מנא הא מילתא דאמור רבנן זיל בתר רובא מנלן דכתיב (שמות כג, ב) אחרי רבים להטות רובא דאיתא קמן כגון ט' חנויות וסנהדרין לא קא מיבעיא לן
§ After discussing the role of presumptive status in determining halakha, the Gemara discusses the role of the majority. From where is this matter that the Sages stated: Follow the majority, derived? The Gemara is surprised at the question: From where do we derive it? Obviously, it is derived from a verse, as it is written explicitly: “After the majority to incline” (Exodus 23:2). The Gemara explains: With regard to a majority that is quantifiable before us, for example, in the case of a piece of meat that was found on the street before ten shops, nine shops selling kosher meat and one shop selling non-kosher meat, one follows the majority and deems that piece kosher. Or when the Sanhedrin adjudicates a case, one follows a majority of the judges in determining the ruling. In these cases, we do not raise the dilemma.
We will define the principle of RDIK (רובא דאיתא קמן) ... roughly as follows: A random object taken from a set a majority of the members of which have property P, may be presumed to have property P. As so defined, the principle does not require any (but perhaps the most naive) probabilistic notions. Nevertheless, it is evident that the classical interpretation is fully adequate for a probabilistic formulation of RDIK: RDIK amounts to specifying the members of the set as a sample space and following the result with probability greater than ½. Note that RDIK refers specifically to a set of q concrete objects, p of which have some property...
כי קא מיבעיא לן רובא דליתיה קמן כגון קטן וקטנה
When the dilemma is raised to us it is in the case of a majority that is not quantifiable before us, for example, the case of a minor boy and a minor girl. If the boy entered into levirate [yibum] marriage with the girl, it is permitted for them to remain married, and there is no concern that when they grow older it will be discovered that the boy or the girl never develop sexually. Rather, one follows the majority, that minors develop sexually at puberty.
Simply put, all examples of RDLK (רובא דליתיה קמן) are statistical laws: most children born to married women are fathered by their husbands, most children are ultimately fertile, most people are not about to die, etc.
מצא בה תינוק מושלך אם רוב עובדי כוכבים עובד כוכבי' אם רוב ישראל ישראל
If there is a city in which both Jews and gentiles reside, and one found an unidentified, abandoned baby in the city, if there is a majority of gentiles in the city the baby is deemed a gentile; if there is a majority of Jews in the city the baby is deemed a Jew.
And furthermore, with regard to all gestating animals, when they give birth, half of their offspring are male and half are female. Therefore, one can combine the minority of animals that resemble another species [are unhealthy] with the half that are females, and arrive at the conclusion that male offspring that resemble their species [are healthy], which are the only offspring that can be consecrated with firstborn status, are the minority. Accordingly, one does not need to be concerned that the placenta found was from an animal consecrated with the status of a firstborn.
והתניא תשע חנויות כולן מוכרות בשר שחוטה ואחת מוכרת בשר נבלה ולקח מאחת מהן ואינו יודע מאי זה מהן לקח ספיקו אסור ובנמצא הלך אחר הרוב
Isn’t it taught in a baraita: With regard to nine stores in a city, all of which sell kosher meat from a slaughtered animal, and one other store that sells meat from unslaughtered animal carcasses, and a person bought meat from one of the stores and he does not know from which store he bought the meat, in this case of uncertainty, the meat is prohibited. The legal status of uncertainty with regard to any item fixed in its place is that of an uncertainty that is equally balanced, and one does not follow the majority. This baraita continues: And in the case of meat found in the street, outside the stores, follow the majority of stores that sell kosher meat. In other words, the meat is kosher.
The parallelism between RDIK and kavua is remarkable. In both, the "source" case involves a technical legal question and includes no elements of empirical uncertainty and in both the standard case is a version of "nine stores" in which the central issue is apparently one of uncertainty. This suggests that RDIK and kavua do not directly concern uncertainty, but rather are dual principles regarding mixed sets which cover cases of uncertainty as a by-product.
The principle of RDIK might thus be formulated this way:
Given a set of objects the majority of which have the property P and the rest of which have the property not-P, we may, under certain circumstances, regard the set itself and/or any object in the set as having property P.
The principle of kavua is the opposite of this:
Given a set of objects some of which have the property P and the rest of which have the property not-P, we may, under certain circumstances, regard the set itself, and consequently any object in the set, as being neither P nor not-P but rather a third status. We can call this status hybrid, or perhaps, indeterminate.
היכי דמי אילימא דאיכא תשעה כנענים ואחד ישראל ביניהם ותיפוק ליה דרובא כנענים נינהו אי נמי פלגא ופלגא ספק נפשות להקל לא צריכא דאיכא תשעה ישראלים וכנעני אחד ביניהם דהוה ליה כנעני קבוע וכל קבוע כמחצה על מחצה דמי
The Gemara asks: What are the circumstances of the case where he threw the stone [which killed someone] and is exempt [from the death penalty]? If we say that there are nine gentiles in the crowd and one Jew among them, even without the verse, let him derive the exemption from the fact that they are a majority of gentiles. Alternatively, even if we say that half of the ten people are considered gentiles and half are considered Jews, let him derive the exemption from the principle: In a case of uncertainty concerning a life-threatening situation, the halakha is lenient. The Gemara answers: No, the verse is necessary only in a case where there are nine Jews and one gentile among them. Were the ruling to follow the majority the one who threw the stone would be liable. But in that case, because the gentile is fixed among them, and the legal status of any item fixed in its place is like that of an uncertainty that is equally balanced, [the killer] is exempt, based on the principle: In a case of uncertainty concerning a life-threatening situation, the halakha is lenient. Apparently, even in cases of Torah law in which the result would be a leniency, i.e., exemption from the death penalty for murder, the legal status of any item fixed in its place is like that of an uncertainty that is equally balanced.
It is important to note that RDIK comes in two varieties: RDIK can assign a single status to the entire mixed set (as in the case of bitul [- when the majority can nullify the minority, such as a Sanhedrin vote or a set of dairy forks with a meat fork in it]) or it might assign a status directly to an individual object in the set (parish [- if uncertainty regarding the status of an individual object which belonged to the set arose only after the object had been isolated from the set, as in our original meat on the street case]). Kavua, on the other hand, comes in only one variety: a hybrid status must be assigned to a set and then only indirectly to an individual item in the set. When kavua is invoked, each individual item in the set loses its individual identity and is regarded simply as a fragment of an irreducibly mixed entity. It is not treated as an individual of uncertain status but rather as a part of a set that is certainly mixed.
Given this, we are ready to answer the central question: When do we apply RDIK and when do we apply kavua?
Roughly speaking, the idea is that when an object is being judged in isolation, it must be assigned a status appropriate to an individual object; when it is judged only as part of a set, it can be assigned some new status appropriate for a set. Kavua can only be invoked in the latter case.
By contrast, a piece of meat that is found in the street is clearly analogous to scenario 1 – the status of a particular item is in question. This is the kind of case in which RDIK is invoked. Now, admittedly, the case of a piece of meat bought in one of the stores might plausibly be regarded as analogous to scenario 1 since the act of buying could be considered analogous to pulling out a specific ball. However, the Rabbinic principle is, somewhat counter-intuitively, otherwise: apparently, the critical moment is the one prior to actually encountering the piece in question. When the piece is found on the street, it is judged as an individual because prior to the moment that it is found, it is already no longer "in the set". When the piece of meat in question is bought in the store, prior to its being bought it is indeed "in the set".
Let us now spell out in detail the precise method for determining when to apply RDIK and when to apply kavua.
1. First, there are a number of cases in which kavua cannot be invoked because a hybrid status is inappropriate.
- In the case of a vote in Sanhedrin which is, by definition, a mechanism for rendering a decision.
- If uncertainty regarding the status of an individual object which belonged to the set arose only after the object had been isolated from the set (parish), then it is this object alone which must be assigned some status. While a member of a set consisting of objects some of which are P and some of which are not-P can be assigned a hybrid status as part of the set, an individual object being assigned a status on its own cannot. Thus, we need to choose either P or not-P for this object and we choose the majority of the set from which it comes...
- Similarly, if the set is somehow "incohesive", so that each object in it is regarded as having left the set, we apply RDIK and not kavua...
- Finally, if it is not certain that the set contains any objects that are, say, not-P, then the set is said not to satisfy the condition of itchazek issura. Such a set cannot be assigned a hybrid status and RDIK is invoked rather than kavua...
To summarize: in all cases in which we are not assigning a status to a mixed set, kavua is not invoked but rather RDIK. Note that although in these cases the membership of the doubtful item in the set, or the cohesiveness of the set itself, may be inadequate for invoking kavua, this does not diminish the relevance of the set for purposes of RDIK. Thus, for example, even though the piece of meat found on the street cannot be assigned a hybrid status because it is not part of the set, the fact that the meat is known to have originated in the set still renders the composition of the set (i.e., the majority) relevant to determining the status of the piece.
2. When the above rule does not apply, so that at issue is the status of a mixed set, we first check if the principle of bitul can be applied. If bitul can be applied, the set is no longer regarded as a mixed set but rather as a uniform set and kavua is inapplicable. Thus, for example, a mixed set consisting of one (non-distinguishable) non-kosher piece of meat and more than one kosher pieces is regarded as a permissible set.
3. Finally, there are a number of cases in which we are dealing with a mixed set but bitul is not applicable:
- First, if the objects in the set are each identifiable as either P or not-P (nikar bimkomo). For example, in "nine stores" the status of each store is known, it is only the origin of a particular piece of meat that is in doubt. Clearly, in such a case, we can't define the set as either P or as not-P; as a set it is both.
- Second, if individual objects in the set are each regarded as sufficiently significant that the status of each cannot be subordinated to the status of the set (chashivi velo beteili) or if bitul is inapplicable for any other reason. Thus, given a herd of oxen including one that has been sentenced to death and is forbidden for use, we can't invoke bitul due to the significance of living creatures and hence we invoke kavua by default (Zevachim 73b).
- Third, if the set includes an equal number of objects that are P as are not-P. In such a case, bitul is obviously not possible.
§ Rav Naḥman says that Rava bar Avuh says that Rav says: With regard to a ring used in idol worship, from which it is prohibited to derive benefit and which is not nullified even in a ratio of one in one hundred, that was intermingled with one hundred permitted rings, and subsequently one of them fell into the Great Sea [Yam HaGadol], they are all permitted. The reason is that we say: That ring that fell into the Great Sea is the prohibited ring.
(ח) כחל מתבטל בתשעה וחמשים: הגה כל האיסורים הנוהגין בזמן הזה כולם מתבטלים בששים מלבד חמץ בפסח ויין נסך כאשר נתבאר בהלכותיהם (טור) ובלבד שהאיסור אינו נותן טעם בקדירה אבל אם נותן טעם באותה קדירה והוא אסור מצד עצמו אפילו באלף לא בטיל כל זמן שמרגישין טעמו ולכן מלח ותבלין מדברים דעבידי לטעמא אם אסורים מחמת עצמן אינן בטילים בששים (בארוך כלל כ"ה עיין ס"ק כ"ז וע"ל סוף סימן ק"ה):
(8) ...An udder is nullified when mixed with 59 pieces of meat (The 60th piece of meat is the meat of the udder itself) Rema- Everything that's prohibited in our days is nullified in 60x more. Except for chametz on Pesach and wine that was libated for an idol as is explained in the proper place. That which everything is nullified in 60x more, is as long as it doesn't add taste to the dish. But if it adds taste to the dish, and it's prohibited because of it's self (As opposed to if it's only prohibited based on the principle of חתיכה עצמה נעשית נבלה, see siman 92 for details), then even if there's 1000x more, it will not be nullified as long as one can discern the taste. Therefore salt and spices from things that are made for giving taste, if they are prohibited because of themselves, they are not nullified when there's 60x more.
If a hatat [one type of bird sacrifice] becomes mixed up with an olah [another type of bird sacrifice], or an olah with a hatat, were it even one in ten thousand, they all must be left to die. If a hatat becomes mixed up with [unassigned] obligatory [bird] offerings, the only ones that are valid are those that correspond to the number of hatats among the obligatory offerings. Similarly, if an olah becomes mixed up with [unassigned] obligatory [bird] offerings, the only ones that are valid are those that correspond to the number of olot among the obligatory offerings [This rule holds true] whether the [unassigned] obligatory offerings are in the majority and the freewill-offerings in the minority, or the freewill-offerings are in the majority and those that are obligatory in the minority, or whether they are both equal in number.
§ Rav Yosef said that Rav Yehuda said that Shmuel said: With regard to saving a life, the Sages did not follow the majority as they do in other areas of halakha. The Gemara asks: What are the circumstances? When does one not follow the majority? If we say that one does not follow the majority in a case where there are nine Jews and one gentile among them and a building collapses on one of them, then in that case the majority of people are Jews and yet one desecrates Shabbat to save the trapped person. In such a case one is in fact following the majority. Alternatively, if the group is half Jews and half gentiles, the ruling is lenient with regard to a case of uncertainty concerning a life-threatening situation. But this, too, is not a case where one follows the minority, as there is an even chance that the victim is a Jew. Rather, it is referring to a case where there are nine gentiles and one Jew. However, this too is obvious. One saves the trapped individual because the group is in a fixed location, and there is a principle that whenever a group is in a fixed location it is considered as though it were evenly divided. In this case, despite the fact that the group’s majority is gentile, it is considered as though it were composed half of Jews and half of gentiles.
The crucial distinction between safek, which reflects uncertainty regarding an individual object, and kavua, which is a definite hybrid status assigned to a set, cannot be over-emphasized. When kavua is invoked, it is the definite mixed status of the entire set that concerns us and not the uncertain status of any individual item in the set...
Finally, there are important halakhic differences between cases which are deemed safek and cases where kavua is applied. For example, if a person had before him two indistinguishable pieces of meat, one kosher and one non-kosher – a case of kavua – and he ate one of them, he is obligated to bring an asham taluy. But if he had before him one piece, possibly kosher but possibly non-kosher – a case of safek – he is not so obligated. Similarly, if a mouse takes a piece from a mixed pile of pieces of chamets and of matzah, in a manner such that the principle of kavua would apply [e.g. the mouse took the piece directly from the pile], into a house which has been inspected for Pesach, the house must be re-inspected. But if it took a single piece of which has an even chance of being chamets or matzah into the house – this is a safek – the house need not be re-inspected. In the case of safek, we can presume that an inspected house remains free of chamets since one possible resolution of the uncertainty regarding the subsequent events is consistent with this presumption. In the case of kavua, however, there is no uncertainty to resolve. Rather, some object of known mixed status has certainly been brought into the house; this is enough to nullify the presumption.
Now that we have established that cases of kavua are not cases of safek, which cases are in fact safek? The status of an object is safek when it is not judged as part of a set (so that kavua and bitul do not apply) and it has not been removed from a set with a majority (so that parish does not apply) and it does not belong to some reference class for which some statistical law is known (so that RDLK does not apply). A clean example of safek is one in which a piece of meat is found in the street and might have come from one of two stores, one kosher and one non-kosher.
R. Osher Weiss (Minchas Osher on Bereishit, Chapter 58) suggests that what Tosafot calls a safek haragil is specifically a case in which some event does not belong to any recognized reference class covered by a statistical law. In such cases, for which von Mises [an Austrian mathematician] would argue that the notion of probability is undefined,... RDLK does not apply. Rather, the safek is ragil only in the sense that a typical observer might find one possibility to be subjectively more likely than not. But this subjective probability is not relevant; a safek haragil is, for legal purposes, no kind of majority at all [and thus, those situations must be approached stringently].
§ It was stated: With regard to objects of idol worship that broke by themselves [were found broken], Rabbi Yoḥanan says: It is prohibited to derive benefit from them. Rabbi Shimon ben Lakish says: It is permitted. The Gemara explains the sides of the dispute. Rabbi Yoḥanan says that it is prohibited, as its owner did not revoke its status as an object of idol worship. Rabbi Shimon ben Lakish says that it is permitted, as the owner presumably revoked its status as an object of idol worship, having said to himself: If the idol could not save even itself from harm, can it save that man, i.e., myself?
The principle of sfek sfeka [compound uncertainty] is this: If a particular prohibition holds only if both conditions A and B hold, and in fact both A and B are in doubt, then we can assume that the prohibition does not hold.
ספק עבודת כוכבים אסורה וספק ספיקה מותרת כיצד כוס של עבודת כוכבים שנפל לאוצר מלא כוסות כולן אסורין פירש אחד מהן לריבוא ומריבוא לריבוא מותרין
An uncertainty of idol worship is prohibited, but its compound uncertainty is permitted. How so? With regard to a cup used in idol worship that fell into a storeroom full of cups, they are all prohibited. If one of these cups separated from the rest and fell into a group of ten thousand other cups, and from that ten thousand cups a single cup fell into ten thousand other cups, they are permitted. This baraita teaches that only one uncertainty is prohibited, not a compound uncertainty.
האומר פתח פתוח מצאתי נאמן לאוסרה עליו ואמאי ספק ספיקא הוא ספק תחתיו ספק אין תחתיו ואם תמצא לומר תחתיו ספק באונס ספק ברצון לא צריכא באשת כהן
A groom who says: I encountered an unobstructed orifice, claiming that when he consummated the marriage he discovered that his bride was not a virgin, is credible to render her forbidden to himself. Although it is not always possible to corroborate his claim with testimony that his wife committed adultery after betrothal, he is credible to render her forbidden to him as though she had in fact committed adultery. The Gemara asks: But why is she forbidden to him? It is a case of compound uncertainty. It is uncertain whether she engaged in intercourse while under his jurisdiction, after betrothal, in which case she would be forbidden to him, and it is uncertain whether she engaged in intercourse while not under his jurisdiction, in which case she would not be forbidden to him. And if you say that she engaged in intercourse while under his jurisdiction, it is uncertain whether she engaged in intercourse by coercion, in which case she would not be forbidden to him, and it is uncertain whether she engaged in intercourse willingly, in which case she would be forbidden to him. In cases of compound uncertainty, the ruling is lenient. Why, then, is his claim deemed credible? No, it is necessary to teach this ruling only in the case of the wife of a priest, who is rendered forbidden to her husband even if she engaged in intercourse by coercion. In that case, there is a single uncertainty.