The Principle of Kavu'a
The gemara (9b) discusses a scenario where nine piles of matza and one pile of chametz are lying around before Pesach. A mouse comes and takes a piece from one of the piles and enters a house. However, we do not know if it took chametz or matza and thus are in doubt whether the house must be checked once again for chametz. The gemara distinguishes between a case where the mouse is seen taking a piece directly from one of the piles ["kavu'a"] and an instance where the piece snatched by the mouse was first isolated from the piles ["parish"]. These two cases are said to be analogous, respectively, to two cases considered in Ketubot (15a): "If there are nine stores which sell kosher meat and one which sells non-kosher meat and someone took [meat] from one of them but he doesn't know from which one he took, the meat is forbidden. But if [a piece of meat] is found [not in a store], follow the majority." Thus if the majority of stores from which the meat might have originated are kosher, the meat is permitted.
The case of the stores is explained in Ketubot on the basis of the principle that: "All cases of KAVU'A are regarded as half and half ('mechtza al mechtza'). All cases of PARISH are presumed to be from the majority."
The cases of the meat bought in the store and the chametz or matza taken directly from the piles, are regarded as cases of kavu'a and judged differently than the respective cases of parish, in which the status of an isolated item is at issue. Thus, in short, there are two types of cases, kavu'a and parish, in which uncertainty must be resolved and different principles of resolution are employed for each type.
There are a dozen cases in the Talmud Bavli in which the principle of kavu'a is invoked implicitly or explicitly. [See Ketubot 15a, Sanhedrin 79a, Bava Kama 44b, Nidda 18a, Chullin 95a, Yoma 84b, Kiddushin 73a, Zevachim 73a, Nazir 12a, Gittin 64a, Berakhot 28a and Yevamot 16b.]
It is often thought that the principle distinguishing kavu'a from parish is a divine decree lacking all rhyme or reason. While it is true that all decision methods are ultimately axiomatic, I intend to define the kavu'a principle in such a way that it does not seem arbitrary at all.
II. A Case of KAVU'A Where the Facts are Known
Let us begin by considering the following unusual case of kavu'a mentioned in Ketubot (15a): "Where do we find [the principle of kavu'a] in the Torah? It is written: '[If] he shall lay in wait for HIM and pounce upon HIM' - [this teaches us that a murderer is not put to death] unless he intended [to kill specifically] him [i.e., that person who subsequently died on his account]. The Rabbis said in the school of Yannai: This excludes the case of one who throws a stone beyond a wall [in order to kill an unspecified victim]. What is the case? ... There are nine Israelites and one Canaanite among them [in the area beyond the wall into which the stone was thrown]. The Canaanite is kavu'a and all cases of kavu'a are regarded as half and half."
Note that in this case there is no doubt that the actual victim was indeed an Israelite and not a Canaanite. The issue under discussion is only whether the intention to kill "some member of this group" can be regarded as the intention to kill an Israelite. Thus, there is no uncertainty regarding any of the facts of this case and no decision-method for resolving empirical uncertainty is called for. What, then, is the meaning of the ruling? Why is the intention to kill "some member of the group" inadequate to mandate capital punishment for the murderer?
Quite simply, an unspecified member of a group consisting of both Israelites and Canaanites (in whatever proportions) cannot be regarded as being specifically Israelite or specifically Canaanite. Rather, the principle of kavu'a tells us that just as the group is of indeterminate nature (neither strictly Israelite nor strictly Canaanite), so too, an unspecified member of the group is regarded as of indeterminate nature.
III. Indeterminate vs. Unknown Status
What I am calling "indeterminate" might be more suggestively called "mixed". I use the term "indeterminate" to emphasize that the item does not have either status assignable to an individual item (e.g. Israelite or Canaanite).
It is important to distinguish the notion of a KNOWN INDETERMINATE status from that of a DETERMINATE BUT UNKNOWN status. In order to appreciate this distinction, consider two scenarios in each of which we have before us a box containing nine white balls and one black ball.
Scenario 1: I reach into the box, pull out one ball without showing it to you and ask: What is the color of this ball?
Scenario 2: I don't reach into the box, but instead ask: If I were to pull a ball out of this box, what color would it be?
In the first case, if you were to answer, say, "black", your answer would be either true or false, but either way would be an appropriate response to the question that was asked. There is a determinate answer to the question, although this answer is unknown to you. In the second case, the answer "black" (or "white") is neither true nor false, since there is no determinate answer to the question. You could say nothing more specific than that the box contains both white and black balls.
Obviously, the case of the stone-thrower considered above is analogous to scenario 2 - asking about the status of an unspecified member of the group is like asking about the color of an unspecified ball. The appropriate level at which to assign status in this case is the level of the GROUP, not the level of the INDIVIDUAL, and the group is indeed mixed. It is only when an item must be assigned a status as an individual item, and not merely as part of some set, that the principle of majority can be invoked.
IV. Kavu'a vs. Parish
When do we assign a status to an item as an individual and when do we assign a status to an item as part of a set? If prior to the raising of the issue of status, the item in question is an undistinguished element of some set (kavu'a), then the item is assigned the status of the set. If, however, the item is in some way distinct from the set (parish), it is assigned its own status.
Consider the case of the stores mentioned above, of which nine out of ten sell kosher meat (Ketubot 15a). The critical moment for our purposes is the moment immediately preceding the initial encounter with the piece of meat in question. If this initial encounter occurs while the meat is in the store, the meat is regarded simply as an undistinguished member of a mixed set and its status is thus indeterminate (mechtza al mechtza). If the initial encounter occurs while the meat is on the street and is thus not associated with one of the elements of the set of stores, it must be assigned its own status. Unlike a mixed set of pieces of meat, an individual piece of meat is either kosher or non- kosher; its status is not indeterminate, but rather unknown. In such a case, we must choose between the two possibilities - kosher or non-kosher - and we use the majority principle in order to do so.
One subtlety must be pointed out in the analogy between the case of the stores and the story of the balls in the box. The case in which the meat is found on the street is indeed analogous to the case in which the ball has been removed from the box. In each case the item in question is of determinate but unknown status. However, the case in which the meat is initially encountered in one of the stores is analogous to the case in which no ball has been removed from the box, only if the critical moment is the moment immediately BEFORE the encounter. Otherwise, the encounter with the meat in the store could itself be regarded as the equivalent of removing a ball from the box. This is a slightly counter-intuitive feature of kavu'a.
One other poabout the definition of kavu'a needs to be emphasized. It is often thought that by definition an item is considered kavu'a if, and only if, it and the other items being considered are fixed in some particular location. This is perhaps a natural conclusion from a number of passages in which kavu'a is contrasted with cases of items which have moved (Yoma 84b, Zevachim 73a, Nazir 12a et al.). According to the above explanation, however, this conclusion is false. Rather, as discussed, an item is considered kavu'a by definition if at some critical moment it is an undistinguished member of a set. It happens that in certain sugyot it is assumed that one of the formal requirements for an item to be considered a member of a given set is that the elements of the set and the item in question must lie in some fixed geographical relationship to each other. This condition is, however, not an inherent part of the definition of kavu'a. (In fact, this condition is not mentioned anywhere except for certain sugyot in the Bavli. See the article by L. Moscovitz in Higayon 4.)
V. Mechtza al Mechtza
Thus far, we have focused on the difference between kavu'a and parish. Let us now consider the meaning of "mechtza al mechtza" more carefully.
It follows from the discussion above that "mechtza al mechtza" means that the item in question cannot be assigned any meaningful status (from among those assignable to an individual item, such as kosher/non-kosher), not that it has some status that we do not happen to know. (Did this last sentence seem out of place? I borrowed it [except for the parenthetic remark] almost verbatim from a physics text describing the state of certain particles according to quantum theory. I mention this not because I think that there is any connection at all between quantum theory and kavu'a but simply to illustrate that fundamental ideas turn up in all sorts of places.)
This interpretation is in contradistinction to the commonly held view that "mechtza al mechtza" is just a kind of leveling of the playing field in which an unbalanced distribution is treated as if it were balanced.
VI. Sample Spaces
The difference between my interpretation of "mechtza al mechtza" and this latter view can be made sharper by considering each of them from a probabilistic point of view. Consider the case of the piece of meat found in the street. Since 9 of the 10 stores from which the meat might have come sell kosher meat, the meat is deemed kosher. But counting stores is not the only option. For example, we might have considered the number of pieces of meat in the town and deemed the meat kosher if, and only if, most of THOSE pieces are kosher.
More generally, we can consider some partition of the meat in the town into q elements (which we call the "sample space") of which p are kosher and p' are not kosher. Then we deem a random piece kosher if there is a majority of kosher elements, that is, if p/q is greater than 1/2 or, ALMOST equivalently, if (q-p')/q is greater than 1/2. Of course, there are numerous ways to choose a sample space, some more natural than others, and the question of whether the majority of elements are kosher depends on the choice of sample space.
An example of a non-standard type of sample space is one in which the two formulas just mentioned, p/q and (q-p')/q, are not equal. This occurs when one or more of the elements are themselves of indeterminate status, neither kosher nor non-kosher. Suppose, for example, that our stores are distributed over three neighborhoods: in two of the neighborhoods only kosher meat is sold and in the third both kosher and non-kosher meat is sold. If we chose the three neighborhoods as our sample space, then p/q equals 2/3 but (q-p')/q equals 3/3. In this case both values are greater than 1/2 so no ambiguity results, but we shall soon see that this need not always be the case.
Two types of sample spaces deserve special attention. One possible sample space consist of two elements: all the kosher meat and all the non-kosher meat. For such a sample space, p/q equals 1/2. Another possible sample space is the one consisting of a single element: all the meat in the town. In this case p/q equals 0 (which is less than 1/2), but (q-p')/q equals 1 (which is greater than 1/2)! Such a sample space leaves us completely in the dark; its single element is neither kosher nor non-kosher.
Obviously, any ruling in cases such as we have been considering hinges crucially on how the sample space is chosen. In fact, the difference between the way a kavu'a case is handled and the way a parish case is handled can be neatly expressed in terms of sample spaces. In the case of parish, some natural sample space is chosen, e.g., the set of stores. (What makes a particular sample space "natural" is an interesting question which I won't attempt to answer here.) In the case of kavu'a, the chosen sample space consists of the SINGLE element consisting of the entire set, which is neither kosher nor non-kosher.
The identification of "mechtza al mechtza" with the sample space consisting of a single element is simply a formal version of the principle formulated above that the elements of a mixed set are judged as a set and are thus regarded as of indeterminate nature.
The interpretation of "mechtza al mechtza" which I reject argues that in a case of kavu'a the sample space consists of two elements: in the case of the meat, for example, the kosher meat and the non-kosher meat. According to that interpretation the status of the item in a case of kavu'a is not indeterminate but rather unknown, with each possibility regarded as equiprobable ("safek ha-shakul").
It must be admitted that this other interpretation does have a certain intuitive appeal, and that, moreover, it fits neatly with the phrase "mechtza al mechtza" (literally, "half and half"). Ultimately, I think it is wrong simply because there is no plausible connection between kavu'a and a sample space consisting of two elements, while there is, as I have argued, a compelling connection between kavu'a and a sample space consisting of a single element. I want to strengthen my case, however, by a)explaining why the phrase "mechtza al mechtza" is meaningful according to my interpretation and b) showing that cases of kavu'a are in fact treated differently than cases of uncertainty between two equal possibilities.
VII. Kavu'a and Ta'arovet
The terminological issue may sound marginal at first but, in fact, it leads directly to one of the thorniest aspects of the kavu'a principle: the relationship between kavu'a and mixtures (ta'arovet). Seemingly, every case of ta'arovet should be regarded as an instance of kavu'a. Nevertheless, according to the well-established principle of "bitul be-rov", a ta'arovet has the status of its majority component. How can bitul be reconciled with kavu'a?
The answer is straightforward: The bitul principle is always activated BEFORE the kavu'a principle. After bitul, the entire set is considered to have the status of the majority. Thus by the time kavu'a ascribes the status of the whole set to each individual in the set, this status is not indeterminate but rather that of the majority.
The ordinary case of kavu'a is the one in which bitul does not apply. There are numerous such cases. First, in instances such as the meat case above which are not true mixtures since each component is identifiable (e.g. each store is recognizably kosher or non-kosher). Second, in cases where bitul is not activated for technical reasons; for example, if the mixture consists of people or animals (in which case bitul is inapplicable by rabbinic decree). Finally, and most plainly, in cases of mixtures in which there is no majority component, that is, mixtures which are evenly divided between, for example, kosher and non-kosher components. In each such case bitul fails to apply and kavu'a is invoked.
A half-and-half mixture is the canonical case of an object of indeterminate status. The principle that every case of kavu'a is like "mechtza al mechtza" can thus be understood as meaning simply that every case of kavu'a isregarded as a half and half MIXTURE (as opposed to a safek ha-shakul), in the sense that its status is indeterminate. This point will be further explained.
VIII. Kavu'a is NOT Safek Ha-Shakul
It remains to be shown that cases of kavu'a in general, and half-and-half mixtures in particular, really are treated as of known indeterminate status (single element sample space), rather than as of determinate though unknown status (two element sample space = safek ha-shakul).
The clearest example of a distinction being drawn between a half-and-half mixture and a safek ha-shakul concerns the obligation to bring the "asham taluy" sacrifice: "R. Nachman said in the name of Rabba bar Avuah in the name of Rav: If a person had before him two pieces, one of non-kosher fat and one of kosher fat, and he ate one of them but does not know which one - he is obligated [to bring an asham taluy].[But if he had before him] one piece, possibly non- kosher fat and possibly kosher fat - he is not obligated. Rav Nachman said: What is Rav's reason? In the case of two pieces some forbidden object is certainly present ("ikba issura"), but in the case of one piece there is not necessarily a forbidden object present." (Kritut 17b)
Clearly, a random element of the half-and-half mixture is judged here as part of the mixture which is of known indeterminate status, and is treated differently than an isolated piece the status of which is unknown. In fact, in restating R. Nachman's explanation, the Rambam (Shegagot 8:2) explicitly identifies "ikba issura" with kavu'a: "A person is not obligated to bring an asham taluy unless there is a forbidden component that is KAVU'A". (Nevertheless, one should not extrapolate too freely from asham taluy to kavu'a in general. Many cases regarded as kavu'a for purposes of asham taluy, would not ordinarily be considered cases of kavu'a.)
In order to show that, in general, cases of kavu'a are treated differently than safek ha-shakul we come full circle to our sugya in Pesachim. We have already seen that our sugya compares the case of a mouse observed removing an item from a set consisting of chametz and matza to the case of a person acquiring meat in one of a mixed set of stores. The gemara then considers separately a case in which a mouse enters a house carrying a piece of something which has an even chance (safek ha-shakul) of being chametz. To be sure, our sugya is concerned primarily with drawing analogies and does not seem to be concerned with establishing rulings. Nevertheless, the flow of the gemara does suggest that the kavu'a case is dealt with differently than the safek ha-shakul case. The Rambam's restatement of our sugya (Chametz u-Matza 2:10-11) makes this distinction totally explicit:
"If one left nine piles of matza and one of chametz and a mouse came and took [from one of them], but we don't know whether it took chametz or matza, and it entered a house which had already been inspected [for chametz], one must inspect [the house again for chametz] since every case of kavu'a is regarded as 'mechtza al mechtza'. [But if there were] two piles, one of chametz and one of matza, and two houses, one inspected and one not inspected, and two mice came, one took chametz and one took matza, and we do not know into which house the one that took chametz entered, it is unnecessary to reinspect [the inspected house] since there is no kavu'a here."
Now in the case of the two piles, it is established that in the event of safek ha-shakul one need not reinspect. Nevertheless in the case of the ten piles, it is established that in a case of kavu'a one must reinspect (even when the majority is matza). This would be inexplicable if kavu'a were regarded as a safek ha-shakul. But it is precisely what one would expect if "mechtza al mechtza" is understood as a known indeterminate status. In the case of safek ha-shakul, we can presume ("chazaka") that an inspected house remains free of chametz since one possible resolution of the uncertainty regarding the subsequent events is consistent with this presumption. In the case of kavu'a, however, there is no uncertainty to resolve. Rather, some object of known indeterminate status has certainly been brought into the house; this is enough to nullify the presumption.
In conclusion, the principles of kavu'a and parish can be summarized as follows:
Suppose a set S includes some elements which have property P and others which have property not-P and the principle of bitul cannot be invoked. Then any item which can be identified only as "some element of S" is regarded as inheriting the known indeterminate status of S regarding the property P. However, an item which is distinguished from the other elements in the set (prior to the raising of the issue of its having or not having property P), for example by being physically isolated from the rest of the set, is judged as an individual and hence must be deemed to have either property P or property not-P. This determination is made on the basis of the majority of elements in S.
The next shiur (which will be in two weeks) will deal with the issue of safek specifically in regard to bedikat chametz. The shiur will refer to the gemara beginning with the colon on 9b ("teisha tzibburim") and will cover the cases up to "safek al" (10a "...safek maza tum'a tamei"). The basic problem is to devise a consistent set of principles when one goes "li-kula" and when "li-chumra" in bedikat chametz.
The basic sources are:
1. Tosafot 9b s.v. "heinu." Tosafot solve the problem by referring some of the cases to biur chametz (d'oraita) rather than bedika (d'rabbanan).
2. Ra'avad (on the Rif, 4b). [until the end of the first column on 5a].
3. Rabbeinu David s.v. "be-shlosha" (pp. 60-68). This is the basic source for the shiur. For the benefit of those who don't have a copy of R. David, we will post this section on the web, at http://www.etzion.org.il/rd.htm . (You will need Hebrew web fonts to read this. If you don't have them, they can be obtained from our website http://www.virtual.co.il/education/yhe).