Gemara

Rav's wife used to pain him. If he would ask her to make lentils, she would make legumes, and vice-versa. When Rav's son Chiya grew up, he told his mother the opposite of what Rav requested.

Rav: Your mother has improved (she fulfills my request)!

Chiya: I switched your request.

Rav: This is as people say, you will learn from your children! However, you should not do so - "They trained their tongues to speak falsely..."

65b (R. Ila'a): It is permitted to deviate (from truth) for the sake of Shalom. Yosef's brothers told him "Your father commanded ... tell Yosef to bear the sin (of his brothers)".

(R. Noson): It is a Mitzvah! "And Shmuel said ... Sha'ul will hear (that I am going to anoint David) and he will kill me." (Hash-m told him to say that he is going to offer Korbanos.)

(Tana d'Vei R. Yishmael - Beraisa): Shalom is so great that even Hash-m deviated (for its sake). Sarah said "And my husband is old". Hash-m told Avraham only that she said "And I am old."

Bava Metzi'a 23b (Rav Yehudah): Chachamim often lie to cover up three things: (knowing) a tractate, a bed, and hospitality.

Question: What is the significance of this teaching?

Answer (Mar Zutra): One who lies only about these three things is considered a Chacham to whom we return an Aveidah if he recognizes it.

Shabbos 11a: R. Yehoshua brei d'Rav Idi came to Rav Ashi's house, they prepared for him a choice calf.

R. Yehoshua: I am fasting today.

Rav Ashi's household: Rav Yehudah taught that one may borrow (eat on a day he intended to fast) and repay later!

R. Yehoshua: I am fasting due to an ominous dream (I must fast today to nullify the decree).

Ta'anis 12a: R. Yochanan said 'I am fasting until I get home' (this shows that one may fast for part of the day)!

Rejection: He merely sought to avoid eating at the Nasi's house (he told them 'I am fasting.')

Kesuvos 77b: Eliyahu announced in Gan Eden that they should make room for R. Yehoshua ben Levi.

R. Shimon (to R. Yehoshua ben Levi): Was a rainbow seen in your day?

R. Yehoshua ben Levi: Yes.

R. Shimon bar Yochai: If so, you are not worthy of this proclamation. (The rainbow is Hash-m's sign not to destroy the world. Your merit did not suffice to protect the world!)

Really, the rainbow what not seen in his day. R. Yehoshua ben Levi did not want to take credit for this.

Makos 14b (Rabah bar bar Chanah citing R. Yochanan): If an Aseh precedes a Lav, this is not considered a Lav she'Nitak l'Aseh. One is lashed for the Lav.

Rabanan asked him if he really said this. He (falsely) denied it (because a Beraisa refutes it).

Rishonim

The Rif and Rosh (21a and 6:21) bring the teachings of R. Ila'a and R. Noson.

Rif (Bava Metzi'a 13a): Chachamim may lie about a tractate, a bed, and hospitality. In Yevamos R. Ila'a and R. Noson taught that it is permitted or a Mitzvah to deviate for the sake of Shalom. Presumably, here we list only optional lies. We did not need to mention when it is a Mitzvah to lie.

Rambam (Hilchos De'os 5:7): A Chacham does not deviate (from the truth), add or detract, except for Divrei Shalom and similar matters.

Rambam (Hilchos Gezeilah 14:13): We return an Aveidah to a Chacham who recognizes it only if the Chacham never lies except for Divrei Shalom, a tractate, a bed or lodging. If he is learning Maseches Nidah he may say that he is learning Mikva'os, in order that people will not ask him about Nidah.

Be'er ha'Golah (9): Tosfos (23b DH Masechta) says that if David wants to know whether or not Levi knows a Masechta, Levi may deny it. If David wants to know the Halachah, Levi should tell him immediately. It seems that the Rambam discusses a question of Hora'ah, and there is someone greater than Levi, so Levi avoids answering.

Rambam (ibid.): He may lie about which bed he slept on, in case semen will be found on it. If he is staying with Shimon he may say that Reuven hosts him, lest others impose on Shimon. Or he makes Shalom among people, and adds or detracts to endear them to each other. This is permitted.

Drishah (CM 262:21). The Rambam says 'v'Omer' (one may say). He holds that one is permitted to deviate. Rashi says that one who is asked denies knowing the Masechta, denies that he had Bi'ah, and says that he did not receive nice hospitality. Rashi says 'v'Yomar' (he says); it is a Mitzvah to be humble and modest about these matters. Tosfos (23b DH b'Ushpiza) says that Rav Yehudah did not list Darchei Shalom because the three things listed are Darchei Shalom. The most common cases were listed. The Rif holds like the Rambam, and answered that we need list only Reshus, not Mitzvos. The Rambam says that one says that he is staying by someone else because it is difficult to host more than one person at a time. However, if one is asked after he left he answers truthfully.

Lechem Mishneh: One may lie about the Maseches to spare himself shame. Perhaps he would be unable to answer the question.

Poskim

Shulchan Aruch (CM 262:21): We return an Aveidah to a Chacham who recognizes it only if the Chacham never lies except for Divrei Shalom, a tractate (when asked if he knows it fluently, he says 'no' to be modest) a bed (he denies sleeping on it, in case semen will be found on it) or lodging (he does not praise his host, lest unfitting people flock to the host).

Be'er ha'Golah (9): Tosfos (23b DH Masechta) says that if David wants to know whether or not Levi knows a Masechta, Levi may deny it. If David wants to know the Halachah, Levi should tell him immediately. It seems that the Rambam discusses a question of Hora'ah, and someone greater than Levi is around, so Levi avoids answering.

Yam Shel Shlomo (Yevamos 6:46): It is permitted and a Mitzvah to deviate for the sake of Shalom, but not on a regular basis, and not what is said between a man and his wife. Rav did not allow his son to do so.

Aruch l'Ner (Makos 15a DH Omru): The Ritva explains that Rabanan asked Rabah bar bar Chanah whether he really said it. He denied it, to spare his Rebbi shame (he realized that it is wrong). This is Darchei Shalom. However, Rashi says that they asked R. Yochanan. It is not clear why he denied it.

Shulchan Aruch (OC 565:6): If one fasts and publicizes this, he is punished.

Magen Avraham (6): It seems that if one is asked, he should not lie. R. Yehoshua said that he is fasting (Shabbos 11a). However, R. Yehoshua ben Levi lied about the rainbow to avoid haughtiness. Likewise, one can deny fasting! If people insist that one eat, he may say that he is fasting if he has no alternative, like R. Yochanan (Ta'anis 12a). If this is not the case, he may deny fasting to avoid praising himself. This is Darchei Shalom, since he intends for a Mitzvah.

Kaf ha'Chayim (33,36): If he can say that he has no appetite or that the food harms him, he should not say that he is fasting. If he is concerned for an Isur, e.g. Bishul Akum or wine of Nochrim, it is praiseworthy to lie and say that he is fasting.

Taz (6): It is forbidden only if he seeks to aggrandize himself. It is Midas Chasidus to deny that he is fasting, like denying knowing a Masechta and the case of R. Yehoshua ben Levi.

Sefer Chasidim (426, cited in Magen Avraham 156:2): The Heter to deviate for Shalom refers only to things of the past. If Levi does not want to lend to Reuven lest he will not pay, Levi may not say 'I have no money.'

Eshel Avraham: Shmuel actually did offer Korbanos, just this was not the reason he went, therefore it is like lying about the past.

Mishnah Berurah (4): One should distance himself from falsity extremely, except for Darchei Shalom. What Sefer Chasidim says requires investigation.

Nesivos ha'Mishpat (12:2): If a judge sees that the other two judges will rule incorrectly, he may say that he is undecided to cause that they will add more judges. This is Darchei Shalom.