Gemara

(Mishnah): If Levi said to David 'Konam Pi Medaber (my mouth speaking) with you, my hands from working with you, or my feet from walking with you', he is forbidden.

(Gemara) Contradiction (Beraisa): There is a stringency of oaths over vows, and a stringency of vows over oaths:

The stringency of Nedarim is that they take effect on Mitzvos, just like on Reshus (something optional). This does not apply to Shevuos;

The stringency of Shevuos is that they take effect on tangible and intangible matters, but Nedarim do not. (Talking, working, and walking are intangible!)

Answer (Rav Yehudah): In the Mishnah he forbade his mouth to speak (with Levi), his hands to work with him, and his legs to walk with him.

Support (Mishnah): 'Konam is my mouth...'

He did not say 'that I will speak...'

14b (Mishnah): If one said "Konam that I sleep", "Lo Yachel Devaro" applies.

Question: If he literally said "that I sleep", this does not take effect, for sleep is intangible!

Answer #1: He said "Konam my eyes to sleep today if I will sleep tomorrow."

Answer #2 (Ravina): Really, he literally said "that I sleep." Bal Yachel applies Mid'Rabanan:

(Beraisa): "Lo Yachel Devaro" - if people consider something to be forbidden, and really it is permitted, you may not be lenient about it to abolish the custom.

Rishonim

The Rif and Rosh (1:11) bring the Gemara on 13a.

Rosh: Rav Yehudah means that it is as if he forbade his mouth to speak or his hands to work with him... Since he wants to forbid himself, it is as if he specified.

Ran (13b DH b'Omer): 'Konam is my mouth from speaking' can mean that he forbids speech, or his mouth. We are stringent about Stam (unspecified) Nedarim, so we say that he forbade his mouth, which is tangible. The Gemara could have answered that even if he referred to speech, it is forbidden mid'Rabanan. It answered the truth, that it is forbidden mid'Oraisa.

The Rif and Rosh (2:3) bring Ravina's answer on 15a.

Rambam (Hilchos Nedarim 3:10): Nedarim do not take effect on something intangible. If one said 'my speech is a Korban to you', he is not forbidden, for speech is intangible. The same applies if he said 'my speech is forbidden to you.' Therefore, if one said 'Korban, I will not speak, work or walk with you', or 'Korban, I will not sleep, speak or walk', or he told a woman 'I will not have Bi'ah with you', it does not take effect at all. It is as if he said 'my speech, walking, working or Bi'ah is a Korban', and these are intangible.

Kesef Mishneh: The Ran (14b DH Masnisin) says that the text should be 'she'Ani' (that I will), not 'she'Eini (that I will not'), for vows take effect on objects, i.e. that which I will...We should likewise fix the text of the Rambam.

Rebuttal #1 (Lechem Mishneh): Also Perush ha'Mishnayos says 'she'Eini'. Perhaps the Rambam teaches that even though it is intangible, and the Neder is in the text of a Shevu'ah, mid'Rabanan he must permit it!

Rebuttal #2 (Yad Avraham on Shach YD 213:1): The Ran said so for he holds that a Neder in the text of a Shevu'ah is invalid. The Rambam holds that it is valid. Elsewhere (e.g. 8:8) he discusses Nedarim not to wear wool, etc.

Rambam (11): However, if one said 'my mouth is forbidden for its speech, my hands for their deeds, my legs for their walking, or my eyes for their sleep', the vow takes effect on them. Therefore, if one said 'Korban is my mouth from speaking with you, my hands from working with you, or my legs from walking with you', he is forbidden.

Beis Yosef (YD 213 DH u'Mah she'Chosav Rabeinu): The Rambam holds like the Rosh and Ran (that it is as if he specified that he forbids his mouth).

Rebuttal (Lechem Mishneh): No, the Rambam explains that Rav Yehudah changes the text of the Mishnah. He is forbidden only if he indicated that he forbids his mouth.

Rambam (12): If one vowed from something intangible and forbade it, even though the vow does not take effect, we do not instruct him to consider it permitted, since he forbade it and wanted the vow to take effect. Rather, we find a different Pesach for him and permit his vow, even though he was not forbidden, so he will not be frivolous about Nedarim.

Tosfos (Kesuvos 59a DH Konam): 'Konam, I will not produce for you mouth' takes effect, just like 'Konam, I will not put straw in front of your cattle' (Nedarim 81b).

Rebuttal (Shach YD 234:86): The Gemara said that such vows take effect only if one forbids his hands from doing the actions! Even the Rosh and Ran say that it is as if he specified only if he mentioned his hands!

Poskim

Shulchan Aruch (YD 213:1): Nedarim do not take effect on something intangible. If one said 'Konam, I will not speak with you, work for you, walk for you or sleep with you', it is not a vow. The same applies if he said 'my speech, working or walking is forbidden to you', or 'sleep is forbidden to me.'

Taz (1): Regarding working, even though what he will produce is tangible, now there is nothing tangible on which the vow can take effect.

Shulchan Aruch (ibid.): However, mid'Rabanan he needs She'elah (i.e. we ask him about his vow to find another Pesach). Therefore, if one forbade himself to hear Shimon's Tefilah, mid'Rabanan he needs She'elah. However, if one said 'Konam is my mouth from speaking with you, Konam are my hands from working for you, my legs from walking for you, or my eyes to sleep', this is a full vow mid'Oraisa.

Beis Yosef (DH Kosav ha'Rashba): The Rashba says that 'I forbid my house that you may not live in it' is a tangible vow.

Shulchan Aruch (ibid.): All the more so, it is a full vow if he said 'my mouth is forbidden to you for my speech, my hands for my working, or my legs for my walking.'

Taz (2): In the previous cases, it was unclear whether he forbade his mouth or his speech; we were stringent. All the more so he is forbidden when he explicitly forbids his mouth!

Rema: Some say that 'speech of my mouth is forbidden to you' or 'taking a rock is forbidden to me' is a vow, because he mentioned his mouth or a rock.

Beis Yosef (239 DH v'Chosav Sham): Tosfos says that whenever he mentions the object he forbids, it is considered tangible.

Gra (6): This is unlike the Ran (above, for here he explicitly forbade speech).