The underlying principle of almost the entire field of practical Kashrut is that of bitul - the ability of a food to be considered "nullified" when it is mixed with other foods, assuming that it does not impart any taste, that it is not noten ta'am. This is intuitively understandable when, say, a drop of milk falls into a large pot of chicken soup, that is, when the two are fully mixed together and become one entity. We can then say: "All we have here is chicken soup. The milk - since it cannot be tasted - no longer exists." But what happens when the items remain separate? What if one piece of treif chicken was mixed with 2 - or even 10, or even 100 - pieces of kosher chicken? Can we even say in such a case that the treif piece no longer exists? The first case, the case of the soup is what is called in halakha lach bi'lach, literally "liquid with liquid," the sense being that it all mixes together to become one larger whole. The second case, that of the pieces of chicken, is called yavesh bi'yavesh, literally "dry with dry," the sense being that the pieces remain distinct. It was this question - the ability for something non-kosher to become batel in a case of yavesh bi'yavesh - which was the focus on our learning this last week.
A number of mishnayot (Trumot 4:7-8, Arlah 3:1-9, Avoda Zara 3:5, Zevachim 8:1, Hullin 7:5) talk about cases of yavesh bi'yavesh, but always with the implicit assumption or explicit statement that the problematic piece is not batel. The Gemara, however, assumes that bitul should work in these cases and asks "Let it be nullified by a rov, majority!" (Chullin 99b, Zevachim 72a), and then explains that each of these cases is an exception. While it is possible that the mishna did not accept this principle - and for good reason, because each piece, being independent, does not lose its identity - the Gemara nevertheless takes it for granted that bitul does work here. The question is why?
Two answers are found in the Rishonim. The first, mostly identified with Rashba (Torat HaBayit 4:1), but also found in Tosafot Rid (Baba Batra 31b, s.v. Shetei), and perhaps implicit in Ramban (Hullin 97b, s.v. Ha di'Amar) is that it functions based on the principle of azlinan batar rubah, in cases of doubt we go by the majority. This principle, the focus on a sugya earlier in Hullin (11a-12a), is a principle for determining how to deal with situations of doubt. How do we know that a certain man is actually the father of a child? How do we know - or why can we assume - that an animal does not have any punctures in its spleen or brain which would render it a treifa? The answer - we go by majority, and we make halakhic assessments and assumptions based on the probability that such is the case.
This, says Rashba, is the operative principle here as well. If 1 treif piece gets mixed up with 2 kosher ones, I can take each piece separately and say - "In most likelihood this is not the treif piece." Halakha determines it to be the kosher piece and I can eat it. Then I can repeat this with the next 2 pieces. Although in the end I would have eaten all 3 pieces, and thus definitely the treif one, each action on its own was permitted. [The Vilna Gaon compares this to a similar case of two people walking down 2 roads, where you know that a grave is under one of the roads. When the people come to the rabbi separately, he is able to rule that each one is tahor]. Of course, the logical consequence of this is that 1 person cannot eat all 3 - or even 2 of the 3 - at the same time, because then he will definitely (or, in the case of 2, most likely) be eating the treif piece. Rashba says this explicitly, and then goes on to say that similarly one cannot cook all 3 pieces together because then each piece will have the taste of all 3, and the person will definitely be eating treif no matter what piece he eats. This logic is taken to an extreme in the Tosafot Rid who claims that if one person eats all 3 - even sequentially - than he has definitely eaten treif, he has sinned, and he must bring a sin-offering. Other Rishonim do not go as far, but Tosafot (Hullin 100a, s.v. Birya) does say that it is possible that one person should not eat all 3, even sequentially, and Rashi (Avoda Zara 74a, s.v. Tarti) says that one of the mixture should be discarded.
In opposition to Rashba, Rosh (Hullin 7:37), along with Raah (Bedek HaBayit, ad. loc.), says that the principle that operates in the case of yavesh bi'yavesh is identical to the one that operates in lach bi'lach. The Torah considers it all one mixture, even though in this case the pieces are independent, and thus the piece that is in the minority loses its distinctive halakhic status. In the words of the Rosh, issur hofekh li'hiyot heter, the prohibited piece becomes a permitted piece. There might still be a difference between this and lach bi'lach. Whereas in the case of lach bi'lach we could go so far to say that the drop of milk, say, that was added, actually ceases to exist, here - in the case of yavesh bi'yavesh - the piece clearly still exists, and the most that we can say is that it is no longer forbidden.
According to Rosh, then, it is obvious that one person can eat all 3 pieces together and can cook them together, and Rosh says so explicitly. Rosh, however, is left with one problem: If everything is permitted in such a case, how can the Talmud talk about cases of treif meat in a stew and assume that you need 60 times it to be nullified? The principle at work here is that since everything is cooking together it is not enough to have a rov, you need to have enough to negate the taste. But, says the Rosh, if all the pieces were mixed together outside the stew and then put in the stew, the treif piece would already become permitted, and you could even intentionally put it in the pot. Why, then, do you need 60 times to create nullification? To answer this question Rosh introduces a principle into the field of kashrut that plays out in a number of different cases. That is the principle of noda ha'ta'arovet - when one becomes aware that there is a problematic mixture. The halakhic change - from issur to heter - says Rosh, does not happen automatically, but only takes place when the person is aware of the mixture. It is at that moment that bitul occurs. Thus, if one became aware of the mixture before putting the pieces of meat into the stew- then bitul would take effect, and they could be intentionally added to the stew. However, if one was not aware then, and only became aware once the pieces were cooking, then it is at that moment that bitul takes effect, and then there is a mixture of tastes, and 60 is required.
[It is unclear from this Rosh what the scope of this concept of noda ha'ta'arovet is or should be. Would it apply also to create issur? What would happen if a drop of milk was cooked with 30 times as much meat, without the person being aware of the mixture, and then this piece of meat was cooked in a stew that had 100 times the amount of the drop, and it was then the person became aware of the problem. When do we assess if the meat became basar bi'chalav - during the first cooking, or when the mixture was known - during the second cooking? Or another scenario. Let's say that one piece of treif meat was mixed with two pieces of kosher meat, and a person ate all 3, and only after she ate it did she become aware of the problem. Did bitul ever take effect? Did she eat heter or did she eat issur, albeit unintentionally? Is Rosh's principle one to use for determining if bitul will take place, or is it only relevant when there are two possible times to determine bitul - the first mixture and the second - and thus used to determine not if, but when bitul will take place?]
We ended our learning of this topic by learning the related siman in Shulkhan Arukh (YD 109). There, the Mechaber rules like Rashba, with all the attendant qualifications, whereas Rema, while advising lichatchila, the preferred practice, that one follow Rashba, fundamentally rules like Rosh. A close reading of Shach and Taz on that siman reveal that they understand that even Rashba fundamentally agrees with Rosh that the operating principle is one of bitul, nullifying the status, and not one of azlinan, using probability to deal with doubt. Shach implies that even Rashba's demand to eat the pieces separately is only a rabbinic requirement to ensure that one is not definitely tasting treif at this moment (although the piece is technically kosher). He proves that Rashba would allow a person to eat 2 of the 3 at one time, and thus it is not probability that is the issue, but a rabbinic requirement, as stated above. A close reading of Rashba in Torat HaBayit reveals that this read is correct, and Rashba states this explicitly in his Mishmeret HaBayit. In contrast, the Beit Yosef, Arukh HaShulkhan, and apparently even the Gra, assume that Rashba argues fundamentally with Rosh, and does require the principle of azlinan to explain how this bitul works.
Having clarified of the bitul of yavesh bi'yavesh works, we turn next week to the classic case of bitul - lach bi'lach and the principle of taam ki 'ikkar, that the taste given off by a forbidden food is forbidden as well.