Gemara

21b - Version #1 (Rav Yehudah citing Rav): One who took one of the four vows needs a Heter Chacham (a Chacham must permit it).

Objection (Shmuel): The Mishnah says that Chachamim permitted them. You cannot say that they need a Heter Chacham!

Version #2 - Rav Yosef - (Rav Yehudah citing Rav Asi): A Chacham may permit a vow only if it is like one of the four vows.

He holds that a vow cannot be permitted through a Pesach (opening) of regret.

24b (Beraisa): Vows of exaggeration are permitted. Oaths of exaggeration are forbidden (some texts - permitted).

Rishonim

The Rif and Rosh (3:1) bring Shmuel's objection to Rav's teaching.

Rosh: In the second version, we say that a Chacham can permit a vow only if it is like one of the four vows. I.e. he must find a Pesach that uproots it from the beginning; he did not vow with this intent. This is like the four vows, which never took effect. The Halachah follows Shmuel; the Mishnah connotes that Chachamim totally permitted the four vows. The Yerushalmi supports this. A Tosefta learns that one should not take a vow that Chachamim permitted, in order to Mevatel it, from "Lo Yachel Devaro" - do not make your word Chulin.

Rambam (Hilchos Shevuos 3:1): If one takes one of these four oaths, he is totally exempt. One kind is Ones, i.e. people stopped him from fulfilling it, or an extortionist made him swear.

Rambam (4): If one swore to an extortionist Stam that he will not eat meat, and in his heart he meant 'today' or 'pig meat', he is permitted. The same applies to all similar cases.

Rambam (5): One is exempt for oaths of exaggeration and Shegagah.

Ra'avad: Chachamim did not need to teach that he is exempt from a Korban. Rather, they taught that just like vows of Shegagah and exaggeration are permitted, also oaths.

Kesef Mishneh: If Chachamim did not teach that he is exempt from a Korban, how would we know this? Perhaps the Gemara said that they are 'permitted' for parallel structure with Nedarim, but really the oath takes effect, just one is exempt. Alternatively, the Rambam agrees that the oath is permitted, and surely one cannot be liable for it. He wrote 'exempt' for parallel structure with the previous laws.

Radvaz (here and Nedarim 4:3): The Rambam holds that Shevuos must have a name or Kinuy of Hash-m (a word that refers to Him). One may not say His name needlessly. The Rambam wrote 'exempt', not 'permitted', lest one think that one may swear l'Chatchilah. B'Di'eved, he need not fulfill the oath. The same applies to oaths of urging. The Ra'avad permits l'Chatchilah, for he holds that an oath does not need Hash-m's name

Kesef Mishneh: A Mishnah permits vows of urging. The Rambam omitted oaths of urging because the Gemara did not say 'just like vows of urging are permitted, also oaths of urging.' The Ran and Rashba permit oaths of urging. The Yerushalmi says so; the Rambam holds that the Bavli argues.

Lechem Mishneh: Perush ha'Mishnayos says that vows of urging must be annulled, therefore such oaths are forbidden. The Gemara says that vows of urging need not be annulled! Rather, he means that since some vows of urging must be annulled, i.e. when he was Ma'amid (intended to vow), we forbid all oaths of urging. Oaths are more severe, so we decree lest he intend for a real oath.

Etzei Levonah (YD 239:1): Salmas Binyamin (1 DH b'Inyan) permits oaths of urging only if he swears not to benefit from a certain matter if he sells for less than four, but not if he swears not to sell for less than four.

Rambam (Hilchos Nedarim 4:1): Vows of Ones, Shegagah and exaggeration are permitted.

Rambam (3): Vows of urging are permitted.

Rambam (4): The four vows are permitted, but one may not vow with intent to Mevatel them. "Lo Yachel Devaro" - do not make your word Chulin.

Rosh (3:4): The Gemara cites the Tosefta, which says 'just like vows of exaggeration are permitted, also oaths of exaggeration.' Some texts forbid oaths of exaggeration. The Yerushalmi brings Beraisos with different texts, and establishes the one that forbids to discuss Ma'amid. I.e. he says that he did not intend to exaggerate; he truly saw the matter. (When he said 'these fruits should be forbidden if I did not see...',) the Ramban permits the fruits, for he did not intend to forbid them. He is lashed for a vain oath.

Tosfos (Shevuos 29a DH b'Omer): One Beraisa permits oaths of exaggeration mid'Oraisa. The other forbids mid'Rabanan, due to the severity of oaths - "Lo Yenake."

Question (Rosh): The fruits are permitted because it is normal to exaggerate; all know that he did not really see as many people as left Mitzrayim. For the same reason, he should not be lashed for a vain oath!

Answer (Rosh, citing the Ri): He is lashed only when he forbade all food if he did not see..., for this is vain (no one can live without eating).

Rosh (Shevuos 3:13): "Ha'Adam bi'Shvu'ah" excludes Ones, i.e. one who thought that he swears truthfully. A case occurrence in which a Shomer was punished even though she thought that he swears truthfully (Gitin 35a). This is because she was negligent from the beginning; she should have been very careful with the deposit, for she will need to swear if it will be lost.

Poskim

Shulchan Aruch (232:1): There are vows that need not be permitted: vows of urging, exaggeration, Onsim (coercion), Shegagah (mistake), and one who makes his vow contingent on something that did not occur.

Shulchan Aruch (13): Even though the four vows are permitted, one may not vow unless he intends to fulfill his words.

Question: The Seifa does not apply to Nidrei Ones. When he vows, he does not know that there will be an Ones!

Answer #1 (Taz 22): Indeed, the Seifa applies only to the other three vows.

Answer #2 (Drishah 4): The Rambam says so about the four vows. I.e. even though the vow is permitted, l'Chatchilah one should vow with intent to fulfill his word even if there will be an Ones. However, if he vowed Stam, it is permitted. A better answer is that should not take one of the four vows unless he intends to fulfill it, even if his friend will not accede to his urging, or Ones will prevent him, or he will realize that he erred about the premise of his vow.

Answer #3 (Etzei Levonah 239:1): It applies when an extortionist forces him to vow. He should try to avoid vowing. The Shach says that if he vowed or swore, it need not be permitted. It seems to me that a Shevuah must be permitted, but not a vow.

Rebuttal (Gra 239:5): The Yerushalmi and Shulchan Aruch (14) explicitly permit swearing to an extortionist.

Maharam Padavah (72, brought in Shirei Keneses ha'Gedolah): Even though vows of urging,... need not be permitted, there is nothing wrong with permitting them, in order that people will not treat vows lightly.

Shulchan Aruch (239:1): Some say that just like vows of urging, exaggeration, Onsim and Shegagah are permitted, the same applies to such Shevuos. A Shevuah of exaggeration is forbidden if he affirms it, and says that he surely saw as many people as left Mitzrayim.

Prishah (4): The Rema (232:4) says that also a Neder takes effect if he affirms it. The Tur says so only here regarding Shevuos of exaggeration, for the Rosh learned this from the Yerushalmi regarding Shevuos of exaggeration. The same applies to all four Shevuos.

Shulchan Aruch (ibid.): Some say that Shevuos of exaggeration are always forbidden. It seems that the Rambam forbids oaths of urging, and also the other (three) oaths. Even though he is exempt from a Korban, they are forbidden.

Shach (9,10): 'They are forbidden' means that one must permit them. It does not mean forbidden l'Chatchilah, for this applies even to vows. However, the Rambam (Shevuos 3:4) explicitly permits Shevuos Onsim!