1) WHEN THE "CHILUFIN" OF A NEDER ARE NOT PROHIBITED
QUESTION: The Mishnah states that when one makes a Neder and says, "These fruits are prohibited to me," he is prohibited not only from eating the fruits but also from eating the "exchange" ("Chilufeihen") of the fruits (if they are traded for other fruits) and from that which grows ("Giduleihen") from the fruits (if they are replanted). When one makes a Neder and says, "The fruits are prohibited to me, that I will not eat them" or "that I will not taste them," he is permitted to eat the Chilufin and the Gidulin of the fruits.
In the Gemara earlier (47a), Rami bar Chama asks what the Halachah is when a person makes a Neder to prohibit his fruits from someone else. Is the Mudar prohibited from eating the fruits received in exchange for the prohibited fruits? The Ran explains that the question of Rami bar Chama is not related to the ruling of the Mishnah here in the case of a person who prohibits fruits to himself by saying "Konam Peros Elu Alai," because when a person says "Elu" ("these fruits") and prohibits the fruit to himself, he certainly intends to prohibit the Chilufin and Gidulin as well. Rami bar Chama's question involves a case in which one makes his fruit prohibited to someone else, with or without saying the word "Elu" ("these"). Even if the Madir intends to prohibit the Chilufin of his fruit to the Mudar, he does not have the power to prohibit the Chilufin because the Chilufin is a "Davar she'Lo Ba l'Olam" (an item which does not yet exist in his possession) and prohibiting them is akin to prohibiting someone else's fruits on someone else (which one cannot do). Rather, the only reason why the Chilufin would be prohibited is if the Chachamim instituted a penalty to prohibit the Chilufin of an item which is Asur b'Hana'ah. The basis for such a penalty is that the person exchanged fruit which was Asur b'Hana'ah for other fruit. Rami bar Chama asks whether the Chachamim instituted such a penalty in such a case.
Why does Rami bar Chama not answer his question from the second case of the Mishnah, in which a person makes a Neder to prohibit fruit to himself by saying "she'Ani (or she'Eini) Ochel," or "she'Ani (or she'Eini) To'em"? If the Chachamim instituted a penalty and prohibited one from benefiting from the items received in exchange for an Isur Hana'ah, then even if a person prohibits fruit by saying "she'Ani Ochel" or "she'Ani To'em," the penalty should apply to prohibit the Chilufin received in exchange for the fruit even though the person did not say "Elu." It must be that there is no such penalty!
ANSWER: If the Chachamim instituted a penalty to prohibit the Chilufin received in exchange for an Isur Hana'ah, they did so only because one is prohibited from exchanging an Isur Hana'ah in the first place since one derives Hana'ah from the object when he receives something in return for it. In contrast, when a person prohibits fruit to himself by saying "she'Ani Ochel" or "she'Ani To'em," he prohibits himself only from eating the fruit (Achilah); he has no intention to prohibit deriving benefit (Hana'ah) from the fruit. Since he is not prohibited from deriving benefit from them, he is permitted to exchange them. Hence, Rami bar Chama agrees that there is no reason for the Chilufin to be prohibited if the person exchanges the prohibited fruit for permitted fruit.
In contrast, in the case of a person who prohibits fruits to himself by saying, "I will not derive benefit from figs," and he does not say "Elu" ("from these figs"), Rami bar Chama's question applies (see Chart).

57b----------------------------------------57b

2) "IKAR" AND "GIDULIN"
QUESTION: The Gemara cites the question of Yishmael Ish Kefar Yama: if a prohibited fruit (for example, a fruit that grew during Shevi'is) grows in size (after Shevi'is) such that the new growth ("Gidulin") is enough to be Mevatel the old growth ("Ikar"), does the fruit become permitted through Bitul?
Most Rishonim explain that Yishmael Ish Kefar Yama assumes that it is obvious that the Gidulin themselves are not like the Ikar and they are Mutar, and the only question is whether or not they have the power to annul the Ikar so that it becomes Mutar as well. The RAN, however, explains that the question is not whether the new growth has the power to annul the original growth. Rather, the question is whether the new growth itself differs from the original growth and is permitted, or whether the new growth has the same status as the original growth and is prohibited (since it grew from the original growth).
The Gemara attempts to prove that the Gidulin are not like the Ikar and are permitted, and that they can annul the Ikar. The Gemara quotes the statement of Rebbi Yitzchak in the name of Rebbi Yochanan who says that when a person separated Terumos and Ma'aseros from onions and then replanted the onions in the ground and they increased in size such that there is more new growth of onion than the original growth of onion, he is obligated to separate Ma'aser not only from the new part that grows but from the entire onion, including the original growth. This ruling clearly indicates that any new growth which sprouts forth from an object which is exempt from Terumos and Ma'aseros is obligated in Terumos and Ma'aseros (that is, the Gidulin are not like the Ikar), and that they can annul the Ikar and cause the Ikar to become obligated in Ma'aser as well.
The Gemara concludes that even if the Gidulin cannot annul the Ikar, the Chachamim treat the Gidulin as distinct from the Ikar, l'Chumra -- when doing so will result in a stringency. Accordingly, the Gidulin are obligated in Ma'aser, and since the Gidulin are the majority (Rov), they annul the Ikar and thus the Ikar is obligated in Ma'aser as well.
The Ran asks that the Gemara's conclusion poses a difficulty to the Rishonim who maintain that the Gidulin certainly are not like the Ikar and that the question of Yishmael Ish Kefar Yama applies only with regard to whether the Gidulin can annul the Ikar. According to these Rishonim, the Gidulin of the onion which was replanted certainly are obligated in Ma'aser mid'Oraisa, while the original onion is exempt from Ma'aser mid'Oraisa. The Chachamim instituted that the original onion, the Ikar, is also obligated in Ma'aser mid'Rabanan. However, if this is true, the Chachamim could not have instituted that Ma'aser be separated from the entire onion as one: if one separates Ma'aser from part of the onion itself, one might separate Ma'aser from the Ikar (which is Patur mid'Oraisa) on behalf of the Gidulin (which is Chayav mid'Oraisa) and thereby separate "Min ha'Petur Al ha'Chiyuv," or vice versa, which is invalid! On the other hand, if one separates Ma'aser from another onion which is obligated in Ma'aser mid'Oraisa on behalf of this onion, he is separating too much Ma'aser since mid'Oraisa Ma'aser needs to be separated only for the Gidulin and not for the Ikar. The Ma'aser which he separates on behalf of the Ikar is not considered Ma'aser and remains Tevel, and it prevents the Levi from eating that bundle of Ma'aseros.
The Ran proves from this question that if the Gidulin cannot annul the Ikar, it is because the Gidulin themselves have the same status, mid'Oraisa, as the Ikar. Therefore, if the Gidulin cannot annul the Ikar and make it obligated in Ma'aser mid'Oraisa, it must be that the Gidulin themselves are not obligated in Ma'aser mid'Oraisa either and the entire onion is obligated in Ma'aser only mid'Rabanan! On the other hand, if the Gidulin are able to annul the Ikar, then the entire onion is obligated mid'Oraisa. According to either possibility, one may separate Ma'aser from one part of the onion on behalf of the entire onion without concern that he is separating "Min ha'Petur Al ha'Chiyuv."
The ROSH, TOSFOS, and other Rishonim disagree with the Ran and explain the question of Yishmael Ish Kefar Yama in the first manner described above: the Gidulin are certainly permitted, and the question is whether or not they can annul the Ikar. How do these Rishonim answer the question of the Ran? Also, according to these Rishonim, why does Yishmael Ish Kefar Yama entertain the possibility that the Gidulin should not be able to annul the Ikar? For what reason should they not be able to annul the Ikar?
ANSWERS:
(a) The ROSH explains that the reason the Gidulin might not be able to annul the Ikar is that they are not really mixed together. Rather, the Gidulin surround the Ikar; they grow out from the Ikar and stand differentiated from it. On the other hand, since the Gidulin entirely surround the Ikar and there is no clear line to distinguish them from the Ikar, perhaps they are able to annul the Ikar.
In response to the Ran's question about separating Ma'aser from the onion, the Rosh writes that all parts of the entire onion nurture equally from the soil. Consequently, every part of the onion grows to some extent after it was planted, and thus when one separates Ma'aser from any part of the onion for the rest of the onion, the proportion of Chiyuv and Petur are equal and the Ma'aser is valid. (Even according to those who apply the principle of "Ein Bilah" to dry objects, in this case the objects are considered like a Davar Lach, a liquid. Since the obligation of Ma'aser depends on the absorption of nutrients and moisture from the soil, it is considered like there are equal portions of Chiyuv and Petur in every part of the object.)
The Rosh seems to contradict what he writes earlier. The Rosh earlier writes that the reason why the Gidulin do not annul the Ikar is that the Gidulin are visibly separate from the Ikar and the parts of the onion are not unidentifiably mixed. However, the Rosh subsequently writes the exact opposite -- that although the Gidulin do not annul the Ikar, there is an equal proportion of Chiyuv and Petur in every part of the onion!
Perhaps this contradiction may be resolved as follows. Visibly, the new portion (the Gidulin) is distinct from the old portion (because it is on the outside, and it is fresher). Internally, however, the new portion is actually distributed throughout the entire onion. (This is why the Rosh writes that the Gidulin do not annul the Ikar; the Gidulin and Ikar "are not entirely mixed together.") Therefore, although there are equal portions of Chiyuv and Petur in every part of the onion, Bitul does not occur because Bitul depends on what is visible to the eye, and the Gidulin and the Ikar are not visibly mixed together. (See the question of the SHITAH MEKUBETZES (end of 58b) on this approach.)
(b) The RASHBA answers that the obligation of Ma'aser of onions is only mid'Rabanan (see Ran to 58b, DH Ochel me'Hem), and thus even the Gidulin are obligated in Ma'aser only mid'Rabanan. Consequently, the Chachamim were able to institute that one may separate Ma'aser either from the Ikar or from the Gidulin on behalf of the entire onion.
(c) TOSFOS explains that the reasoning of the view which maintains that the Gidulin do not annul the Ikar is that the Ikar is considered a Davar Chashuv (a significant entity) in comparison to the Gidulin, and a Davar Chashuv does not become Batel (see Chulin 100a). However, the Halachah that a Davar Chashuv is not Batel is only mid'Rabanan; mid'Oraisa a Davar Chashuv is Batel. According to Tosfos, therefore, everyone agrees that mid'Oraisa the Gidulin annul the Ikar. Consequently, according to Tosfos it is obvious why there is no problem with separating Ma'aser from the Ikar on behalf of the Gidulin -- both the Ikar and the Gidulin are obligated in Ma'aser mid'Oraisa.
The RASHBA explains like Tosfos that mid'Oraisa the Gidulin annul the Ikar. Nevertheless, the Rashba asks the question of the Ran -- why may one separate Ma'aser from the Ikar on behalf of the Gidulin?
Why is the Rashba concerned with this question? Since the Rashba maintains that mid'Oraisa the Gidulin annul the Ikar, one should be able to separate Ma'aser from the Ikar on behalf of the Gidulin!
The Rashba might not have accepted this answer to the Ran's question because this answer is so obvious that the Gemara's Havah Amina is difficult to understand. If it is true that mid'Oraisa the Gidulin annul the Ikar, what was the Gemara's question in the first place when it attempted to prove from the case of Ma'aser that the Gidulin can annul the Ikar? It is obvious that one must separate Ma'aser for the entire onion in this case because mid'Oraisa the Gidulin annul the Ikar, even according to the opinion that Gidulin of Heter do not annul an Ikar of Isur.
It seems that the Rashba understands the Gemara's question differently. The Gemara is asking that mid'Oraisa, objects of Heter can annul objects of Isur, but objects of Isur cannot annul objects of Heter (as the Gemara says on 59a, and as explained by the Ran to 59b, DH v'Ad Kan). However, the Gemara assumes that when Rebbi Yitzchak says that the Gidulin of Isur can annul the Ikar and thus the entire onion is obligated in Ma'aser, he must mean that the onion is obligated mid'Rabanan because the Chachamim enacted a Chumra that the Isur can annul the Heter. The Gemara asks that if this Bitul is only mid'Rabanan (because it is a case of an Isur annulling a Heter), and the Chachamim have said that the Gidulin do not annul the Ikar because the Ikar is a Davar Chashuv, then there should be no Bitul here at all, even mid'Rabanan!
The Gemara answers that the Chachamim considered the Ikar to be a Davar Chashuv (and hence not Batel) only as a Chumra and not where it would lead to a leniency, a Kula. Therefore, in this case the Gidulin are obligated in Ma'aser mid'Oraisa, while the Ikar is obligated in Ma'aser mid'Rabanan. This is why the Rashba asks that one should not be able to separate Ma'aser from the Ikar on behalf of the Gidulin -- because one will thereby be separating "Min ha'Petur Al ha'Chiyuv."