Gemara

If one swore not to eat Neveilos, Treifos...' and he ate them, he is liable.

Question: Why is he liable? The oath of Sinai already forbids them!

Answer #1 (Rav, Shmuel and R. Yochanan): Because his oath is Chal (takes effect) on permitted food, it is Chal also on forbidden food.

Answer #2 (Reish Lakish): The Torah forbids only eating a k'Zayis of these things. His oath forbids eating any amount;

According to Chachamim, this is when he specified (any amount). According to R. Akiva, it is even without specifying.

R. Yochanan did not answer like Reish Lakish because he prefers to establish the Mishnah like Chachamim and R. Akiva.

27a (Beraisa) Suggestion: Perhaps if one swore to transgress a Mitzvah and did not do so, he is liable.

Rejection: "Lehara Oh Leheitiv" - just like doing good refers to something optional, also doing evil. This excludes one who swore to transgress a Mitzvah and did not do so, for this is not left to his whim.

Suggestion: If one swore to fulfill a Mitzvah and did not fulfill it, he should be liable!

Rejection: "Lehara O Leheitiv" - just like "to do evil" does not refer to a Mitzvah, also "to do good". One is not liable for an oath to fulfill a Mitzvah.

Also, just like "to do good" is optional, also "to do evil". This includes one who swore to harm himself.

Nedarim 16a (Mishnah): A stringency of Nedarim over Shevuos is that if one said 'Konam Sukah, I will not make one' or similarly for Lulav or Tefilin, he is forbidden. Such a Shevuah is void. One cannot swear to override Mitzvos.

(Rav Gidal): "Lo Yachel Devaro" - one may not profane his own word, but he may for the sake of Hash-m's word (an oath to transgress a Mitzvah is void).

Question: Presumably, "Neder la'Shem Lo Yachel" obligates observing a Neder against a Mitzvah. We should similarly expound "Shevuah la'Shem Lo Yachel"!

Answer #1 (Abaye): One can (vow to) forbid Hana'ah (pleasure) from a Sukah to himself. One cannot (swear to) forbid himself to benefit from a Sukah.

Objection (Rava): Mitzvos Lav Leihanos Nitnu (fulfilling Mitzvos is not called Hana'ah. Forbidding Hana'ah from a Sukah does not forbid the Mitzvah!)

Answer #2 (Rava): A Neder forbidding sitting in a Sukah is Chal, but a Shevuah not to sit in a Sukah is not.

Question: Rav Gidal learns from "Lo Yachel Devaro" that oaths cannot override Mitzvos. The Beraisa (above) learns from "Lehara Oh Leheitiv"!

Answer: "Lehara Oh Leheitiv" exempts from a Korban (for transgressing Shevuas Bituy). "Lo Yachel Devaro" exempts from a Lav.

8a (Rav Gidal): If one said 'I will get up early to learn tractate Ploni', this is a great Neder (many explain that really, it is a Shevuah.)

Question: The oath Yisrael accepted of Sinai already obligates him!

Answer: Since the Torah does not (explicitly) obligate more than saying "Shma Yisrael..." every morning and evening, the Shevuah is Chal.

Rishonim

The Rif concludes like Rava.

Rambam (Hilchos Shevuos 5:7): If one swore not to eat any amount of Neveilos and Treifos, and he ate less than a k'Zayis, he is liable for the Shevu'ah, for the Shevu'ah of Sinai does not apply to a half Shi'ur.

Radvaz: Indeed, the Torah forbids this, but it is not explicit in the Torah, therefore, a Shevu'ah takes effect on it. A proof of this is that Shevuos take effect on Isurim mid'Rabanan, even though Lo Sasur obligates observing them, because the Isurim are not explicit in the Torah.

Rosh (Shevuos 3:10): A Neder forbids an object to himself, therefore, it takes effect on a Mitzvah, for the object is not obligated that a person use it for a Mitzvah. A Shevuah forbids himself to the Sukah. It does not take effect, for he is obligated to do the Mitzvah. However, if so, what is the stringency of Nedarim over Shevuos? Also a Shevu'ah takes effect in such a case, i.e. 'sitting in a Sukah is forbidden to me through a Shevu'ah.' This is considered a Shevu'ah (29a). We can say that the stringency is that the same wording of a Neder that forbids Reshus, forbids Mitzvos. When one forbids himself on the object, e.g. my body is Konam on this object, this does not take effect even for Reshus. In Shevuos, there is a wording that forbids Reshus, but not Mitzvos. Alternatively, if he said 'sitting in a Sukah is forbidden to me through a Shevu'ah', the Shevu'ah is not Chal on the object, rather, on the person. The wording of a Shevu'ah must forbid the person to do an action. On 29a, he said 'all Peros are forbidden to me bi'Shvu'ah if I did not see...' Shevuos take effect of intangible matters because he forbids his body, which is tangible. A Neder forbids the object, so it cannot take effect on intangible matters.

Ran (8a DH Ha): A Shevu'ah is Chal on something expounded by Chachamim that is not explicit in the Torah. The Torah does not explicitly require learning more than Kri'as Shema morning and evening, therefore a Shevu'ah is Chal on more than this, even to obligate a Korban for transgressing it.

Ran (Teshuvah 32, cited in Beis Yosef YD 239 DH v'Zeh): The Rambam supports me.

Ran (on Rif Shevuos 10a DH Malkin): A Shevu'ah not to eat for seven days is vain, because this would kill him, so it is against Torah.

Rashba (1:616): R. Yochanan did not establish the Mishnah to discuss a Shevu'ah about Chetzi Shi'ur, for he forbids Chetzi Shi'ur mid'Oraisa (Shevuos 23b). This shows that if the Torah forbids Chetzi Shi'ur, a Shevu'ah is not Chal on it. Reish Lakish agrees that Chetzi Shi'ur is forbidden mid'Rabanan. We asked why the Shevu'ah is Chal, and answered that since mid'Oraisa it is permitted, the Shevu'ah is Chal. If there were no Heter mid'Oraisa, the Shevu'ah would not be Chal. We said that R. Yochanan did not answer like Reish Lakish, for he wanted to establish the Mishnah like everyone. Do not infer that he could explain it to discuss Chetzi Shi'ur according to one Tana; the Gemara merely gave one of two reasons why he did not say that it discusses Chetzi Shi'ur. Alternatively, we answered also on behalf of Rav and Shmuel. Perhaps they permit Chetzi Shi'ur mid'Oraisa.

Rosh (Nedarim 2:7): Rava answers that a Neder forbids objects, e.g. a Sukah. It does not look like he uproots the Mitzvah from himself, for he did not accept anything on himself. A Shevuah forbids himself. One may not uproot his obligation to do a Mitzvah! Therefore, we expound "la'Shem" to refer to Neder, which was written earlier, and not to Shevu'ah, which is written later.

Question: Why does a Shevu'ah forbid sitting in a Sukah? Mitzvos Lav Leihanos Nitnu!

Answer (Ran 16b DH Omar Rava): He forbade sitting, even if it is not Hana'ah. However, Stam Konam forbids only Hana'ah. Even though sitting in a Sukah is intangible (and Nedarim take effect only on tangible things), he said 'Konam a Sukah regarding sitting in it (it is forbidden) to me.' He did not give the precise text; he just teaches that the Neder was not about Hana'ah. Tosfos says that even 'sitting in a Sukah is forbidden to me' takes effect. Something intangible is only when he does not mention what he forbids, e.g. 'that I will sleep or speak.' When he mentions the object forbidden, this is considered tangible.

Poskim

Shulchan Aruch (YD 239:4): A Shevu'ah is not Chal on a Mitzvah, whether it was said in the text of a Shevuah, e.g. 'I will not sit in a Sukah', or said in the text of a vow, e.g. 'sitting in a Sukah is forbidden to me through a Shevu'ah.'

Beis Yosef (DH v'Chosav): Even when he forbids sitting in a Sukah in a Neder, why does it take effect? This is not Hana'ah! Tosfos answered that even though it is not Hana'ah, since he forbade it, it takes effect. If so, one can explicitly forbid throwing a rock into the sea. If he Stam forbids a rock or Sukah, he forbids only Hana'ah.

Bach (DH v'Af): Many explain that 'this is forbidden to me bi'Shvu'ah' does not forbid even a tangible matter of Reshus. However, the first Perush in the Rosh and the Semag forbid even 'sitting in a Sukah is forbidden to me bi'Shvu'ah.' One should be stringent.

Rema: This is only when he swore only about the Mitzvah. If he swore through Kolel (he also forbade Reshus), it is Chal also on a Mitzvah.