Yevamos Chapter 15, Mishnah 4. In the previous Mishnah we learned that the woman herself is believed when she says that her husband died. Our Mishnah comes to discuss the idea that there are certain other people who are not believed to testify about this.
The Mishnah opens by establishing: "Hakol ne'emanim leha'idah" - not only the woman herself, but any single witness may testify to the fact that her husband died, and his testimony is believed. The Mishnah immediately lists the exceptions: "chutz mechamosah, u'vas chamosah, v'tzarasah, vi'vimtah, u'vas ba'alah" - except for her mother-in-law, her mother-in-law's daughter, her rival wife, her sister-in-law, and her husband's daughter.
These five women are not believed, because they have a motive and a reason to want to place this woman in a terrible situation - where her husband returns after she has already remarried, and she becomes liable for all of those severe penalties. Here they are, along with the motive of each one:
Her mother-in-law - the husband's mother, who is liable to say: this woman is going to consume all my pain and all my toil by inheriting my son.
Her mother-in-law's daughter - the daughter of the husband's mother, who says: you are going to consume all my parents' hard labor through this woman married to my brother.
Her rival wife - another woman married to the same husband; like any rival, at times she does not think highly of her counterpart.
Her sister-in-law - a woman married to her husband's brother, who is concerned that she may become her rival wife should a situation of yibum arise.
Her husband's daughter - the husband's daughter who is not her own daughter, who says: this woman who came in to take my mother's place is going to consume everything, all of my mother's hard labor.
"Mah bein get l'misah?":
The Mishnah raises a difficulty on itself from the Mishnah in the second chapter of Maseches Gittin: what is the difference between our case, where these women are not believed, and the case of a get, where they are believed? For we learned there that although they are not believed to say that the husband died, they are believed to bring the get even from overseas, where they must testify "b'fanai nechtam, b'fanai nechtam" - it was signed in my presence, it was signed in my presence - that is, to testify to the fact that the get was written and signed in their presence.
The Mishnah answers that the difference is "shehu shtar sheb'yadam" - that they have a document in their hand: with a get they bring along a document, and the document itself testifies to the truth. Therefore we are not relying on their testimony alone that the document was written and signed in their presence, but we also have in hand a document that proves it - unlike the statement that the husband died, which rests on their testimony alone.
Testimony against testimony:
From here the Mishnah moves to an entirely different area within the same subject: "echad omer mes v'nisses, v'acher omer lo mes - harei zu lo teitzei" - one says he died and she married, and another says he did not die, she does not have to leave. One witness testified that the husband died and she married, and then another witness came and said the opposite, that he did not die, she does not leave her husband.
The Gemara explains that although it appears from the wording of the Mishnah that this applies specifically after she married, that is not the case: even if we merely permitted her to marry and she has not yet married, she does not lose her permission to marry another man. The reason is that the moment the first witness testified about the husband's death, the Sages granted that single witness the power of two witnesses, and we view his testimony as the testimony of two. Therefore the witness who comes afterward is not believed, since his status is that of one against two - and once she was permitted, she remains permitted.
The Mishnah continues: "echad omer mes u'shnayim omrim lo mes - af al pi shenisses, teitzei" - one says he died and two say he did not die, even though she married, she must leave. Even though she already married, she must leave that marriage. Here too the Gemara qualifies and says that the Mishnah is not dealing with ordinary valid witnesses, but with those who are disqualified from testifying - women, slaves, and people who are generally not fit to testify, but who were made fit regarding testimony that the husband died.
And this is the novelty of the Mishnah: even in a case of two against one among those disqualified from testifying, we follow the majority. That is, if one woman testifies that he died and two women testify that he did not die, we follow the two and say that she must leave.
The Gemara adds, however, that if the first witness was a valid witness and the two witnesses who came after him were disqualified witnesses, she remains in her marriage and does not even lose her permission to marry, because that first witness is a fully valid witness, and his power is stronger even than the two witnesses who come after him.
And finally: "shnayim omrim mes v'echad omer lo mes - af al pi shelo nisses, tinasei" - two say he died and one says he did not die, even though she has not yet married, she may marry. Two witnesses testify that he died and one testifies that he did not die, and therefore she may marry. Here too, says the Gemara, we are dealing with those disqualified from testifying who are generally not fit, and nevertheless we follow the majority of the witnesses and permit her to marry on the strength of the two who testified that he died.
In summary: in this Mishnah we learned that everyone is believed to testify that the husband died, except for five women who have a motive to harm her - her mother-in-law, her mother-in-law's daughter, her rival wife, her sister-in-law and her husband's daughter; that regarding a get they are believed, because they hold a document in hand and the writing supports their testimony; and that in a clash between testimonies, a single witness who testified about the death has the power of two, while among those disqualified from testifying we follow the majority of those who testify.