Gemara

Question: Rabah says that people in Chutz la'Aretz are ignorant about Lishmah. Why is a Shali'ach believed to say that he saw the Get written? We should require two witnesses, like all testimony!

Answer: (Only monetary cases require two witnesses.) One witness is believed about Isurim (what is forbidden).

Objection: We say so when no Isur was Muchzak (established), e.g. a piece of meat that is Safek Chelev (forbidden lard), Safek Shuman (permitted lard). One witness cannot permit a woman who was Vadai married (and forbidden to all other men)! Also, two witnesses are needed for Devar sheb'Ervah (Isurei Bi'ah)!

Answer: (Even in Chutz la'Aretz,) most people know about Lishmah, especially the scribes, who write (almost all) Gitin. (Mid'Oraisa, no testimony is needed.) It is a mere stringency mid'Rabanan that the Shali'ach must testify about it.

Yevamos 87b (Mishnah): It was established to permit a woman to remarry if we heard that her husband died through a witness who heard from a witness, or a woman who heard from a woman or slave.

Question: What is the source that one witness is believed?

88a - Answer #1: Reasoning teaches that one witness is believed, e.g. if a piece of meat is Safek Chelev, Safek Shumen, he is believed to permit it.

Objection: There, the meat was never Muchzak to be forbidden. Here, she was married, and two witnesses are needed for Devar sheb'Ervah!

Answer #2: One witness is believed (to permit an established Isur) like regarding Tevel, Hekdesh, and Konamos (vows to forbid objects).

Objection: We cannot learn from these cases!

If it is b'Yado (the witness could permit the Tevel, Hekdesh or Konam by tithing, redeeming it or annulling his vow), we cannot learn to here! (If her husband is alive, the witness cannot permit her.)

If it is not b'Yado, also here we do not know a source to believe one witness!

Kesuvos 72a: If a man does not know that his wife is Nidah, he may believe her that she is Tehorah.

(Rav Chinena bar Kahana): "V'Sofrah Lah" teaches that a woman counts for herself (seven clean days that enable her to immerse, and she is believed).

Rishonim

Rif (Kesuvos 32b): "V'Sofrah Lah" teaches that a woman is believed to say that she is Tehorah.

Rambam (Hilchos Edus 11:7): One witness is believed about Isurim even though he is not believed for other testimony. We find that a Rasha is believed to say that he slaughtered properly. However, someone suspected about a matter is not believed about his own, but he is believed about others'.

Rambam (8): Therefore, one who is suspected about something can judge cases about it and testify for others. There is a Chazakah that one does not sin (solely) for the benefit of others. An Am ha'Aretz or one suspected to sell Bechor is believed to say that Ploni's produce is tithed and his meat is Chulin. The same applies to other Isurim. This is because Resha'im fear Isurim, but not money.

Rambam (Hilchos Shechitah 10:14): Any butcher who knows what makes animals Tereifah and is Muchzak to be proper may slaughter and check by himself and sell without concern. One witness is blessed about Isurim, whether or not he benefits from his testimony.

Rosh (Gitin 5:8:3,4): If there was a Chazakah that something is Asur, one witness is believed to permit it only if it was b'Yado, e.g. Tevel was fixed. Everyone is believed about his own things, for it is b'Yado to fix them, e.g. Tevel or Hekdesh.

Rosh (Mo'ed Katan 3:32): One witness is believed in Isurim to permit, but not to forbid. We learn from "v'Sofrah Lah."

Nimukei Yosef (27b DH mid'Oraisa): Rashi explains that reasoning teaches that one is believed about Shumen unless we have reason to suspect him. If not, one could not eat by his friend or rely on his household.

(Nimukei Yosef, ibid): We did not prove that one witness is believed when the piece itself was Muchzak to be forbidden. If we are concerned whenever an Isur is Muchzak in the area, then when it is known that there is a Tereifah in the market, one could not buy without witnesses.

Question: Why don't we learn from Nidah that one witness is believed even when the Isur was Muchzak?

Answer (Ri, brought in Nimukei Yosef, ibid.): There is no alternative (we cannot have witnesses). Also, it is normal for the blood to stop. After it stops, it is b'Yadah to immerse, and one is believed about something b'Yado. One is believed about Nikur (removing Chelev and Gid ha'Nasheh from beef) because it is b'Yado.

Nimukei Yosef (28a DH d'b'Yado): We say that it is b'Yado to annul one's Hekdesh. Normally, we say that it is not so easy to annul vows, for he must get a Chacham to agree. It is easy to annul Hekdesh, because it suffices to get three commoners who know about permitting vows.

Poskim

Shulchan Aruch (YD 127:3): One witness is believed to permit Isurim, but not to be stringent.

Gra (21): This is difficult. If there is no Chazakah, he is believed in either case. If there is Chezkas Isur or Heter, he is not believed!

Rema: Whenever something was Muchzak to be forbidden, e.g. meat requiring Nikur, or Tevel, a witness cannot permit it unless it was b'Yado.

Gra (25): Tosfos (Gitin 2b DH Ed) says that he is believed if it was b'Yado, even if it is no longer b'Yado. The Re'em disagrees.

Rema: If there was one piece of Heter and one of Isur, a witness is believed to say which is which. One is believed about his own property even if it was Muchzak to be Asur. A woman is believed to say that she fixed something forbidden. This is only if there is surely Isur here, e.g. meat from which Chelev or the Gid ha'Nasheh must be removed.

Shach (29): This is only if it is b'Yadah to fix it. She is not believed more than one witness, who is believed against Chezkas Isur only if it is b'Yado!

Rema: If it is doubtful whether or not there is an Isur here, e.g. removing Tamei fish among Tahor fish, or if there are reasons to be lenient, a woman is not believed. Her mind is easily swayed.

Shach (30): Similarly, she is not believed about something that entails great exertion, because women are lazy.

Gra (28): Even in such cases she is believed about an Isur mid'Rabanan, e.g. Bedikas Chametz. The Rosh (Pesachim 1:3) says that one opinion in the Yerushalmi says that she is not believed even for Bedikas Chametz. The Mordechai says that if Bedikas Chametz were mid'Oraisa she would not be believed it is a Safek (and she will assume that there is no Chametz).

Rema: A minor is not a witness to be believed for Isurim.