Gemara

86b (Mishnah): If Levi's wife vowed, and he thought that his daughter vowed, or vice-versa, he can annul again after he learns of his mistake. (His initial Hafarah or Kiyum was invalid.)

Gemara: We must say that "he will annul her" requires that he know whose vow he annuls.

Question: If so, we should similarly learn from "(David tore his clothing) for Sha'ul and for Yonason" that one must know for whom he tears. This is not true!

(Beraisa #1): If they told a man that his father died, and he tore his clothing, and later he learned that really, it was his son who died, he was Yotzei (he fulfilled the Mitzvah to tear).

Answer: In the Beraisa, the man was told only that a relative died. He thought that it was his father, but he did not say that he tears for his father;

Hafarah is invalid when he specified (that he annuls his wife's vow, and really, his daughter vowed, or vice-versa).

Support (Beraisa #2): If they told a man that his father died, and he tore his clothing, and later he learned that it was his son who died, he was not Yotzei;

If they told him that a relative died, and he thought that it was his father, and he tore, and later he learned that it was his son who died, he was Yotzei.

(The Reisha contradicts Beraisa #1. We must answer like above (4), that Beraisa #1 is imprecise. Really, the case is like the Seifa of Beraisa #2.)

Rejection (Rav Ashi): If he learned of his mistake Toch Kedei Dibur (within the time needed to say three or four words), he was Yotzei. If he learned after this, he was not Yotzei.

In Beraisa #2, he found out after Toch Kedei Dibur. In Beraisa #1, he found out Toch Kedei Dibur.

(Beraisa #1): If they told a man that his father died, and he tore his clothing, and later he learned that really, it was his son who died, he was Yotzei (he fulfilled the Mitzvah to tear).

Contradiction (Beraisa #2): If they told a man that his father died, and he tore his clothing, and later he learned that it was his son who died, he was not Yotzei;

If they told him that a relative died, and he thought that it was his father, and he tore, and later he learned that it was his son who died, he was Yotzei.

Resolution #1: Beraisa #1 is imprecise. Really, he heard that a relative died and thought that it was his father (like the Seifa of Beraisa #2).

Resolution #2 (Rav Ashi): If he learned of his mistake Toch Kedei Dibur (within the time needed to say three or four words), he was Yotzei. If he learned after this, he was not Yotzei.

In Beraisa #2, he found out after Toch Kedei Dibur. In Beraisa #1, he found out within Toch Kedei Dibur.

Support (Beraisa #3): If a sick person (Levi) fainted and it appeared as though he died, and Yakov (his relative) tore, and afterwards Levi really died, Yakov was not Yotzei.

(R. Shimon ben Pazi): Yakov was Yotzei only if Levi died Toch Kedei Dibur of Kri'ah (tearing).

Rishonim

The Rif brings the Gemara verbatim.

Rif and Rosh (Mo'ed Katan 16a and 3:69): The Halachah follows R. Shimon ben Pazi.

Nimukei Yosef (DH Garsinan): Just like one can retract testimony Toch Kedei Dibur, he can say 'I want that my Kri'ah was not for Ploni, rather, for Almoni.' Therefore, he was Yotzei. If he tore without knowing which relative died, and he found out later (even after Kedei Dibur), he was Yotzei, because Yesh Breirah.

Rambam (Hilchos Evel 8:8): If a sick person (Levi) fainted and Yakov thought that he died, and he tore, and afterwards Levi really died, Yakov must tear again only if Levi died after Kedei Dibur of the Kri'ah. Similarly, if they told a man that his father died, and he tore his clothing, and later he learned that it was his son who died, or if they told him that a relative died, and he thought that it was his father, and he tore, and later he learned that it was his son who died, he was Yotzei only if he found out Toch Kedei Dibur.

Rambam (Hilchos Nedarim 12:21): If Levi's wife vowed, and he thought that his daughter vowed, and he annulled with this intent, he must annul again after he learns of his mistake. "He did not annul her" requires intent for the Noderes.

Question: Why does the Rambam hold that regarding Nedarim, it does not help to find out Toch Kedei Dibur?

Answer #1 (Beis Yosef YD 234 DH u'Mihu): The Rambam did not discuss when he learned Toch Kedei Dibur, or when he annulled Stam for whoever vowed. He holds that Rav Ashi argues with the first answer. Since this is mid'Oraisa, he does not rely on either opinion, and he is stringent. However, he should rule like Rav Ashi, who is Basra! Perhaps since the Stam Gemara gave the other answer, we do not hold like Rav Ashi against it.

Rejection (Lechem Mishneh): The Rambam should have said that it is a Safek whether or not the Hafarah worked! Regarding Kri'ah, the Rambam rules like Rav Ashi! We cannot say that this is because we always follow the lenient opinion in Aveilus. This rule does not apply to Kri'ah (Mo'ed Katan 26b)! Also, if so, the Rambam should have ruled like the first opinion, which is more lenient. (It holds that Stam, one is always Yotzei!)

Answer #2 (Lechem Mishneh Hilchos Evel 8:8): Since Kri'ah is mid'Rabanan, the Rambam rules like the latter opinion. Vows are mid'Oraisa, so he is stringent. This is difficult.

Answer #3 (Lechem Mishneh Hilchos Nedarim 12:21): The Rambam rules like Rav Ashi also regarding Nedarim. He did not need to say that it helps if he found out Toch Kedei Dibur, for Toch Kedei Dibur always helps.

Poskim

Shulchan Aruch (YD 340:24): If they told a man that his father died, and he tore, and later he learned that it was his son who died, he was Yotzei only if he found out Toch Kedei Dibur. If they told him that a relative died, and he thought that it was his father, and he tore, and later he learned that it was his son who died, he was Yotzei even if he found out after Kedei Dibur.

Ran (87a DH Rav): Rav Ashi agrees that one was Yotzei if he intended for the wrong Mes, but did not specify. He merely gives a better resolution of the Beraisos.

Beis Yosef (DH v'Chen) and Kesef Mishneh: It seems that the Rif and Rosh agree. Since Rav Ashi explained that in the Reisha of Beraisa #2 he was not Yotzei after Kedei Dibur, also the Seifa discusses after Kedei Dibur, and it says that he was Yotzei if he did not specify. However, the Rambam, Ramban and Tur hold that Rav Ashi does not distinguish between specifying and Stam. In either case he was Yotzei only if he found out Toch Kedei Dibur. Even though the Reisha of Beraisa #2 discusses after Kedei Dibur, the Seifa discusses Toch Kedei Dibur. Alternatively, Rav Ashi's text of the Seifa said 'he was not Yotzei'. We follow the Rif, Rosh and Ran.

Rebuttal #1 (Radvaz): We should not abandon the Rambam just because it seems that the Rif disagrees.

Rebuttal #2 (Bach DH Omru): The Tur would not rule unlike the Rosh without mentioning this! Also, regarding vows the Tur is lenient in both cases! Rather, both regarding vows and Kri'ah, if he specified, i.e. intended for one person, he was not Yotzei if he realized his mistake after Kedei Dibur. Stam (he intended for whoever vowed or died), he was Yotzei.

Shulchan Aruch (25): If a sick person (Levi) fainted and Yakov thought that he died, and he tore, and afterwards Levi really died, Yakov need not tear again only if Levi died Toch Kedei Dibur of the Kri'ah.