1) HALACHAH: ARGUING WITH ONE'S TEACHER
OPINIONS: The Gemara states that one who argues with his Rebbi ("ha'Cholek Al Rabo") is considered as though he argues with the Shechinah. The Gemara derives this from the verse that states that Korach's argument against Moshe Rabeinu, the teacher of the Jewish people, was an argument "against Hash-m" (Bamidbar 26:9).
Does this mean that a person is not permitted to question his Rebbi's teachings?
(a) RASHI comments that one who argues with his Rebbi is one "who argues on his Yeshiva." What does Rashi mean?
The BE'ER SHEVA explains, in his first approach, that Rashi is emphasizing that even one who argues with his Rebbi's other students (his "Yeshiva") is considered as though he argues with the Shechinah. The Gemara derives this from Korach, who did not challenged the position of Moshe, the Rebbi, but who challenged the position of Aharon and his sons (the other students of Moshe Rabeinu).
The Be'er Sheva, however, prefers a different explanation for the words of Rashi and for the meaning of "ha'Cholek Al Rabo," one who argues with his Rebbi. He suggests that Rashi understands the Gemara the way the RAMBAM understands it. The Rambam (Hilchos Talmud Torah 5:2) describes one who argues with his Rebbi as "one who establishes a place in which he teaches and lectures without the consent of his Rebbi, while his Rebbi is alive, even though he is in a different country." That is, the Gemara does not refer to a student who argues with his Rebbi about a specific issue in Halachah. Rather, the Gemara refers to a student who establishes an entirely separate academy without his Rebbi's consent. This is also the ruling of the SHULCHAN ARUCH (YD 242:3).
The Be'er Sheva adds that the TERUMAS HA'DESHEN (#238, and cited by the REMA YD 242:3) rules that a student is allowed to argue with his Rebbi about a Halachic ruling when he provides proof to support his view. (The LEVUSH implies that this applies only in singular situations. When he quotes the Terumas ha'Deshen, he writes that a student may argue with his Rebbi "in a certain, single ruling," implying that a student may not argue regularly. The ARUCH HA'SHULCHAN further qualifies the words of the Rema and says that they apply only where one's Rebbi eventually agrees with his argument.)
The Be'er Sheva elaborates on this and proves that a student is permitted to argue with his Rebbi in matters of Halachah. He points out that this has been the method of learning Torah throughout all of the generations. Among the many examples that he cites are, among the Tana'im, Rebbi, who argues with his father and teacher, Raban Shimon ben Gamliel; among the Amora'im, Rava, who argues with his teacher, Rabah; and among the Rishonim, the Hagahos ha'Ashiri who argues with his teacher, the Maharam, and the Tur who argues with his father and teacher, the Rosh. The Be'er Sheva says that throughout the generations, it has been the acceptable mode of conduct for a student to disagree with his Rebbi whether or not his Rebbi was present, whether others sided with him or not, and whether the student was young or old (see TOSFOS to Nidah 14b).
However, the Be'er Sheva questions his explanation from the Gemara in Kidushin (end of 31b) that states that "one may not contradict the words" of his father, which the Poskim explain refers to arguing with his Halachic ruling, and which applies to one's Rebbi as well (SHULCHAN ARUCH YD 242:16). The Gemara there clearly prohibits one from arguing with the ruling of his Rebbi! (See BEIS YOSEF.)
The Be'er Sheva suggests that the Gemara in Kidushin means that one may not contradict the words of his father (or Rebbi) in a confrontational manner, such as by saying, "No, that is incorrect," but rather he must express his disagreement in a respectful manner, as the Gemara earlier in Sanhedrin (81a) teaches.
Alternatively, the Be'er Sheva suggests that the Gemara in Kidushin does not mean (as Rashi and other Rishonim explain) that one may not argue with the Halachic ruling of one's father or Rebbi. Rather, it means that one may not contradict the mundane, non-Halachic statements of one's father or Rebbi. One certainly is permitted to argue (in a respectful manner, of course) with the Halachic ruling of one's Rebbi.
He proves this from the Gemara in Kidushin (30b) which derives from verses (Tehilim 127:5 and Bamidbar 21:14) that "even a father and son, or a Rebbi and student, learning together become like enemies to each other, and they do not move from there until they become beloved to each other." The Gemara is describing a Rebbi and a student who argue in Halachic matters, and it clearly sanctions such arguments when done for the sake of clarifying the truth about a Torah matter. He cites a Teshuvah of the ROSH (55:9) who writes that when the clarification of the Torah is involved, one is obligated to argue.
(b) The SHACH disagrees with the Terumas ha'Deshen. He quotes the MAHARIK (Shoresh 170) who writes that a student may argue with his Rebbi only when he has reached an equal level of scholarship as his Rebbi. Otherwise, he may not argue even if he has proofs that support his argument. The Shach says that the proofs cited by the Terumas ha'Deshen to support his view are refutable, since, in each case of a student who argued with his Rebbi, the Rebbi might have given explicit permission to the student to argue with him, or the student may have been arguing with his Rebbi's ruling only after his Rebbi's death. (He adds that the matter needs further elucidation.) It is important to note that even the Shach is stringent only in a Rebbi-student relationship, but not in the relationship of a "Talmid Chaver" who is "close to being as great as his Rebbi" and thus may argue with him.
(c) The RADVAZ asserts that all the proofs from the Gemara and throughout the generations that a student may argue with his Rebbi apply only with regard to theoretical matters, but not with regard to practical Halachah, Halachah l'Ma'aseh. The student is not allowed to rule in opposition to his Rebbi's ruling.
The SHE'EILAS YA'AVETZ (#5) says that this is also the opinion of the Terumas ha'Deshen himself, and he presents a strong proof for this. The Shulchan Aruch, Rambam, and other Poskim write the Halachah that a student who issues a Halachic ruling in the presence of his Rebbi ("Moreh Halachah Bifnei Rabo") is Chayav Misah. If it is true that a student is permitted to argue with his Rebbi even with regard to the actual Halachah, then how can it be that he would be Chayav Misah for issuing a Halachic ruling, which does not even contradict his Rebbi's ruling, in the presence of his Rebbi? It must be that the Terumas ha'Deshen refers to the theoretical aspects of the Halachah, and only in such matters does he permit a student to argue with his Rebbi.
The She'eilas Ya'avetz agrees, however, that a student whose wisdom is comparable to his Rebbi's may argue even in Halachic matters, as many cases of such arguments throughout the generations have been recorded (see IGROS MOSHE YD 3:88).
The She'eilas Ya'avetz states further that a student may not rule even for himself and conduct himself in a stringent manner in accordance with his own view of the Halachah, when his Rebbi rules leniently. However, the MAHARSHAL (cited by the MAGEN AVRAHAM and the MISHNAH BERURAH OC 63:7) rules that one is allowed to be stringent against the opinion of his Rebbi if he has proofs which refute his Rebbi's lenient ruing. RAV CHAIM KANIEVSKY shlit'a understands that the Mishnah Berurah implies that a student is allowed to be stringent even in front of his Rebbi.

110b----------------------------------------110b

2) THE FATE OF THE TEN LOST TRIBES
OPINIONS: In the Mishnah, Rebbi Akiva and Rebbi Eliezer argue about the fate of the Ten Tribes that were exiled by Sancheriv in the times of first Beis ha'Mikdash. Rebbi Akiva maintains that the Ten Tribes will not return from their exile. He bases his view on the verse, "And he exiled them to another land, [where they remain] like this day" (Devarim 29:27). Rebbi Akiva explains that this verse means that just as a day passes by and never returns, the Ten Tribes will never return. Rebbi Eliezer maintains that they will return. He explains that the verse means that just as the light of day comes after the darkness, the Ten Tribes will again shine after the exile.
When Rebbi Akiva says that the Ten Tribes will not return, to what period does he refer? The Beraisa quoted by the Gemara says that the Ten Tribes have no share in Olam ha'Ba. Is this what Rebbi Akiva means in the Mishnah when he says that they will not return?
(a) The RAN writes that Rebbi Akiva in the Mishnah refers to Olam ha'Ba, but he maintains that only the people of that generation who were exiled have no share in Olam ha'Ba. The Ran explains that this is because they turned away from Hash-m and they degraded Eretz Yisrael. However, their descendants are included in the "Nidchei Yisrael" who will be gathered in when Mashi'ach comes. The Ran concludes by saying that no one ever argued with this. RASHI agrees with the Ran in his first explanation.
Rashi questions Rebbi Akiva's opinion from the Gemara in Megilah (14b). The Gemara there states that the Ten Tribes already returned to Eretz Yisrael in the times of Yirmeyahu. How is that Gemara to be reconciled with the opinion of Rebbi Akiva in the Mishnah here, who states that the Ten Tribes will remain in exile permanently?
Rashi answers that Yirmeyahu only returned some of the exiles of the Ten Tribes; the Mishnah refers to the remaining exiles.
The TIFERES YISRAEL (Yachin #26) and the ME'OR EINAYIM have difficulty with this explanation. The places of exile mentioned in the verse in Melachim II (18:11, cited by Rashi here) are known to be in China and India. However, there are very few Jews there compared to other lands such as Africa, Europe, and Western Asia. The Tiferes Yisrael suggests that much of the Ten Tribes became mixed up with the natives in their lands of exile. Indeed, it is known that there are groups of people in those places who observe various forms of Jewish traditions (while they are also involved with idol-worship). (See Tiferes Yisrael there for several examples. For further discussion on the topic, see the book, "Jewish Identities -- real and imagined" by Shemon Matlofsky.) The Tiferes Yisrael suggests that the discussion in the Mishnah concerning whether or not the Ten Tribes "will return" refers to whether or not they will return to Torah after being estranged for such a long period of time.
(b) In Rashi's second explanation, he cites an opinion that the phrase in the Mishnah, "they will not return," refers to the times of Mashi'ach, and not to Olam ha'Ba. Mashi'ach will not accept them into Eretz Yisrael because they scorned the land. This implies that they still have a portion in Olam ha'Ba.
The BE'ER SHEVA questions Rashi's explanation. The Beraisa explicitly states that the Ten Tribes will have no share in Olam ha'Ba. The words "Olam ha'Ba" are not used to refer to the times of Mashi'ach; the Mishnah and Gemara use separate phrases to refer to the times of Mashi'ach and to Olam ha'Ba. Also, the Gemara earlier (99a) says that that "the prophets prophesied only about the times of Mashi'ach, but not about Olam ha'Ba," clearly differentiating between the two. Therefore, Rebbi Akiva here also means that the Ten Tribes have no share in Olam ha'Ba.
It seems that Rashi's explanation is based on the wording of the Mishnah, in which Rebbi Akiva says that the Ten Tribes "will not return," which implies a physical return to Eretz Yisrael, and not Olam ha'Ba.
The Ran questions Rashi's explanation from the Gemara in Bava Basra (122a). The Gemara there, based on verses in Yechezkel (ch. 48), clearly states that in the times of Mashi'ach, Eretz Yisrael will be re-divided among all of the Shevatim. How, then, can Rashi say that the Ten Tribes will not return in the times of Mashi'ach?
It could be that Rashi is consistent with his earlier statement (DH Ein Asidim), that the Mishnah does not mean to say that none of the members of the Ten Tribes will return. On the contrary, at least some of the Ten Tribes certainly did return (as the Gemara mentioned earlier, and as is clear from the verses in Ezra). Rather, The Mishnah means that not all of the members of the Ten Tribes will return when Mashi'ach comes.