Q&A: Most Sides in a Double Doubt
Most Sides in a Double Doubt
Question
Following Rabbi Akiva Eiger, responsa no. 6, which was discussed in another thread: https://hebrewbooks.org/pdfpager.aspx?req=1161&st=&pgnum=11
There is a well-known question about how the game “even or odd” is fair. After all, if both are even and if both are odd, the result is even, and only
if one is even and one is odd is the result odd. In practice the game is fair because the possibility that one is even and one is odd has double
the weight.
A doubtful mamzer and a doubtful mamzeret—are they permitted to one another?
There are four possibilities: kosher man and kosher woman (permitted), disqualified man and disqualified woman (permitted), kosher man and disqualified woman (forbidden), disqualified man and kosher woman (forbidden).
Mahari Alfandari says (with slight adaptation) that this is considered one doubt. Because out of four equally weighted possibilities there are two
for prohibition and two for permission.
Rabbi Akiva Eiger disagrees with him and says this is a double doubt leniently. Because the possibility of kosher man and disqualified woman, and the possibility of disqualified man and kosher woman, are one
side. So there are three possibilities (kosher man and kosher woman, disqualified man and disqualified woman, one side disqualified
and one side kosher), of which two are for permission
and one for prohibition.
That is, Rabbi Akiva Eiger looks at the sides by categories and ignores their weight.
The general issue is known: “a majority of sides” instead of a statistical majority. What is the logic?
Answer
It is odd to present the matter of even or odd as a question and answer. It is obvious.
Rabbi Akiva Eiger on the matter of a mamzer and a mamzeret is, at first glance, very strange. True, a doubtful mamzer is fundamentally permitted, and this is only a rabbinic stringency. Perhaps his intention is that the stringency was stated according to sides and not according to probability (for probability does not play a role in mamzer status). That is, they were stringent when there is doubt in the sides, but when there is doubt in probability and not in the sides, they were not stringent.
However, from his wording it seems that he means this generally. His claim is that with a mamzer, intercourse with “the congregation of the Lord” was forbidden, and therefore our doubt is not about the reality of who is a mamzer and who is not, but whether there is here intercourse of a mamzer with the congregation of the Lord or not, and in that respect there are only three sides. By contrast, in Grace after Meals there is a separate doubtful side for each one, the one fulfilling the obligation for others and the one being fulfilled.
As an aside, I would add that one could formulate this differently. In doubts of mamzer status there is really one doubt and not a double doubt. To see this, let us discuss it for example from the man’s side: if he is a mamzer, then she is forbidden to him out of doubt (which is one doubt). If he is kosher, then she is forbidden to him as well (again, out of one doubt). So either way, he has one doubt before him, and therefore it is forbidden for him to have relations with her. The calculation is not that there are two sides out of four, but that he has one doubt either way. Perhaps this depends on the question whether the obligation to be stringent in a doubt is an independent obligation, as was discussed in that thread. If it is an independent obligation, then there is certainly a prohibition here—a prohibition of doubt. But if it is merely concern for the original prohibition, then there are two different doubtful prohibitions here. And logically, there seems to be no reason to distinguish.
Discussion on Answer
[By the way, regarding someone in doubt about Grace after Meals—can he fulfill the obligation for another person who is also in doubt? In the previous thread you wrote that logically he cannot (leaving aside the discussion of double doubt). I understand that logic this way: the side that says a doubtful person cannot fulfill the obligation for someone certain is that an obligation arising from doubt is not identical to an obligation arising from certainty. And still, one doubtful person cannot fulfill another doubtful person’s obligation even though their obligations are identical, because the obligation of doubtful cases arises derivatively in a situation where there really is doubt. And since in truth it would not help if he were certainly exempt, then the listener would remain a definite doubtful case and still be obligated out of doubt. If that is not the logic you meant, then what is?]
This is like the doubt of the lion: perhaps it entered, and if it entered, perhaps it mauled. I have always wondered about this double doubt, because all that matters is whether it mauled; it does not matter whether it entered. And likewise in Bava Kamma 11 regarding the doubtful placenta: it is treated as a double doubt—perhaps part of a placenta can exist without a fetus, and even if not, perhaps it is not a majority. Even so, these two are treated as double doubt.
Logically it seems that there is no significance at all to the intermediate doubts, except for the doubt whether there is a round rigid green plastic object or not. And that is one doubt. One can of course say that if you have no information, then most objects are not like that, and therefore it is not a doubt but a majority.
I did not understand your point about Grace after Meals (I no longer remember what was written there). According to the calculation I wrote above, if I already recited the blessing, I cannot fulfill his obligation, and if I did not recite it, then I can (because even if he already recited it, then in any case he has already fulfilled his obligation). Bottom line: there is a doubt whether I fulfilled his obligation, and doubt is treated stringently.
Seemingly this problem of “one doubt” with an axis of progression is represented by the rule that a double doubt must be reversible. In the lion and the placenta cases it is not reversible. The green circle is reversible. True, Rabbi Ovadia rules that it does not need to be reversible, but still they are not similar. In every double doubt in the world (not just a doubt on top of a doubt whether it mauled), you can produce a conjunction and set it up as one doubt, and the rule is that every branching is a separate doubt.
Correct. But as you wrote regarding reversibility, there is a dispute. Beyond that, in the past I reached the conclusion that the requirement of reversibility is not equivalent to the requirement that it not be sequential (as in the cases I mentioned here). There is some overlap, but it is not identical. I once thought of writing something about this. Maybe when I get around to it.
May it be God’s will that you do.
As a side note, for visual illustration: https://ibb.co/hfPN8g9.
[If one takes the idea of unweighted sides as it appears on its face, then condition A and condition B for prohibition is a double doubt for permission, but if condition A and B prohibit, with a condition to that condition that if A and B and C and D and E and F all hold then it is permitted, then there is a majority of sides for prohibition. Of course that cannot be.]
My answer:
Two people play even or odd (and for simplicity let us say one can put out 1 or 0).
“I am hereby a nazirite if the result is odd” — its doubtful case is forbidden.
“I am hereby a nazirite if the result is 1” — its doubtful case is permitted: maybe the result was 2, and even if not, perhaps it was 0.
The difference is what the doubt is about: whether the possibilities are even or odd, or whether the question is what the result is. When the question is what the result is, and there are more possibilities for permission, that is double doubt.
And even though from the standpoint of probability the chances are equal, the creation of doubt is not based on estimating that it is 50:50 but on the side of permission—thus according to Rabbi Akiva Eiger. That is reasonable in light of the fact that in most doubtful situations we do not try to estimate probability so long as there is no clear majority for one side.
In the tree drawn here, it is obvious that even Rabbi Akiva Eiger would say it is permitted, since the doubts for prohibition are at a lower hierarchical level—there is already a double doubt for permission, so they are irrelevant. And this is not like 0, 1, or 2 mamzerim, which are two permissive states that do not depend on one another.
I don’t understand you, Avishai.
A. The logic itself is hard for me to understand. [But in my view, generally speaking, the whole idea of forms of clarification that are not just majority was probably given to the Jewish people so that they would await the renewal of the Sanhedrin with eager longing, and then they would abolish them with wisdom and quorum. And even about following the majority in many cases one can wonder a great deal, since it seems to have no reason at all.]
B. Why, in the case of doubtful mamzer and doubtful mamzeret, where according to Rabbi Akiva Eiger the doubtful case is permitted, are you comparing it to doubt whether the result was 1 (where the doubtful case is forbidden), rather than to doubt whether the result was prohibited?
C. I did not understand why in the tree it is obvious to you that it is permitted. One can simply understand the idea of double doubt by saying that all the branches have equal probability (50:50), and then proceed as usual as though following a reasonable majority of probabilities. But if equal probability is assigned to the leaves (and not to the branches), then why are there not four leaves against three? What does it mean that there is already a double doubt for permission? We look at all the leaves (as Rabbi Akiva Eiger does, after he combines disqualified-man/kosher-woman with kosher-man/disqualified-woman) and see four against three.
A. The reasoning is based on the fact that in every doubt where we do not know the reality, it is not really 50:50. Is there a 50 percent chance that the bill of divorce was closer to him and not closer to her? The truth is that we simply do not know. Some would say that therefore one may treat it as 50:50. Some would say that what needs to be clarified is the sides of the doubt, since we really have no ability to proceed here by majority.
B. In the situation of the mamzerim there are 3 situations perceived as different: intercourse involving 0 mamzerim, 1, or 2. Those are the sides of the doubt according to Rabbi Akiva Eiger. One cannot say that the doubt is whether there was prohibited or permitted intercourse (in the analogy, whether it was even or odd), because if so every double doubt could be said to be one doubt—whether a prohibition occurred here—and we do not say that.
C. One does not assign equal probability to leaves at different heights of the tree. In Rabbi Akiva Eiger’s case there are 3 different possibilities as to how many mamzerim were involved in the intercourse, and all three are at the same hierarchical level—on the upper branch of the tree. In your case, the entire lower part of the tree is already after there is a double doubt for permission, and therefore it is permitted.
I understand that you assumed that if one does not relate to doubt as percentages, then hierarchy among the leaves is irrelevant. But if event B depends on event A, then even Rabbi Akiva Eiger agrees that it is lower down, and that has nothing to do with whether one treats doubt as 50 percent or as sides.
A. But on that very same factual map (“what is the law in these states of affairs in the world”), you distinguish based on “the form of our uncertainty.” Do you have another example of such a thing?
B. Please explain why 0 mamzerim is perceived differently from 2 mamzerim.
C. I understand that according to Rabbi Akiva Eiger too there is a tree with two levels, like every double doubt in the world: is there a mamzer here or not, and even if there is, perhaps the other is also a mamzer. Then there is one leaf for prohibition (there is a mamzer here and the other is not a mamzer) and two leaves for permission (there is no mamzer here, or there is a mamzer here and the other is also a mamzer). And the fact that there is a difference in the weight of the leaves if one assigns equal probability to each state (each of the two permissive leaves is a quarter and the prohibitive leaf is a half) does not interest Rabbi Akiva Eiger. In other words, he gives equal probability to all the leaves of the tree.
[By the way, at the beginning of that responsum Rabbi Akiva Eiger also distinguishes between applying double doubt in such a way that overall there is certainly a prohibition, in which case one does not do as Tosafot say in Niddah, and a situation where there is even a tiny possibility of permission, in which case one does apply double doubt. In my opinion that too shows that he ignores the idea of probabilities. To me it seems totally unreasonable to draw the line specifically between 0 percent chance of permission and 0.0001 percent chance of permission.]
A. Nothing comes to mind; I’ll try to think of one.
B. 0—there is no prohibition in the picture. 2—there is permission for intercourse that is forbidden to other people. A bit like doubt whether he had relations with his late brother’s wife or with an unmarried woman, and doubt whether he is obligated in levirate marriage or forbidden because of a brother’s wife. (By contrast, if one is a mamzer, it makes no difference who is the male and who is the female.)
C. According to Rabbi Akiva Eiger, the doubt between 0 and 1 or 2 is not viewed as one quarter against three quarters (as said, we have no idea of the real percentages, so it is not relevant to relate that way), but as an evenly balanced doubt. But he does not ignore the fact that if event B depends on event A, then clearly the chance that it will happen is less than or equal to the chance that A will happen, so everything lower down in the tree does not matter if there is already a double doubt for permission.
The reason he does not calculate as you do—half, quarter, and quarter—is not because he thinks one should count leaves instead of calculating, but because he relates to the halakhic questions that the event raises and not to an invented 50:50 probability regarding each person. Therefore one first asks whether there is any mamzer here at all—(in his eyes this is an evenly balanced doubt even if one doubtful mamzer had relations with a million women, each one of whom is doubtful)—and afterward one asks whether, assuming there was a mamzer here, this is permission or prohibition (again, an evenly balanced doubt).
And it seems to me that if a doubtful mamzer were to have relations with a thousand women of doubtful mamzer status, one still could not flog him (even if he were warned about all the acts together). And even though the probability that he did not violate a prohibition approaches 0, it would still be a double doubt as I described. That is another practical difference between counting leaves—according to which there are certainly more leaves for prohibition (1–999)—and the way I explained it. In your opinion, would he be flogged in that case?
B. One can always find a practical difference somewhere else (intercourse that is forbidden to other people), and I do not see why that should affect this. Why not say that kosher-man/disqualified-woman is different from disqualified-man/kosher-woman because maybe someone forbade himself benefit from a kosher person who was with a disqualified woman (but did not forbid himself benefit from a disqualified person who was with a kosher woman)? Rather, obviously we discuss the case before us as such. So from the standpoint of halakhic questions there is no difference between 0 and 2; rather, we discuss the factual questions.
A hint in support of this I saw not long ago in Rabbi Akiva Eiger’s own responsum (second edition, 128) on the matter of a double doubt from the same “name,” that if one of the doubts permits more, it is not considered the same name. Rabbi Akiva Eiger says there as follows: “Consider the case of ‘I found an open doorway,’ where Tosafot wrote that the category of coercion is one single name. Would one then say that if this occurred with two women in whom an open doorway was found, and regarding one of them it is known that she was guarded and had not had prior relations in her youth, we would permit the other through a double doubt because one doubt permits more than the other—for the doubt of her being a minor does not apply to this woman, while the doubt of coercion applies to her as well? Rather, certainly this is nonsense, since they are two acts and one does not depend on the other, for even on the possibility that perhaps it was through coercion, still the other is not thereby permitted, for perhaps she consented.”
That is, we do not discuss the type of doubt according to its implications for other people, but only according to the case before us.
C. It does not seem very convincing to me at the moment, but I will think about it.
You convinced me regarding the thousand mamzerim. Indeed it is clear that when the Torah instructed about double doubt, then in the course of the world people will certainly also stumble into prohibitions (say, in 25% of cases). And Tosafot’s words in Niddah—that one does not apply double doubt if the sides contradict each other (from doubt male she is pure in the second week, and from doubt female she is pure when seeing blood on day 34 and again on day 41, so if there were two acts of intercourse at those times one cannot take the first as permitted from the possibility of male and the second as permitted from the possibility of female)—indeed must be interpreted to mean only when it is absolute certainty, as Rabbi Akiva Eiger wrote, and not like the Turei Even, who says even when it is not absolute certainty but only leads to near certainty. Thanks. [But that is an internal Torah matter. Outside Torah, there is no logic to distinguish specifically at the arbitrary line between 0 and 0.001. Everything should be continuous and smooth as much as possible, without jumps.]
B. The example I brought—doubt whether levirate marriage applies, or she is unmarried, or she is a brother’s wife—perhaps explains better that if the permission derives from two different categories, then one can separate them.
And perhaps so too with mamzer status: there is an object-based prohibition on intercourse with a mamzeret/mamzer that exists generally. If the second partner is also a mamzer, then he is permitted to violate that prohibition. In other words, what I meant was that the fact that it is forbidden to other people is a sign (not a cause) that one can distinguish the reason for permitting a mamzeret to a mamzer from the mere absence of prohibition in the case of an unmarried man and unmarried woman.
Of course, one can disagree and say that there is no prohibition corresponding to a permission that applies only to a specific person in whose case the doubt exists.
It does not sound reasonable to me that even for a mamzer there is an object-based prohibition regarding a mamzeret, only that it was permitted to him. It is hard even to understand what the words mean. It is like saying that even for an ordinary Jew there is an object-based prohibition regarding a divorcee, only that she was permitted to him. In any case, it seems to me that your reasoning here has implications, and I will try to remember the matter so that if I come across some implication that proves it one way or the other, I’ll bring it to the table.
[Among us it is common to stump children with this riddle about even or odd, and in line with Rabbi Akiva Eiger’s view, so I presented it as a question and answer].
If Rabbi Akiva Eiger’s intention is general, and one really always just counts sides, then one can imagine a case where adding options for permission turns the ruling into a stringency.
Reuven forbade himself peaches if in the next room there is a round green object. It is permitted because of a double doubt: maybe it is not round, and even if round, maybe not green.
Shimon forbade himself peaches if in the next room there is a round green object, but even if it is round and green, if it is made of rubber and rigid and hollow and spiky, then it would be permitted. Now if we ignore weights, there are four sides for prohibition and three sides for permission. Three for permission: if it is not round, or round but not green, or round and green but made of rubber and rigid and hollow and spiky. Four for prohibition: round and green but not rubber; round and green and rubber but not rigid; round and green and rubber and rigid but not hollow; round and green and rubber and rigid and hollow but not spiky.
So it comes out that if one does not look at weights, adding a possibility in reality for permission produces a majority of sides for prohibition. Really? Can that be?