1) A "NAVI" WHO WAS NOT A "CHACHAM"
QUESTION: The Gemara quotes Rav Avdimi d'Min Chaifah who said that "from the time that the Beis ha'Mikdash was destroyed, Nevu'ah was taken from the prophets and given to the Chachamim." The Gemara asks that the Chachamim certainly had Nevu'ah before the Churban. The Gemara explains that Rav Avdimi meant that even though Nevu'ah was taken from the prophets, it was not taken from the Chachamim. RASHI explains that Nevu'ah was taken from the prophets who were not Chachamim, and it was left with the prophets who were Chachamim.
How can Rashi suggest that there were prophets who were not Chachamim? The Gemara in Nedarim (38a) states clearly that one of the four qualifications of a prophet is that he must be a Chacham (see also Shabbos 92a). (RAMBAN)
ANSWERS:
(a) The RAMBAN cites some who answer that when the Gemara in Nedarim lists four characteristics necessary for a person to be a prophet, it refers only to a prophet who receives Nevu'ah constantly, with the Shechinah resting upon him without interruption. There are prophets, however, who receive occasional visions of prophecy for limited purposes. Such Nevu'ah can come even to a person who does not have the qualifications mentioned in the Gemara in Nedarim.
The Ramban himself, though, writes that he is not satisfied with this answer.
(b) The RAMBAN therefore gives a different explanation for the Gemara. He asserts that all Nevi'im certainly were Chachamim, as the Gemara in Nedarim says. When the Gemara here says that Nevu'ah was taken away from the prophets but not from the Chachamim, it means that the Nevu'ah of the sort that comes to a person in a prophetic vision was taken away, but not the type of Nevu'ah that a person has through Chochmah, wisdom. Even though they no longer are able to have prophetic visions, the Chachamim are still able to achieve knowledge of the truth through the Ru'ach ha'Kodesh that rests upon them. (See also CHASAM SOFER and YA'AVETZ here.) (I. Alsheich)

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2) THE LAW OF PATRIMONY IN COMMUNAL POSITIONS
QUESTION: The Gemara relates that the Chachamim voted to appoint Rav Acha mi'Difti as the Rosh Yeshiva in Masa Mechasya.
Why did the Chachamim take a vote to decide to appoint Rav Acha mi'Difti as the Rosh Yeshiva? Rav Ashi was the Rosh Yeshiva in Masa Mechasya, and when he died the normal protocol should have been followed: his son, Mar bar Rav Ashi, should have been appointed to take his place (as the RAMBAM writes in the beginning of Hilchos Melachim). Mar bar Rav Ashi was certainly a great Talmid Chacham at that time and was fit for the position, as the Gemara in Chulin (99a) implies. (CHASAM SOFER, KOVETZ SHI'URIM)
ANSWERS:
(a) The KOVETZ SHI'URIM proves from the Gemara here that the law of patrimony, as learned from the laws of kingship, applies only to positions of governmental authority. A son can inherit only governmental positions from his father. The law of patrimony does not apply to a position of Torah authority, such as the position of Rosh Yeshiva.
The CHASAM SOFER cites this view in the name of the MAGEN AVRAHAM (end of OC 53:33), who cites it in the name of the TESHUVOS RASHDAM (YD 85), who writes that when a Chacham must be chosen to teach Torah or to issue Halachic rulings, the position is not given automatically to the son of the previous Chacham who held the position. (This ruling applies, however, only when the other candidate is greater in Chochmah than the son. When they are equally qualified for the position, the son is given precedence.)
(b) The CHASAM SOFER writes that Rav Acha mi'Difti was greater in Chochmah than Mar bar Rav Ashi and was more qualified to be the Rosh Yeshiva, and that is why the Chachamim decided to appoint him. However, it was decreed in Shamayim that, in this case, the son -- Mar bar Rav Ashi -- would take the place of his father as Rosh Yeshiva. (See also Teshuvos Chasam Sofer OC 13.)
(Regarding the practical Halachah as to whether a son is given precedence over other candidates to take the place of his father in positions of Torah authority, such as Rosh Yeshiva or Rav of a community, see AVNEI NEZER OC 312.) (I. Alsheich)