Gittin, Chapter 4, Mishnah 7. This mishnah deals with cases in which a man divorces his wife, and we tell him in advance that he will not be able to take her back afterward.
"HaMotzi es ishto mishum shem ra":
The mishnah opens: "HaMotzi es ishto mishum shem ra - lo yachazir" - one who divorces his wife because of a bad name may not take her back. A man who divorces his wife because of a bad name, meaning that a rumor circulated that she had committed adultery, is not permitted to remarry her. This is not a case where it is known with certainty that she committed adultery, for then she would be forbidden to him in any event, but a case of mere rumor. As a matter of strict halachah she is permitted to marry him again, but we tell him in advance: be aware, one who divorces for this reason can no longer take her back.
The Gemara explains that the reason is mishum kilkulah - because of the damage that could result. The concern is that she may marry another man after her divorce, and in the meantime it will become clear to the first husband that the rumor was false, and he will say: "Had I known this, I would never have divorced her." Such a statement creates the appearance that the get he gave was invalid from the outset, and that her children from the second husband are mamzerim. The commentators emphasize that they are not actually mamzerim, since he has no power to nullify the get he gave; it merely looks that way to outsiders.
Divorcing because of a vow:
"Mishum neder" - he divorced her because of a vow she took, saying that he does not want a wife who makes vows. Here too "lo yachazir" - he may not take her back, and we warn him in advance that he will not be permitted to marry her again, because of that very same concern of damage: perhaps she will find grounds for releasing her vow and a sage will annul it for her, and then the husband will say, "Had I known the vow could be annulled, I would never have divorced her" - and her children from the second husband will appear to be mamzerim.
Rabbi Yehudah's view - a penalty, not a concern of damage:
Rabbi Yehudah applies a different standard regarding a vow: "Kol neder sheyad'u bo rabim - lo yachazir, veshelo yad'u bo rabim - yachazir" - any vow that many people knew about, he may not take her back; and one that many people did not know about, he may take her back. If the vow was made publicly, he cannot take her back; and if it was a private vow, he may take her back.
In his opinion, what the Sages said - both regarding a vow and regarding a bad name of adultery - is not because of the concern that the matter will turn out to have been false, or that grounds will be found to release the vow, and that he will then claim, "I would never have divorced her." That is not the reason at all; rather, it is a penalty:
So that Jewish women should not be immodest and should not have a reputation for adultery.
So that they should not make vows, which is likewise improper.
For this reason he speaks specifically of a vow made publicly: a public vow is a more severe type of vow, and generally a vow made in the presence of many people is not annulled. Under these circumstances the Sages ruled that he cannot take her back, since the vow is more severe and also involves a greater element of immodesty and lack of propriety.
Rabbi Meir's view - a vow requiring the investigation of a sage:
Rabbi Meir applies a different standard, one close to the first opinion in the mishnah: "Kol neder shetzarich chakiras chacham - lo yachazir, veshe'eino tzarich chakiras chacham - yachazir" - any vow that requires the investigation of a sage, he may not take her back; and one that does not require the investigation of a sage, he may take her back. Rabbi Meir holds like the first opinion, that the reason is because of kilkula:
A vow requiring the investigation of a sage: the husband cannot annul it himself, and it is necessary to go to a sage. Here there is a concern that he will say, "Had I known she could be released from the vow, I would never have divorced her" - and therefore he may not take her back.
A vow that does not require the investigation of a sage: a vow that the husband himself can annul. Here there is no room for the claim "had I known," since it was in his hands to know and to annul it himself, and he chose not to do so. Since there is no concern of this sort of damage, he may take her back.
Rabbi Elazar's view - "lo asru zeh ela mipnei zeh":
Rabbi Elazar disagrees with Rabbi Meir and reverses the matter. He too agrees that the reason is because of damage, but in his view the situation is exactly the opposite: with a vow that requires the investigation of a sage, a man does not want his wife to be humiliated in court, and therefore he cannot claim that had he known she could have her vow released he would not have divorced her. With a vow that he himself can annul, however, he can say, "Had I known it was in my power to annul the vow, I would not have divorced her." It emerges that the true reason for the prohibition against taking her back was stated regarding a vow that the husband can annul, and not regarding a vow that requires the investigation of a sage.
Nevertheless, the Sages forbade taking back even a woman who made a vow requiring the investigation of a sage, even though the reason does not apply to her, extending the prohibition to that case as well. This is Rabbi Elazar's intent when he says "lo asru zeh ela mipnei zeh" - they forbade this only because of that. They forbade taking back the woman who made a vow requiring the investigation of a sage because of the one who made a vow that can be annulled, where the true logic applies.
When the vow comes from the husband's side:
At this point several words are missing in the mishnah: instead of "forbidden to be taken back" the text should read "Bameh devarim amurim" - in what case was this stated? In what case was it stated that he cannot take his wife back? When she made the vow. But if he made the vow - he may take her back. That is, if he vowed to divorce her and did divorce her, he is permitted to take her back.
"Ve'amar Rabbi Yehudah: ma'aseh beTzidon be'echad she'amar le'ishto: konam im eini megarshech, vegirshah, vehitiru lo chachamim sheyachazirenah" - Rabbi Yehudah said: there was an incident in Tzidon involving a man who said to his wife, "Konam if I do not divorce you," and he divorced her, and the Sages permitted him to take her back. A man vowed that he would divorce his wife, and divorced her because of his vow; the Sages annulled his vow for him, and consequently he was permitted to take her back.
The reason is as follows: the prohibition against taking her back when the divorce was because of a vow is for the betterment of society, out of the concern of damage - that he may later claim he would never have divorced her. That claim is possible only with regard to a vow that she made, but not with regard to a vow that he himself made, and therefore he is permitted to take her back.
In summary: in this mishnah we learned that one who divorces his wife because of a bad name or because of a vow may not take her back. According to the first tanna and Rabbi Meir the reason is the concern of damage, that the husband may claim, "Had I known, I would not have divorced her," thereby casting aspersions on the get and on her children from the second husband. According to Rabbi Yehudah it is a penalty, so that Jewish women should not be immodest and should not make vows, and therefore the distinction is between a vow that many people knew about and one that is not known. Rabbi Elazar reverses the matter and rules that the reason applies specifically to a vow that can be annulled, and because of it they forbade even the vow requiring the investigation of a sage. And finally, all of this applies when she made the vow, but when he made the vow he is permitted to take her back, as in the incident that occurred in Tzidon.