than a harmful person). If there is an equal side, then in everything, there is less than a harmful person. This is my great objection to your new interpretation, and there is almost certainly explicit evidence for it. In the future, I need to learn to arrive on time and not start dancing in the square after the lights have already been turned off. [And since I'm babbling, I'll say that I especially enjoy and look forward to your discussions on logical structures in issues. Because in general, all your teaching is pure, etc. But four horsemen of the apocalypse are galloping within it, and whenever I hear the clatter of one of their hooves in the distance, I put my sensitive stomach on alert, and these are the first, your apostasy in consequentialism, the second, your belief in free choice, the third, your devotion to the categorical imperative, and the fourth, the small foal, autonomy in halacha. When you deal with matters of logical structures in issues, then there is no dust that deontology raises, and then my stomach and I are very satisfied, and I pat it with pleasure and purr with satisfaction.]
I went back to this and I still can't seem to get the new explanation for the serious side sorted out. I ask you to explain to me again, as if the slow-moving transporters are.
A. You explained that the interpreter is in the position of a protector, but he too needs a basis for suspicion. He needs to suspect two suspicions: a first suspicion that the theoretical factual characteristic is shared by both teachers, and a second suspicion that this factual characteristic does not exist in the learner. The first suspicion (the sharing) has a basis in Occam's razor. Is there a basis for the second suspicion that this characteristic does not exist in the learner?
If the learner does not have any serious halakhic side of his own, then there is also a basis for the second suspicion, since if this characteristic were in the learner, then we would expect it to give rise to some serious halakhic side in him. But if the learner does have a serious halakhic side of his own, then there is no basis for the second suspicion (on the contrary, the razor will inform us that the suspect does not). And after all, the interpretation of a serious side exists even if the learner has a serious halakhic side of his own (Sotah 29:2, a different generation refutes a serious side, even though the second rabbi also has a serious side that is rejected in the rabbinic sense). The conclusion is that the second suspicion does not need a basis and is sufficient in the possibility of absolution since the interpreter is in the position of a protector.
However, if this is the case, then even in a regular father's construction from one text there is a possibility of absolution for the second suspicion, meaning that there is a possibility that the factual reason for the law does not exist in the learner and therefore we cannot learn. And it is important that the interpretation of a serious side will also refute every study and study in the world.
B. Clarifications following the significant note 6.
1. The suggestion that the halakha of Rabbi Yehuda does not refute a serious side and therefore the Gemara follows his method. This is only a possibility, and there is no reason to think that the halakha of Rabbi Yehuda in this is against the Sages, right? The halakha is not that there is no action in it, there is no lukin on it and there is no halakha Yehuda and according to the issue in Matot 4:2, there it follows that according to the halakhah, the interpretation of the severe side is a local matter that depends on the judgment of each study on its own merits. And you reiterate that it is a principled interpretation that R. Yehuda does not interpret and the Sages do. So wherever the Shas does, it is not R. Yehuda, and when we use the severe side, for example, to make a need for why a verse was written as in Pesachim ez 2, then the matter is not settled for R. Yehuda. And wherever there is an equal side and the interpretations are halakhic (almost everywhere I looked I saw it, at least 10) then the issue is that it is not according to the Sages of Dr. Yehuda, because according to their view, it is possible to turn a serious party, and by no means would I have omitted the Shas in any doctrinal statement (that I have seen) to say to the sages, Dr. Yehuda, may I not be a witness to the mime (or to the Rabbis, may I not be a witness to the mime). Apparently, the chance of such a systematic ignoring of the dispute is low, given that your hypothesis is correct.
You yourself write that the lesson has no serious side of its own and therefore there is no reason to suspect that it has the serious factual side of the melamids. This is a simple explanation, and this is the situation in most places that explain a serious side. In cases where the lesson also has a serious side, there is room for this suspicion and therefore there is no room for explaining a serious side. I do not have time to go into the issue of the sota that you mentioned, but in my opinion there should be a specific explanation (we need to see what the serious side of the lesson is and perhaps it is clear for some reason that it fundamentally does not have the serious factual side of the melamids).
B. 1. The fact that in most issues a serious side is not explained. Hence, it is probably the halakha of Rabbi Yehuda on this. What about the subject of the debate? You yourself said that perhaps they believe that witnesses are plotting a conspiracy (and this is the halakha. See Rambam, Edut Pih 5:8).
2. Everything is correct. I just didn't understand why when making a tserikuta (with halakhic characteristics) it contradicts Rabbi Yehuda's method. On the contrary, when there is a tserikuta, one can learn from both teachers anywhere else because according to the halakhah, a severe side is not interpreted. Furthermore, according to our rabbis, this is also settled, since in such a tserikuta there is a severity in each of the two sources compared to the other, but not necessarily compared to the other contexts. In the other contexts, the severity that is in one or the other is possible. In a context where there really will not be both severity, then we really cannot learn from the method that interprets a severe side.
I have no claims of the kind of wisdom of deduction, but I will continue to present the side. At most, you will answer “there is no lowest”.
A. It turns out that the interpretation of a severe side according to your method is a special kind of interpretation. In ordinary interpretations, no one is interested in whether the meaning also contains some degree of gravity or a hundred degrees of gravity (that is why they make interpretations even on the most extreme). But according to you, in the interpretation of a severe side, it does become interesting. And who said that ”this is the situation in most places that interpret a severe side”? No one checked that it is impossible to find some special law in the interpretation (because, as stated, it is usually not interesting). You are essentially saying that if you start with the least extreme and then make an equal side (as in Sota 29:) then it is impossible to interpret a severe side.
B.
1. It is indeed a fact that a severe side is not usually interpreted, and the simplicity is that the reason is that a severe side does not belong there. Because simplicity is the law as the sages against Rabbi Yehuda. Therefore, simplicity is that there is no such general dispute as to whether or not one refutes a severe side, but rather each teaching on its own merits. It is possible that Rabbi Yehuda in another place will refute a severe side and in the same place the sages of Rabbi Yehuda will not refute it. Therefore, we do not see (as far as I was able to find in a search for “repeated ruling” or “serious side”) that the Shas asks about such a system: “and you may refute a severe side, but you may not refute it” or “and you may not refute a severe side, but you may not refute it”. We see a lack of formal systematicity in the Gemara, and therefore if we assume that there is systematicity, then each of the exceptions must be explained (in both directions, as I presented them above). Apparently, a systematic explanation here is not an advantage but a disadvantage.
2. I meant the cases in which the Gemara explains that a certain verse is ‘tserika’ because without it we would not be able to learn (about it) from two other teachers because they have a serious side of the argument, and therefore the verse was written that way. It turns out that according to you, Rabbi Yehuda, we could have learned and therefore the verse is still unnecessary (and we would have to say Milta Datiya, etc., and then all the Gemara's effort to make it tserikotot there was in vain). This is what happens in Pesachim Ez 1:1 (I mistakenly wrote above page 2).
A. Indeed. But in any case, this is a special case and therefore there is a dispute about it.
B. 1. I said what I had to say.
2. I don't have time now to look at the Pesachim.
There was a difficulty with the Gemara of the owners of the Navel, where they did not refer to the equal side of two teachers (a person who harmed an ox and a person who violated its protection), and to answer it you answered "because they do not have an equal side" and even the explanation of the Gemara does not know an equal side, and therefore the interpretation of the serious side is broken.
What is difficult for me is that precisely in this logic of induction and synthetics and the equal side, although we do not recognize the microscopic parameters, that is, although we do not recognize what the equal side is, we nevertheless assume that there is one (because of Ockham's razor) and then conclude by force of induction.
In other words, we need a positive reason to say that there is no equal side, and not simply "we do not know of an equal side" because even though the MM is not known, we assume that there is.
Therefore, your answer fails. Although from a thief and a robber we see that the equal side "damage has occurred and there is Navel" is incorrect, but in 27 it must be assumed that there is another equal side!
You tried to explain that the side of "damage has occurred and there is decay" is not considered an equal side because it is itself the subject of grief, of course it will be in all discussions and objects because it is about it. It is not a special equal side.
The above is completely true and understandable. So the other endings that bring the subject of the discussion itself as an equal side are not understandable (such as Kama and Kerem, both for pleasure. Of course they are both for pleasure because that is the discussion. Apparently, we need to look for something else)
The markup is gone:
A. There was difficulty, etc.
B. You tried to explain, etc.
Correction:
Second line: The Gemara* does not know* that it has an equal side, etc.
Fourth line from the end: It is not considered an equal side* because it is itself the subject of the discussion* so certainly*
Indeed, I have always been puzzled by the conclusions that present the subject of the discussion as an equal side. For example, in the example given in Baraita D'Examples: Every command is from now and for generations. There must probably be some equal side behind this.
Regarding your question, perhaps the sages had a feeling that there was an equal side or that they even knew what it was, and only I, when I analyze their inferences, do not know what it is and only call it alpha and beta. Hence, if there is a case in which they come to the conclusion that there is no equal side, then such an inference should not be made.
Consider the example given by some of the authorities to learn to require a sash to be covered with a tzitzit: And what four-winged garment that is exempt from a mezuzah is required to be covered with a tzitzit, a sash that is required by a mezuzah is not required to be covered with a tzitzit?! Why is this not true? Because it is clear to us that there is nothing equal between a four-winged garment and a sash (in fact, between the parameter that requires a mezuzah to the one that requires a tzitzit) and therefore one should not learn from one to the other. After all, the sages can come to the conclusion that there is no equal side.