1) THE APPLICATION OF A "MIGU"
QUESTION: The Mishnah teaches that the father of a Ketanah is believed to say that he married off his daughter and that he accepted a divorce on her behalf her (and thus she may not marry a Kohen). The Mishnah adds that he is not believed to say that his daughter was captured and that he redeemed her. The Gemara concludes that the reason the father is believed in the first case but not in the second is the verse, "Es Biti Nasati l'Ish ha'Zeh" (Devarim 22:16), which teaches that the father is believed to testify about the marriage of his daughter but not about her captivity.
Although the Torah does not teach that the girl's father is believed to testify about her captivity, the father should be believed because of the principle of "Migu." Since the father is believed to say that he married her off, he is believed to say that he married her off to a Pasul (a man whom she is prohibited to marry by a Chiyuv Misah, according to the Gemara's conclusion) and thereby disqualify her from marrying a Kohen and from eating Terumah. Accordingly, when he says that she was taken captive, he should be believed because if he wanted to disqualify her from Kehunah he could have said that he married her off to a Pasul. Why is the father not believed with a "Migu"?
ANSWER: The RAN describes certain guidelines for when the Torah accepts the testimony of a father about his daughter. When the Torah says that a father's word is believed, it clearly does not refer to a man who is a sinner. Whenever the Torah teaches a Halachah it refers to a situation in which everything was done according to the law. The Halachah that a father is believed applies only in situations where the Kidushin which the father claims to have accepted for his daughter is permissible. In a case of a forbidden marriage, the Torah does not accept the father's word.
If the father would say that he married off his daughter to a Pasul, he would not be believed because he would be testifying that he committed a prohibited act. Consequently, the foundation of the "Migu" does not exist and there is no basis to believe him when he says that his daughter was taken captive.
However, although the father is not believed to prohibit her from eating Terumah by saying that she was taken captive, he at least should be believed to prohibit her from marrying a Kohen. Although he has no "Migu" that he could have said that he married her off to a Pasul, he does have a "Migu" that he could have said that he married her off to a permitted man and that he then accepted a divorce on her behalf. (This question relies on the concept of "Palginan Ne'emanus" (see Bava Basra 36a) -- a person's testimony may be accepted for only part of its consequences even though it is not accepted for all of its consequences.) The father's testimony that she was taken captive should be accepted with regard to disqualifying his daughter from marrying a Kohen, since he has a "Migu" that he could have said that he married her off and then accepted a divorce for her.
The RAN offers two answers to this question.
1. Testimony is accepted based on a "Migu" only when the testimony will be accepted in its entirety, but not when only parts of the testimony will be accepted or when the testimony will be accepted only with regard to certain consequences (and not all consequences).
The logic of the concept "Migu" is that if the witness wanted to lie, he would have said a more believable lie. Since he did not say the "better" lie, he is assumed to be telling the truth.
If the father would be believed when he says that his daughter was taken captive, there would be two consequences: his daughter would become disqualified from marrying a Kohen, and she would become prohibited from eating Terumah. If the father would say that he married her off and he accepted her divorce, she would become disqualified only from marrying a Kohen, but she would remain permitted to eat Terumah. Hence, when he says that she was taken captive, he is not believed with a "Migu" that he could have said that he married her off and accepted her divorce, since that "Migu" would accomplish only one of the two consequences of testifying that she was taken captive. In that case, the claim of the "Migu" is not a "better" lie than his actual claim because it would not have achieved the same consequences that it would have achieved had he explicitly made that claim.
2. The Torah's law that a father is believed to testify about his daughter is a Chidush. Had the Torah not taught that the father is believed, there would have been no basis to accept his testimony. Two witnesses are required for a "Davar sheb'Ervah," a matter of marriage or Arayos. Moreover, the testimony of a relative is not valid.
Since the father's trustworthiness is a Chidush, his trustworthiness cannot be extended to cases in which there are other grounds not to believe him. Accordingly, a "Migu" does not lend support to his testimony. His trustworthiness is limited to the unique and specific cases for which the Torah establishes it.

64b----------------------------------------64b

2) THE STRENGTH OF A "MIGU" AGAINST A "CHAZAKAH"
QUESTION: The Gemara explains that Rebbi and Rebbi Nasan disagree about the power of "Mah Li l'Shaker," the principle that gives credence to a person's claim based on the logic that a person who lies will say the most effective lie. In the case of the Gemara, a man claims that he has sons (and that his wife, therefore, is exempt from Yibum). The principle of "Mah Li l'Shaker" gives his claim credibility because he did not need to lie in order to exempt his wife from Yibum; he could have merely said that he would give her a Get sometime before his death, and that would exempt her from Yibum. The fact that he did not exempt her with that statement indicates that he is telling the truth. However, in this case a Chazakah -- that he had brothers and no sons -- counters his claim. Rebbi maintains that the principle of "Mah Li l'Shaker" has the power of witnesses and, therefore, it overpowers the Chazakah. Rebbi Nasan maintains that "Mah Li l'Shaker" has the power of a Chazakah and, therefore, it cannot override the other Chazakah that says that he has no sons (and that his wife must do Yibum).
The Gemara in Bava Basra (5b) discusses which is more powerful, a "Migu" or a Chazakah. This question seems to be the subject of the dispute between Rebbi and Rebbi Nasan, as a "Migu" is essentially the same instrument of Ne'emanus as "Mah Li l'Shaker." Since Rebbi maintains that a "Migu" is stronger than a Chazakah and Rebbi Nasan maintains that it is not stronger than a "Chazakah," why does the Gemara in Bava Basra not mention their dispute?
ANSWER: The RASHBA answers by differentiating between the two types of "Migu." The Gemara here discusses the "Migu" of "b'Yado." Since it is within the man's ability to give his wife a Get and thereby free her from the obligation of Yibum, he should be believed to free her from Yibum by merely saying that he has sons or has no brothers.
The Gemara in Bava Basra discusses a different type of "Migu," a "Migu" of a claim which the person could have said. Since he could have said a different claim which would have been more advantageous to his cause but instead he said a less beneficial claim, he is assumed to be telling the truth (for otherwise he would have said the better claim). This type of "Migu" is weaker than the "Migu" of "b'Yado" because the claim of the "Migu" would not have changed anything in a practical way; it merely would have been a more acceptable claim. Accordingly, the "Migu" which is the subject of dispute between Rebbi and Rebbi Nasan is not related to the "Migu" in the question of the Gemara in Bava Basra.