Gemara

(Mishnah): If a girl above 11 (full) years vows, we check her (to see if she understands that Nedarim are to Hash-m). If a girl above 12 vows, it is valid (we do not check her). During her 12th year we check her. (Every law applies similarly to a boy a year older.)

If she vows before (11 full years), even if she knows (that vows are to Hash-m), it does not take effect. If she vows after (12 full years), even if she says that she did not know, it takes effect.

Question: The Mishnah taught that we do not check her vows after 12 years. Why must it teach that during her 12th year we check? We can infer this!

Answer: Since 30 days in a year are considered like a year, one might have thought that if she did not know in the first 30 days of year 12, we need not check the rest of the year. The Mishnah teaches that this is not so.

(Mishnah): If a boy vows after (year 13), even if he says that he did not know that vows are to Hash-m, it takes effect.

Inference (Rav Hamnuna): The (13th) year is like the year before. (If he brings two hairs, they are Shuma, i.e. not a sign of adulthood.)

Rav Hamnuna infers from the Seifa itself. It cannot be that he did not grow hairs, for if so he is still a minor! Rather, he grew hairs. The hairs are significant after the year. During the year they would be Shuma!

(Beraisa): "Ish Ki Yafli Lindor Neder" includes a boy above 13. Even though he does not know to Whom he vowed, it takes effect.

Question: If he did not grow hairs, he is still a minor!

Answer (R. Zeira): Rather, he grew hairs. The hairs are significant after 13. During year 13, they would be Shuma!

(Beraisa): The Torah considers a minor to be like an adult regarding intentional transgression of oaths and Lo Yachel.

Inference: He is (lashed) like an adult regarding "Lo Yachel"!

Rejection: No, he is like an adult regarding the Isur, but he is not lashed.

Question: In any case this is difficult!

If Mufla Samuch l'Ish is mid'Oraisa (it is forbidden even to him), he should be lashed;

If it is mid'Rabanan, he should be permitted!

Answer #1: Chachamim commanded the one who supervises the minor to stop him from transgressing.

Inference: Beis Din (i.e. all adults) are commanded to stop minors from transgressing! (This is unlike R. Pedas (Yevamos 113b).)

Rejection (and Answer #2): No. The case is, the minor was Makdish and adults ate it.

Question: This is like R. Yochanan and Reish Lakish, who say that adults are lashed for (benefit from) a minor's Hekdesh. Rav Kahana says that adults are not lashed for it. How can he answer?

Answer: He is lashed mid'Rabanan. What we expounded from "Ish Ki Yafli" is only an Asmachta.

Rishonim

Rambam (Hilchos Nedarim 11:1): If a boy or girl at least a day past 12 or 11 years, respectively, swore or made a vow of Isur or Hekdesh, we check him (or her). If he knows to Whom he vowed or swore, it is valid. If not, it is void. He must be checked the entire 13th year (or 12th for a girl).

Rambam (3): Before his 12th (and her 11th) year, even if he knows to Whom he vowed, it is not a vow. After 13 (or 12) years and a day, even if he says that he does not know to Whom he vowed, his vow or Hekdesh is valid, even if he did not bring two hairs. This is called Onas ha'Nedarim.

Rambam (4): Once a child reached the years of adulthood, his vows stand, even if he did not bring Simanim and he is not an adult for anything. This is mid'Oraisa, that the vow of a Mufla Samuch l'Ish is a vow. Even so, if he transgressed his vow or oath he is not punished until he matures and brings two hairs.

Rambam (Hilchos Shevu'os 12:7): If a minor swore and he understands oaths, even though he is not liable, we force him to fulfill his words, in order to train him and put fear on him, so he will not be frivolous with oaths. If he vowed about something he cannot fulfill without damage, e.g. to fast or not to eat meat for a long time, his father or Rebbi lashes him or rebukes him and shows him that his oath is permitted, so he will not be frivolous with oaths.

Magid Mishneh: The Mishnah in Nidah teaches that vows of a minor (more than a year before adulthood) are totally invalid. The Ge'onim say that we force him to fulfill it so he will not be frivolous about Shevu'os. We permit it even if it is not dangerous, for even an adult's vow would be permitted then! Rather, the minor will be in great pain. Alternatively, we are concerned lest he get sick.

Bach (DH v'Chasav Od): The law of vows and oaths is the same.

Rashi (46b DH Isura): If Mufla Samuch l'Ish were mid'Rabanan, Chachamim would not forbid minors, for they need not accept on themselves enactments of Chachamim.

Poskim

Shulchan Aruch (YD 233:1): If a boy or girl is at least a day past 12 or 11 years, respectively, and he (or she) knows to Whom he vowed or swore, his vows and oaths are valid, even if he did not bring two hairs. We check him during his 13th (or her 12th) year. Before his 12th (or her 11th) year, even if he knows to Whom he vowed, it is not a vow. From 13 years (for a girl, 12 years) and a day and onwards, even if he does not know to whom he vowed, his vow is valid.

Prishah (1): 'Until he matures' means 13 years and one day, and two hairs. The Tur wrote 'even if he did not bring two hairs' not for the law itself, for two hairs do not help before 12 years for a girl or 13 years for a boy. They are Shuma! Rather, it is for the Seifa, to teach that they are not lashed until they mature, i.e. years and hairs.

Bach (Kuntres Acharon): I wrote that mid'Oraisa they become adults through Mufla Samuch l'Ish. Their Hekdesh or vow takes effect, even without two hairs.

Bach (DH Bodkim): 'Before the 13th year' means before Rosh Hashanah of the 13th year, and similarly regarding 'before the 12th year.' Rashi explains like this. Other texts of the Tur say 'before 12 years for a boy or 11 years for a girl', and so says the Shulchan Aruch. This refers to before the completion of 12 or 11 years.

Birkei Yosef (Shiyurei Berachah 1): If a minor vowed or swore and was not checked whether he knows to Whom he vowed, and he matured, and we do not know whether he knew when he vowed, presumably we say that he did not know. If he claims that he did not know at the time, he is believed (Bnei Avraham YD 9). I recently saw Kehilas Yakov and Rav Achai Gaon. He concludes like Keneses ha'Gedolah. In practice, one must consider the matter

Shulchan Aruch (OC 343:1): If a minor is eating Neveilos, Beis Din is not commanded to stop him, but his father must rebuke him and separate him (Rema - from an Isur mid'Oraisa). One may not feed him even an Isur mid'Rabanan.

Rema: Some say that this applies only to a child before he reached the age of Chinuch, but once he reached the age of Chinuch, we must separate him. Some say that Chinuch applies only to the father, not to Beis Din.

Gra (DH v'Yesh): This opinion learns from Yevamos and Gitin, in which the Gemara suggested that we should allow a minor to transgress. This is even if he reached the age of Chinuch. The Gemara said so in Nidah regarding a Mufla Samuch l'Ish and an Isur Torah. The Re'em (in Tosfos Yeshanim Yoma 82a DH Ben) says that Chinuch applies only to Mitzvos Aseh. Rebbi says that it applies only to the father. The Rambam (Hilchos Ma'achalos Asuros 17:28) agrees: The Ramban asked against the first opinion (of the Rema), for the Gemara (Yevamos 113a) asked why we let a minor eat Terumah, and in Nidah we ask from Mufla Samuch l'Ish. It seems that both of these are after he reached the age of Chinuch.

Damesek Eliezer: I do not understand the question from Terumah. There it discusses a deaf-mute, and not a minor. Chinuch does not apply to a deaf-mute, for he will never be obligated in the Mitzvos!

Gra: The Ramban challenged also the Rambam. The Gemara in Nidah should have answered that his father must separate him! The Rashba left this difficult, and concluded like Tosfos Yeshanim, for all the cases of Chinuch at the end of Sukah apply to Mitzvos Aseh.

Note: There is a Mitzvas Aseh "k'Chol ha'Yotzei mi'Piv Ya'aseh" for vows and oaths.