Gemara

(Shmuel): It does not suffice to think the oath. He must say it - "Levatei bi'Sfasayim."

Question (Beraisa): "Bi'Sfasayim" - not in the heart. "L'Chol Asher Yevatei" teaches (that it is an oath) even if he resolved in his heart

Objection: The Seifa contradicts the Reisha!

Answer #1 (Rav Sheshes): "Bi'Sfasayim" excludes one who resolved to say an oath, and never uttered it. If he resolved to accept an oath in his heart, this is binding.

Answer (and Answer #2 - Rav Sheshes): "Bi'Sfasayim" excludes one who wanted to forbid wheat bread, and mistakenly said 'barley bread';

Question: If he wanted to swear 'I will not eat wheat bread', and he mistakenly swore 'I will not eat bread', what is the source that this is an oath?

Answer: We learn from "l'Chol Asher Yevatei."

Question (Beraisa): "Motzei Sefasecha Tishmor" refers to what he uttered (vows to bring Korbanos). "Kol Nediv Lev" (donated towards the Mishkan) teaches (that it is a vow) even if he decided in his heart.

Answers: We learn from "Kol Nediv Lev" that intent suffices for Hekdesh. It is not enough for an oath. We do not oaths from Hekdesh, because Terumah and Kodshim are Shnei Kesuvim ha'Ba'in k'Echad (both of them teach that deciding in the heart is enough). They do not teach about other laws. Alternatively, we do not learn laws of Chulin (oaths) from Kodshim.

Nedarim 20a Mishnah - R. Meir): If one said '(this is like) Cherem' and said later that he meant a fishing net (it is also called Cherem), he need not ask a Chacham to permit it. If he asks, we punish him and are stringent on him:

(Rav Yehudah): A Chacham need not ask to permit his vow. If an Am ha'Aretz vowed and asks to permit it, we punish him and are stringent on him.

27b (Mishnah): One may vow falsely to extortionists.

28a - Question: If he says '(all) Peros are forbidden to me if this is not the king's', they indeed become forbidden to him!

Answer: He says, '(all) Peros are forbidden to me today if this is not the king's'. He says 'today' only in his heart, but not with his lips. Even though unspoken conditions are ignored, in the case of Ones they are valid.

Pesachim 62b (Beraisa - Others): (If one slaughtered Korban Pesach with intent that Mulim and Arelim (circumcized and uncircumcized men) eat from it,) if intent for Mulim was first, it is Kosher. If intent for Arelim was first, it is Pasul.

(Rabah): He intended for both of them, but did not finish saying the second intent until after slaughter. R. Meir (Others) does not require equality of mouth and heart, so only the first intent takes effect, unlike his desire.

Objection (Mishnah): If one intended (to vow or swear) 'I will not enter this house', and he mistakenly said another house, his words do not take effect, unless there is equality of mouth and heart. (A Stam Mishnah is R. Meir.)

Rishonim

Rif and Rosh (3:14): If one intended to vow from wheat bread, and he said 'barley bread', wheat bread is permitted, for he did not say it. Barley bread is permitted, for he did not intend to say it. His mouth and heart must be the same. However, if he intended to vow from wheat bread, and he said only 'bread', he is forbidden wheat bread, for it is called bread, and his mouth and heart were the same. Also, a Mishnah teaches that if one intended to say 'Olah' and said 'Shelamim', or vice-versa, or he intended to say 'I will not enter this house' or 'benefit from Ploni', and he said 'I will not enter that house' or 'benefit from Almoni', his words have no effect, for his mouth and heart were not the same.

Rosh: Shmuel taught about Shevuos, and the same applies to Nedarim. In Nedarim, we say that Devarim sheb'Lev are valid only in a case of Ones. If so, when he meant to say 'wheat bread', and he said only 'bread', he should be forbidden all bread! The Ramban answered that there is different, for he did not err. He intends to say forever (Piplulei Charifta (1) - i.e. to say Stam, which forbids forever), but he intends in his heart 'today', therefore, his mouth overrides, for Devarim sheb'Lev Einam Devarim. Here, what he said was a mistake, therefore, we ignore what he said. Letter of the law, also his intent should be Batel, for his lips did not say his intent. A verse teaches that we follow his intent, for his mouth did not contradict it, for wheat bread is called bread.

Rambam (Hilchos Shevuos 2:10): If one intended in his heart not to eat today, and it should be forbidden through a Shevu'ah, but he did not say it with his lips, he is permitted.

Rambam (12): If one swore 'I will not eat today', and he ate, and they wanred him, and he said 'I meant to forbid leaving. My tongue slipped, and I said 'eat' by mistake, he is not lashed.

Kesef Mishneh: This is like a Tosefta (Taharos 6:9) and Toras Kohanim. However, the Ra'avad in Toras Kohanim explains that he is believed to say 'I had a Tanai (condition) in my heart, and based on it, a Chacham permitted my vow.' Had he not asked a Chacham, Devarim sheb'Lev Einam Devarim. We need not say so. We can say that he said his Tanai quietly with his lips.

Rambam (14): If he resolved in his heart not to eat wheat bread, and he swore about bread Stam, he is forbidden wheat bread, for it is called bread.

Rambam (Hilchos Nedarim 2:2): One who vows is forbidden only if he said it with his lips and his mouth and heart were the same, like we explained in Shevuos.

Mordechai (Shevuos 755): Avi ha'Ezri explains that the case when he resolved in his heart to say wheat bread, and he said bread Stam, is when he thinks that he said wheat bread. Do not say that he knows that he said bread Stam, and intended to merely think 'I intend only for wheat bread.' If so, he would be forbidden Stam bread, for Devarim sheb'Lev Einam Devarim.

Beis Yosef (YD 210 DH Kosav ha'Mordechai): The Sugya seems unlike this.

Mordechai (ibid.): Some err and transgress Shevuos, for they rely on what it says in Nedarim (that one may limit an oath based on intent in his heart). There is different, for it is Ones. Maseches Kalah brings a case in which R. Akiva swore (to bring a woman to the world to come if she will reveal the lineage of her brazen son), and he annulled his oath (while saying it) in his heart. That was the ultimate Ones, for he needed to clarify a Halachah (if the impudence was due to being a Mamzer or a Ben Nidah or both). Some say that he quietly said words to invalidate his oath, and she did not hear him; he swore based on his own intent, and not on hers.

Tosfos (26b DH Gamar): One may vow to extortionists Stam, and intend in his heart that it is only for one day, but only due to Ones. Here, without Ones his intent affects the vow! There we discuss an Am ha'Aretz (ignoramus). He is permitted only due to Ones, lest he take Nedarim lightly. Here we discuss a Chacham. In Nedarim (20a) we are more lenient about Chachamim. Alternatively, perhaps regarding Ones we allow even when vowing Al Da'as (based on the understanding of) the extortionist. This is permitted only regarding Ones. Alternatively, here we follow his heart because Stam bread is of wheat.

Poskim

Shulchan Aruch (YD 210:1): A Neder does not take effect until he says it with his lips, and his mouth and heart are the same. Therefore, if he intended to vow from wheat bread, and he said 'barley bread', both are permitted. However, if he intended to vow from wheat bread (Rema - or barley bread), and he said only 'bread', he is forbidden wheat (Rema -or barley) bread.

Shach (2): Also barley bread is included in Stam bread. The Bach says that if he intentionally said bread Stam, with intent only for wheat bread, all the Poskim forbid all bread, for Devarim sheb'Lev Einam Devarim. This is unlike the Beis Yosef.

Gra (3): If one vowed on his own Da'as, he is believed to say that he had a Tanai in mind (Tosefta Taharos 6:9).

Maharik (112, brought in Beis Yosef DH v'Chosav Mahari): If Reuven swore to pay Shimon on a certain day in Ploni (Shimon's city), and due to Ones Shimon needed to leave the city that day, if Shimon is now further from Reuven than Ploni is, surely Reuven need not take the money to him. If it is the same distance, Reuven is obligated, even though his oath mentioned only Ploni. How can the oath take effect on what he did not say? We require "Levatei bi'Sfasayim" (to say it)! This refers to oaths and vows of Isur. When one swears to another to fulfill a stipulation, it depends on the stipulation. Whatever the stipulation takes effect on, the oath takes effect on.

Shulchan Aruch (239:1): Shevuos are like Nedarim in every way, i.e. one must say it with his lips.