DOES KNOWLEDGE OF THE MIXTURE PERMIT? [Ta'arovos: knowledge]
Gemara
4b (Mishnah - R. Yehoshua): The general rule is, Me'ilah applies only to things that never had She'as Heter to Kohanim;
The following had She'as Heter -- it was left overnight, became Tamei, or was Yotzei;
The following never had She'as Heter -- it was slaughtered with intent Chutz li'Zemano or Chutz li'Mekomo, or Pesulim did Kabalah and they did Zerikah.
5a (Chizkiyah): He refers to Heter Shechitah;
(R. Yochanan): He refers to Heter Achilah.
(Zevachim 104a: R. Chanina Segan ha'Kohanim never saw a flayed skin taken to Beis ha'Sereifah due to a Pesul.
He holds like Rebbi, who says that Zerikah is Meratzeh even for the skin. (Zerikah permits the skin to Kohanim, even if the Korban was Pasul.).
If a Korban was found to be Treifah in the intestines, even though it was Pasul before Zerikah, since the Pesul was not known before Zerikah, it is Meratzeh.
Pesachim 13b: To publicize when one may eat or benefit from Chametz, we use loaves of a Todah that was slaughtered, but the blood spilled.
This is like Rebbi (who says that Shechitah, even without Zerikah, is Mekadesh the bread).
Rejection: It is even like R. Elazar b'Rebbi Shimon (who requires both to be Mekadesh). The case is, the blood was received in a Keli, and then it spilled;
i. R. Elazar holds like his father, who says that since the blood was ready for Zerikah, it is as if Zerikah was done.
Terumos 5:8 (Mishnah): If a Se'ah of Terumah fell into 100 of Chulin, (it is Batel. We remove a Se'ah, and treat it like Terumah, so Kohanim will not lose.) If before he was able to remove a Se'ah, another Se'ah fell in, it (the entire mixture) is forbidden;
R. Shimon permits.
Tosefta (on this Mishnah - Terumos 6:5): R. Elazar b'Rebbi Shimon says, this is when he did not know before the latter fell. If he knew before the latter fell, it is permitted, for he should have removed a Se'ah.
Rishonim
Rambam (Hilchos Terumos 13:6): If a Se'ah of Terumah fell into 100, and before he was able to remove a Se'ah, another Se'ah fell in, if he knew about the first before the second fell in, he separates two Sa'im and the rest is permitted. Since he should have removed, it is as if he removed. If he did not know before the second fell in, the mixture is forbidden, as if both fell in at once.
Ra'avad: This is like an individual, i.e. R. Elazar. The first Tana does not distinguish! Whether or not he knew, he forbids. A Tosefta explicitly permits if two Sa'im fell one after the other into 200, but if they fell into less than 200, it is forbidden, even though he knew in between.
Rosh (Chulin 7:37): Min b'Mino forbids up to 60 times (the amount of Isur) before it is known that it became mixed. Even though it does not give taste, Chachamim decreed this due to Min b'Eino Mino. However, after the mixture became known and the Isur was Batel in the majority and was transformed to all Heter, and one may eat all of them even at once, we cannot say that its emissions forbid.
Rosh: Regarding Terumah that became mixed, the Yerushalmi says that Chachamim hold that removing is Mekadesh, and R. Shimon holds that knowledge is Mekadesh. This is like he holds in general, that if blood was ready for Zerikah, it is as if Zerikah was done. From R. Shimon we learn to Rabanan regarding other Isurim that need not be removed. Knowledge causes the Heter. In Zevachim, we find that knowledge (of a Pesul before Zerikah) can cause Isur (to forbid the skin).
Rashi (5a DH Oh Heter Zerikah): Even though the Korban was slaughtered properly, also the Kabalah must be without a Pesul. Once he received properly, it was permitted to throw it. Even though it was not yet thrown; it is as if it was thrown, so there is no Me'ilah.
Rashi (5a DH Oh Heter Achilah): Even though it was slaughtered and received properly, there is Me'ilah until Zerikah, which gives Heter Achilah to Kohanim. If a Pesul occurred, even so there is no Me'ilah.
Poskim
Rema (YD 99:6): If an Isur became Batel, e.g. there were 60 times as much Heter, and later more of the Isur was added, the first Isur is Chozer v'Ni'ur (becomes Asur again and joins to forbid the mixture). This is whether it is Min b'Mino or Min b'Eino Mino, whether it is dry or wet, whether or not he found out in between (that Isur was mixed in).
Beis Yosef (DH Chatichas): If a piece of Isur fell into 60 times as much Heter, and he did not realize and more of the Isur fell in, if there is not 60 times as much as both Isurim together, it is forbidden. If he knew in between that there is enough Heter to be Mevatel the first piece, we do not need 60 times as much as both. We learn from the Mishnah and Tosefta in Terumos. The second Se'ah forbids only if he did not know in between. The Mordechai (Bava Kama 119,120) and Rambam say so. R. Shimshon brings oppositely from the Yerushalmi, that they argue only when he knew in between. If he did not know, all forbid. Also the Ra'avad argues with the Rambam. It seems that even the Rambam does not learn from here to other Isurim, for he did not bring this in Hilchos Ma'achalos Asuros.
Gra (15): The Rambam rules that knowledge is Mekadesh, based on the Tosefta. He holds that R. Elazar b'Rebbi Shimon explains the first Tana. The primary Perush is like the Ra'avad, like the Yerushalmi says. R. Elazar holds like his father (it is as if the Isur was removed - Pesachim 13b). However, this is only for Terumah, for which one must remove (an amount equal to what fell in). For other Isurim, Chachamim agree, until there is a majority of Isur.
Taz (14): This is unlike a spoon inserted twice into a pot (94:2), for here there is a new Isur.
Shach (21): This is like Torah Chatas (85:10, citing the Terumas ha'Deshen's Hagahos on Sha'arei Dura). However, it seems that the Terumas ha'Deshen forbids when he knew in between only regarding an Isur that gives taste. He said 'Avi ha'Ezri forbids even if he knew. It seems that this is due to the Rosh's reason. Since there is more Isur, it can be tasted.' If a dry Isur was Batel b'Mino is a majority, once he finds out, it does not join to forbid, since mid'Oraisa one is Batel in two. It seems that the first piece was Batel, and even joins to be Mevatel the new Isur that fell in, just like Orlah helps to be Mevatel Orlah (Orlah 2:3). The Yerushalmi explains that this is when he knew (in between). However, the Rosh holds that Chozer v'Ni'ur even for dry mixtures, even if he knew. It is hard to resolve the Mishnah in Orlah according to him.
Shach (ibid.): R. Shimshon's opinion is primary. Even Rabanan hold that knowledge permits other Isurim in dry mixtures, as long as they do not give taste. They are not Chozer v'Ni'ur. Terumah is different, for one must remove an amount equal to what fell in. The Ramban and Ran bring that the Ra'avad says so, and the Rashba says so. (The Ra'avad connotes that it is permitted even if he did not know in between, and even if it gives taste.) They argue only because taste is not Batel, and the Isur can be tasted. Even regarding Min b'Mino, which cannot be tasted, since enough fell to give taste in Eino Mino. This does not apply to a dry mixture Min b'Mino.
Shach (ibid.): The Mordechai and many Poskim say that if a piece of Isur fell in 60 pieces of Heter, and it was known, and another fell in, each that falls is Batel. We hold unlike this, rather, like Avi ha'Ezri, for the Terumas ha'Deshen's reason, for it can be tasted. However, this does not apply to a dry mixture Min b'Mino. When Isur was Batel in a majority of Heter, it is not Chozer v'Ni'ur, and helps to be Mevatel more Isur. Isur v'Heter (24:10) says so, even for a dry mixture Min b'Eino Mino, like the Or Zaru'a. It seems that we do not hold like this. The reason we require 60 in Min b'Eino Mino is lest one cook them together, and the Isur will give taste. If so, the same applies here. Isur v'Heter is lenient because he holds that the stringency of a dry mixture b'Eino Mino is not lest one cook them together, rather, like I wrote in 98:6. (It is as if it has a solution, for one could recognize the Isur and remove it. I.e. it is like Davar she'Yesh Lo Matirim - PF.) The same applies here. This is why the Poskim say that Avi ha'Ezri forbids even if a piece of Isur fell into 60 pieces of Heter. They discuss a dry mixture b'Mino. If not, they should have said 60 parts of Heter. Terumas ha'Deshen says that even though it is a good reason, for it can be tasted, i.e. when it will be cooked. He says that Avi ha'Ezri forbids even if he knew, unless they were removed. Removal does not help for a wet mixture, for it already emitted taste. The Yam Shel Shlomo (Chulin 7:57) says that Avi ha'Ezri permits (even for wet mixtures), and the Terumas ha'Deshen disagrees, for it gave taste. It seems that he and the Rema hold that even a dry Isur b'Mino is Chozer v'Ni'ur. I cannot oppose them, especially since they are stringent. To avoid a big loss, one may be lenient for the reasons I gave above. Perhaps the Rema says 'it does not matter whether or not he knew in between' only to when we need 60. We can explain also the Yam Shel Shlomo like this.
Shulchan Aruch (109:2): If a dry piece of Isur became Batel in two pieces of Heter, if they were cooked together, one may not even eat each by itself unless there are 60, for the gravy receives taste and is absorbed in the pieces.
Rema: Some say that if the Isur was known before they were cooked together, everything is permitted. They do not become forbidden again, for they became Batel when they were dry. If there would be a loss (if one is stringent), one may rely on the lenient opinion.
Beis Yosef (DH v'Chasav Od): The Rosh holds that when there is Bitul b'Rov, one may eat all three pieces together or cook them together. However, if more Isur was mixed in before Heter was added, the Isur is revived. This applies to all Isurim, even for Min b'Mino. The new and old Isurim join, even though they do not give taste. Chachamim decreed to require 60, even for a dry Isur Min b'Mino, like the Mishnah in Terumos. R. Shimon permits only because he holds that what it is destined to be removed, it is as if it was removed. For other Isurim, which need not be removed, they join to forbid. This is because even after the Isur was Batel is a majority of Heter, if it would be recognized, one may not eat it. When more Isur became mixed, it joins with the first Isur, as if it was recognized. We say so about Kodshim (Zevachim 31a) and Tum'ah (Bechoros 22b).
Gra (11): This is like the Rosh, who holds that it is transformed to Heter, and it is not Chozer v'Ni'ur. This is like the Mechaber said in 99:6, that if an Isur mid'Rabanan became known, it is not Chozer v'Ni'ur.
Taz (4): If it was known, it is permitted, because it was already called Heter.