Q&A: Majority in Derivations of the Torah
Majority in Derivations of the Torah
Question
Rabbi Michael,
It has been a long time since we were in touch. I thought you were the right address for the attached question.
I would be glad for any answer or referral.
With blessings,
Z’
In the Talmud, tractate Hullin 115b, we state a principle in the name of Resh Lakish: any refutation of a mah ha-tzad that comes from the cases themselves we can make; a refutation from elsewhere we do not make.
The meaning is that if we derive something from the common denominator of two source cases, we cannot refute that common denominator by saying, “So-and-so proves otherwise, for it too has that common denominator and yet that law does not apply to it.” One may refute the common denominator only by attacking the common denominator itself, that is, by finding a stringency, leniency, or rationale that exists in the common denominator—the two source cases together—which does not exist in the derived case.
The reason for this is: (also in order to explain how it can be easier to refute a mah matzinu from one source than a mah matzinu from two sources!)
Since we find two source cases that are alike in “AAA” and have the law “BBB,” then regarding the derived case, which also has “AAA,” we say that “AAA” is what causes the law “BBB.” And we do not say that so-and-so proves otherwise, since it too has “AAA” and nevertheless does not have the law “BBB,” because on account of one exceptional case we do not cancel out what is common in two places; rather, the Torah made a novelty in the case of “so-and-so,” but in other matters we compare to two places rather than one place.
So wrote the author of Korban Aharon in Middot Aharon, chapter 2, part 9, derivation 4, and his words are cited by many later authorities (Acharonim).
(The Pri Megadim in Ginat Veradim, principle 18, which is devoted to this topic, brings two additional approaches to explain this principle. One approach is that this is a law given to Moses at Sinai, that is, a scriptural decree; see there, and this is not the place to elaborate.)
The novelty I see here is that there is a majority—perhaps this even derives from the law of “follow the majority”—without any probabilistic majority at all. That is, there is law A and law B on one side, and on the other side there is law C. We prefer to derive from the first side because it is the majority; consequently that is the default assumption, and we treat law C as the novelty. Usually when we use the rule of majority, we say there is a probability that this piece before us, or this case before us, is not different from the majority. Here there is no probability at all to say that from the fact that the Torah commanded a certain law in A and B, it would likewise command it in other places, and that law C is the novelty. Even so, we follow the majority.
My question is: do we find other examples in which we use the concept of “majority” to decide on a particular derivation?
I have another example, but it can be rejected; see below.
One who still lacks atonement is permitted to eat terumah but forbidden to eat sacrificial foods, because sacrificial foods are more stringent.
The Talmud in Yevamot 74b and elsewhere asks: on the contrary, terumah is more stringent. “It is reasonable that sacrificial foods are more stringent, for they have these features: PNKA’KHS. On the contrary, terumah is more stringent, for it has these features: MKHPZ! Those are more numerous.” PNKA’KHS and MKHPZ are mnemonic signs for certain laws that apply to one and not the other; see Rashi there. Sacrificial foods are more stringent because more matters apply to sacrificial foods than to terumah—“those are more numerous.”
But this is not such a good example. When one wants to decide whether something is more stringent than something else, one certainly should use our own reasoning, and when most of the stringencies apply to one rather than the other, then perforce the first is more stringent. But in the first example, we see that the very fact that the majority is on one side is enough for us to know that we should incline after the majority without any further reasoning.
Answer
Hello.
I should note that, as far as I remember, in the passage in Kiddushin 5 (regarding huppah) there are refutations from a third case against the common denominator. I think there are other such examples too, but I have not checked the matter.
I think this is not necessarily a question of majority and minority. The claim is that when a law appears in two places, that is probably not incidental, somewhat like Rabbi’s reasoning regarding a presumption after two occurrences. True, in practice in most cases we rule that a presumption is established after three occurrences, but not in every context (see the passage in Yevamot 64a and the halakhic decisors). In a case of refutation from a third source, we have two possibilities: 1. accept the refutation and then assume that the law is not correct and the two source examples are incidental; 2. reject the refutation and assume that the law is correct and then the third case is incidental. It seems to me that option 1 is less reasonable—or rather, that saying two laws are incidental is less reasonable than saying one law is incidental—especially since this does not come to uproot any prior presumption (as opposed to cases of a presumption after three occurrences). After all, we have two possibilities: either the law is correct or it is not, and the two are evenly balanced in principle (there is no presumption here, as noted). So why should we not follow the more reasonable of the two possibilities? You need three occurrences only when you are trying to change an existing status and uproot a presumption. Note that in cases of presumption, once a presumption is created by three occurrences, one occurrence is not enough to remove it and restore the previous state. That is, a refutation based on one instance (for example, an ox that became established as goring and then did not gore on one day) is not accepted.
It may be that this is more similar to the law of nullification than to the law of following the majority. Two possibilities nullify the one possibility (somewhat like Rabbi Shimon Shkop’s explanation in Gate 3 regarding the law of following the majority in a religious court).
Discussion on Answer
I disagree.
The third option does not really exist until you actually show that there is a third reason, meaning until you present it. It is not enough simply to say that this is not incidental and that there is a third reason without presenting that reason. After all, the common denominator is a plausible and sensible explanation that is offered for the two source cases. To reject it, it is not enough merely to claim that perhaps there is another explanation; you have to present it. And if you do have such an explanation, then that itself would be a regular refutation of the common denominator (finding a stringency shared by the two source cases), and then indeed we would accept the refutation. What is not accepted is only a refutation from a third case.
That is not correct.
Necessarily there is something here that is not understood: there is a contradiction between the two source cases in the first group and the other source case in the second group. Since “incidental” or “mistake” is not an option, then necessarily there is some unknown factor on which the difference between the two groups depends. If so, on what grounds do we say that the derived case belongs more to the first group than to the single source case in the second group? Just because the first group has two items and the second has only one?
It seems to me we are going in circles. I will explain once more, and if you still do not accept it then we will remain in disagreement.
When I speak about a law being incidental, I do not mean that the law is arbitrary and without a reason. Obviously every law has a reason. What I mean is that the law comes out stringently not because of a stringency or shared reason that also applies to our derived case—the common denominator of the source cases that exists also in the derived case—but because of some side reason that each of the source cases has and the derived case does not, and therefore one cannot derive from them to it. Now we have two possibilities: 1. the two source cases are stringent because of one shared reason that causes the stringency, and that reason also exists in the derived case, while the third case is stringent because of a side reason; or, 2. the two source cases are stringent incidentally—meaning each one because of a side reason that does not exist in the derived case—and the third case is the essential model in its similarity to the derived case. Option 1 is more reasonable.
Now I understand. You are saying that to say there is a side reason in two places that does not apply to the derived case is less plausible than to say there is a side reason in one place.
I understand. I would ask that you continue to clarify and sharpen this further. (By the way, this has practical halakhic relevance for me, and I will, God willing, send you my thoughts when this topic becomes clear in my mind.)
But that itself needs explanation: what exactly is the logical reasoning here? I understand saying that there is some “incidental” feature or something unclear and unnatural in two places. But to say there are side reasons in two places when it is clear that at least in one place there is a side reason—what is illogical about that?
Maybe the point is that one should use the principle of Ockham’s razor, and take the simpler option, the side that requires making fewer assumptions.
Do you agree?
A peaceful and blessed Sabbath, and a good and happy new month!
That is the principle of Rabbi Chaim at the beginning of Hagigah regarding the signs of a mentally incompetent person and the general presumption of three occurrences. Even when an ox gores, there is some local cause for it (there is no true randomness in the world at all). And even so, it is preferable to attribute it to one cause. All scientific and other generalization is built on that. And yes, this is a specific application of Ockham’s razor.
May his strength be increased.
I still do not understand the whole need for this.
You can call something “incidental” when it happened on its own without planning. But for example, if a judge is presented with a question and he rules leniently, we see that he is a lenient judge. So we estimate that on another question that comes before him, absent other information, he will also rule leniently. True, if there is a specific reason why he was lenient, then of course nothing can be proven from that. Then the same judge is presented with a second question and again he rules leniently—this is not like that, etc.; in short, he is a lenient judge. Then afterward there comes a question in which he rules stringently. What are we supposed to think now—that really he will still rule leniently in my case, which is similar in essence to both of the first two? No. I would say that apparently there is some additional factor unknown to me, either in the first two questions or in the third question, that caused him to rule as he did.
You wrote that there are two options, as above. I see a third option: there is nothing incidental here at all; everything is carefully planned, except that we are missing one component of the story. And the doubt still remains perfectly balanced.
To put it a bit differently: you can only speak of “incidental” where there is a possibility that something happened incidentally and that there may be no particular calculation behind it. Here the law of presumption comes and says that it is more reasonable that the minority happened incidentally than the majority. But when it is clear that both sides alike were done intentionally, then what does the majority or presumption add? At the end of the day there is some rationale here that we do not know, so how can we rely on the analogy?