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Shiur #19: Ketubot 15a Rov and Kavua

  • Dr. Moshe Koppel

 Based on a shiur delivered in the yeshiva by Dr. Moshe Koppel, Instructor of Mathematics at Bar-Ilan University



            The Gemara on 15a begins discussing the relationship between rov and kavua.  Generally, when a safek arises in halakha, we follow the rov – the statistical majority.  Rabbi Zeira, however, introduces an exception to this rule: "Kol kavu'a ke-mechtza al mechtza dami" – when the object about which we are in doubt is kavua, or stationary, we do not follow the rov, regardless of whether this will yield a stringency or leniency.  As an example of a situation of kavua, the Gemara brings a beraita which describes a case of one who found a piece of meat, and does not know whether it came from a properly slaughtered animal or from a neveila.  The beraita says:


"Nine stores, all of which sell meat from a properly slaughtered animal, and one store sells meat of a neveila, and one purchases from one of them but does not know from which one he purchased – this safeik is forbidden.  When it is found – we follow the majority."


            When a person finds meat in the marketplace, he follows the majority of stores in the area, and the meat is thus permissible (since nine out of the ten stores sell kosher meat).  If, however, the individual purchased meat from one of the stores and does not remember from which, then he must consider the meat forbidden.  The difference between the two cases relates to the point around which the safeik revolves.  In the second case, the safeik is about the store – from which store the meat originated.  Since the shops are stationary, this is a situation of kavua, which halakha considers "ke-mechtza al mechtza" – a case of two statistically equal possibilities; in other words halakha requires that we overlook the rov.  In the first case, however, the meat left the store before the individual came upon it.  This is called "parish," a case where the item in question had been removed from other items, in which case we follow the rov.


            This beraita thus shows how kavua can yield a stringency: the rov would have allowed us to rely on the majority of stores, which were kosher, but kavua eliminates the rov, such that the meat may not be eaten.


            The Gemara also provides an example of how kavua can yield a lenient ruling.  A Jew is liable for capital punishment for killing another Jew only if he had intended to kill a Jew.  If a group of ten people stood together, nine Jews and one gentile, and another Jew threw a rock into the group and killed a Jew, we might expect that since the Jews comprised the majority in the group, the killer is considered as having intended to kill a Jew and is thus liable.  The halakha of kavua, however, dictates that since the gentile is stationary, we look at the group as if it consisted of five Jews and five gentiles, such that the killer is exempt from capital punishment.


            In this shiur we will try to explain the conceptual underpinnings of this distinction between kavua and parish, when we follow the rov and when we do not.  In the course of our discussion, we will employ mathematical concepts relating to the laws of probability.


Safeik and Procedural Decision-Making


            The Gemara in Masekhet Chulin brings the basic source for the halakha that we follow the statistical majority:


"From where is that which the rabbis said, 'Follow the majority'?  From where?!  It is written, 'acharei rabim le-hatot' ('To lean in favor of the majority' – Shemot 23:2).  Regarding a 'ruba de-ita kaman' [to be explained later], such as the cases of nine stores or [a decision of] the Sanhedrin, we never asked; we asked only regarding a 'ruba de-leita kaman'…" (Chulin 11a)


            The Gemara indeed concludes that in a case of ruba de-ita kaman, where we have a majority of items within a group of items before us, we follow the rov based on this verse of "acharei rabim le-hatot."  This verse refers to the rulings of the Sanhedrin, which are decided based upon the majority view of its members.  The Gemara extends this concept of rov to all areas of sefeikot in halakha.


            Rav Elchanan Wasserman Hy"d, in his "Divrei Sofrim," questions this comparison between the vote in the Sanhedrin and the ten shops of which nine sell kosher meat.  Imagine that Eliyahu Ha-navi suddenly comes along and gives us two pieces of information.  First, he tells us the Sanhedrin voted incorrectly on a given matter of halakha, and the minority view was in fact the correct ruling.  Secondly, he informs us that the meat in question is in fact forbidden, it came from a non-kosher butcher shop.  Would we accept this information?  Clearly, we would relate much differently to the two pieces of data.  Despite Eliyahu's definitive assertion, we would continue to follow the majority ruling of the Sanhedrin.  On the other hand, we would undoubtedly take his information into account when determining the status of the piece of meat.  This difference reflects a fundamental distinction between these two decisions.  Arriving at a pesak halakha based on the majority ruling of the Sanhedrin is a definitive, procedural decision.  We follow their ruling not out of doubt, but with certainty.  By contrast, regarding the meat that was found in the street, we confront a question of "metzi'ut," of what actually happened.  Following the majority view is simply a method of deciding how to proceed in light of the safeik.


            To which of these two categories does the rock-throwing case belong?  Would rov in such a case resolve the doubt, or simply dictate procedure?  At first glance, it would seem that here we have no safeik at all.  All the data is clear: the murderer's identity, the victim's identity, and even the thrower's intent – to kill somebody at random from among the group of people.  We thus have no question with regard to the metzi'ut, but rather confront a halakhic safeik – whether or  not the intent to kill one of the people in the mixed group suffices to warrant capital punishment.


            In effect, we can formulate this question more generally: What is the nature of this mixed group?  If we look at this group as a "group of Jews," then the stone thrower is liable for capital punishment.  If, however, the one gentile in the group transforms its definition to a "group of gentiles" or even a "mixed group," then we would not sentence the killer to death.  The Gemara establishes that "kol kavua ke-mechtza al mechtza dami" – and therefore we must look at the group as a "mixed group," despite the fact that it consists almost entirely of Jews.  Here, then, the halakha of kavua serves as a means of establishing the formal definition of this group.


Kavua as a Means of Defining Groups


            Thus far, we have encountered two instances where the goal is not to resolve a safeik, but rather to lend a definition to a mixed group.  When the members of the Sanhedrin debate a certain issue, there is no safeik at hand that we must resolve.  (As mentioned, even if Eliyahu Ha-navi would come along and inform us of the "correct" ruling, we would not accept it.)  Rather, we must determine whether the Sanhedrin, as a body, rules leniently or stringently.  Similarly, when a person throws a rock at a group consisting of both Jews and gentiles, no safeik arises that calls for a resolution; we must merely determine the formal status of the mixed group.  We may therefore suggest that both kavua and ruba de-ita kaman are not means of resolving sefeikot, but rather means of determining the status of a mixed group.  In certain situations of this kind of group, we follow the rov and grant it the status of one of its components (kosher, tamei, forbidden, etc.).  In other cases, halakha tells us to consider the group a mixed group rather than establishing a clear-cut status, due to the principle of "kol kavua ke-mechtza al mechtza dami."


            Let us now try to bring an example from the laws of probability in order to clarify the criteria by which we define a group as a "mixed group" and when we can grant it a definitive status.


            If a basket contains nine black balls and one white ball, then the chances of pulling out a black ball are 90%.  Therefore, if someone pulls out a ball at random, and asks: "what is the color of the ball in my hand?" there is a 90% chance that it is a black ball.  Let us now ask a different question: What is the color of a ball in this basket?  We haven't taken any ball out from the basket; they are all still there.  But we nevertheless ask: What color is a ball in this basket?


            Obviously, we cannot answer such a question.  There is no "color" to a ball in this basket, since the basket contains different balls of different colors.  We can say that the basket contains black balls and white balls, but we cannot determine the color of a ball in the basket.


            In a case of "parish," for example, when someone finds a piece of meat in the street, and he asks whether it is kosher or non-kosher, one of these two possibilities must certainly be true.  We therefore implement the principle of ruba de-ita kaman and determine the meat's status based on the majority of stores.  When, however, a person throws a stone into a group of people, we must ask the question, "Did he try to kill a Jew or a gentile?" or, in other words, "What is the race of a person in this group?"  This question, which parallels the question concerning the basket of balls, can obviously not be answered.  We cannot characterize a "typical person" belonging to this group, since the group consists of different types.  In this case, therefore, we apply the rule of kavua, we give the group the status of a "mixed group" and thus exempt the killer from capital punishment.


            One might, however, challenge this approach based on the case of one who walks into a store and purchases meat, and later cannot remember which store he entered.  Seemingly, the moment the person enters the store he has isolated the piece of meat.  The question thus becomes, "Is this meat kosher or treif?" – and this question clearly does have an answer!


            It emerges from the discussions in the Gemara that the halakha of kavua applies in this instance, as well.  We focus our attention not on the moment at which the person entered the shop, but rather on the immediately preceding moment, when the purchased piece was identical to all other pieces in the market.  At this moment, we cannot answer the question, "What is the nature of a piece of meat in the marketplace?" since the market has both kosher and non-kosher meat.  By contrast, when a person finds a piece of meat cast into the street, even before it was discovered the meat had already left the ta'arovet (mix of kosher and non-kosher meat).  Its status is therefore determined based on the majority of pieces of meat in the marketplace.


            Let us try to formulate this idea in a more general form.  When we deal with an object in isolation, for whatever reason, we must decide upon one of the two possibilities, and we employ the principle of ruba de-ita kaman for this purpose.  When, however, we deal with a mixed group, we leave it with this status of a "mixed group" and implement the rule of kavua.


"Bittul Be-rov"


            At times, we determine the status of a piece of food based on the rov even though we should seemingly apply the rule of kavua.  For example, when a drop of milk falls into a pot of meat soup, the soup is permitted (at least according to Torah law, before rabbinic enactment) based on the concept of "bittul be-rov" – the majority "nullifies" the minority, allowing us to simply ignore it.  Why does the rule of kavua not apply?


            Tosefot in Masekhet Pesachim (9b s.v. hayenu) ask this question and provide the following answer:


"That is different, because it is not totally kavua, since the forbidden substance is mixed together with the permitted substance and is not discernible… As far as Torah law is concerned, we consider it kavua only when the forbidden substance is identifiable in its place."


According to Tosefot, we apply the rule of kavua only when the minority item is identifiable.  We find, however, other cases where the minority is not identifiable and yet we do apply the halakha of kavua.  For example, when a shor ha-niskal (an ox sentenced to stoning for killing a person, from which one may not derive any benefit) mixes with other oxen, we apply the rule of kavua and forbid benefit from any of the oxen – even though the shor ha-niskal itself is not identifiable in its place.


            The Rashba (Chulin 95a, s.v. u-ve'nimtza) resolves Tosefot's question differently.  He claims that the bittul occurs before the rule of kavua takes effect.  Therefore, in a situation where the minority can be nullified, bittul takes place and we do not implement kavua.  The minority lends the group the status of a "mixed group" only if bittul does not take place:


"If you should ask, since when the forbidden substance mixes with a permitted substance we apply 'kavua' to it, how can we ever have a forbidden substance 'nullified' by the majority?  We may answer that we apply this [rule of kavua] only with regard to a significant forbidden substance that is not batel, such as an ox, which is significant and not batel – either according to the view that animals are not batel, or we deal with a piece of meat worthy of serving to guests ['chatikha ha-re'uya le-hitkabed' – which is not batel]."  However, whenever the forbidden substance can be nullified, we do not apply kavua, because it is batel."


            This is the meaning of the concept "kol kavua ke-mechtza al mechtza dami."  Whenever we have something stationary, the situation resembles one of a mixture of kosher and non-kosher food in which neither side is nullified by the other.  The mixture thus remains a "mixed group" and no resolution is possible.  However, one should not explain that "mechtza al mechtza" refers to equivalency since this would run counter to statistical probability.


            We may illustrate our claim that kavua serves as a means of determining the status of a mixed group, rather than a means of resolving sefeikot from the case of asham taluy.


In his discussion of the asham taluy (guilt-offering required of one who might have committed a "karet" transgression), the Rambam writes (Hilkhot Shegagot 8:2):


"One is not obligated to bring an asham taluy unless there was an 'issur kavua.'  How does this work?  If one ate chelev [forbidden fats], and he is unsure as to whether he ate more than a ke-zayit or less than a ke-zayit; or if he had before him a piece of chelev and a piece of shuman [permissible fat], and he ate one of them but does not know which he ate; or if his wife and sister were with him in the home, and he slept with one of them but does not know with which he slept… he brings an asham taluy, and the same applies in all similar situations.


If, however, he had before him only one piece, about which he is unsure as to whether it is chelev or shuman, and he ate it – he is exempt [from an asham taluy], since there is no 'issur kavua' here… Similarly, if one sleeps with a woman about whom he is unsure as to whether she is a nidah or perhaps a relative forbidden to him – he is exempt from an asham taluy."


When a person has only a single piece, and he does not know whether or not it is kosher, we can reach a conclusion based on the majority.  If he eats it, he need not bring an asham taluy.  In such a case, we can ask, "What is the status of this piece?" and thus we do not apply the rule of kavua.  When, however, a person has before him two pieces of meat, one of chelev and one of shuman, the question "what is the status of a piece in this group?" has no meaning.  We therefore define the group as a "mixed group," and one who eats from it must bring an asham taluy.