And the halakha is that she is permitted to both of them.

MISHNA: Beit Shammai say: A man may not divorce his wife unless he finds out about her having engaged in a matter of forbidden sexual intercourse [devar erva], i.e., she committed adultery or is suspected of doing so, as it is stated: “Because he has found some unseemly matter [ervat davar] in her, and he writes her a scroll of severance” (Deuteronomy 24:1).

And Beit Hillel say: He may divorce her even due to a minor issue, e.g., because she burned or over-salted his dish, as it is stated: “Because he has found some unseemly matter in her,” meaning that he found any type of shortcoming in her.

Rabbi Akiva says: He may divorce her even if he found another woman who is better looking than her and wishes to marry her, as it is stated in that verse: “And it comes to pass, if she finds no favor in his eyes” (Deuteronomy 24:1).

GEMARA: It is taught in a baraita that Beit Hillel said to Beit Shammai: But isn’t the word “matter” already stated in the verse, indicating that any disadvantageous matter is a legitimate reason for divorce? Beit Shammai said to them: But isn’t the word “unseemly [ervat]” already stated?

Beit Hillel said to them: If the word “unseemly” had been stated and the word “matter” had not been stated, I would have said that a wife should leave her husband due to forbidden sexual intercourse, but she should not have to leave him due to any other matter. Therefore, the word “matter” is stated. And if the word “matter” had been stated and the word “unseemly” had not been stated, I would have said that if he divorced her merely due to a disadvantageous matter she may marry another man, as the Torah continues: “And she departs out of his house, and goes and becomes another man’s wife” (Deuteronomy 24:2). But if she was divorced due to her engaging in forbidden sexual intercourse, she may not marry another man, as she is prohibited from remarrying. Therefore, the word “unseemly” is stated, indicating that even a wife who is divorced due to adultery is permitted to remarry.

The Gemara asks: And what do Beit Shammai do with this word “matter”? How do they interpret it? It seems superfluous, as in their opinion the verse refers specifically to a wife who engaged in forbidden sexual intercourse. The Gemara answers: The word “matter” is stated here, with regard to divorce, and the word “matter” is stated there, with regard to testimony: “At the mouth of two witnesses, or at the mouth of three witnesses, a matter shall be established” (Deuteronomy 19:15). Just as there, it is stated that a matter is established only through two witnesses, so too here, a matter of forbidden sexual intercourse justifies divorce only if it is established through two witnesses.

And Beit Hillel would respond to this analogy in the following manner: Is it written: Because he has found something unseemly in a matter [erva bedavar], indicating that it was established through the testimony of two witnesses that she engaged in adultery? And Beit Shammai would respond to Beit Hillel’s interpretation as follows: Is it written: Because he has found either something unseemly or another matter [o erva o davar], in accordance with Beit Hillel’s understanding?

And Beit Hillel would respond that for this reason the expression “some unseemly matter [ervat davar]” is written, as it indicates that interpretation, i.e., that a husband is not obligated to divorce his wife unless there are two witnesses to her having engaged in forbidden sexual intercourse, and it also indicates this interpretation, i.e., that he may divorce her due to any deficiency, be it adultery or any other shortcoming.

§ It is stated in the mishna that Rabbi Akiva says: He may divorce her even if he found another woman who is better looking than her. With regard to what do they disagree? They disagree with regard to the application of Reish Lakish’s statement, as Reish Lakish said that the term ki actually has at least four distinct meanings: If, perhaps, rather, and because.

Beit Shammai hold that the verse “And it comes to pass, if she finds no favor in his eyes, because [ki] he has found some unseemly matter in her” means that she did not find favor in his eyes due to the fact that he has found some unseemly matter in her. And Rabbi Akiva holds that the phrase “because [ki] he has found some unseemly matter in her” means: Or if he has found some unseemly matter in her.

§ Rav Pappa said to Rava: According to Beit Hillel, if the husband found about her neither forbidden sexual intercourse nor any other matter, but divorced her anyway, what is the halakha? Is the divorce valid?

Rava said to him that the answer can be derived from what the Merciful One reveals in the Torah with regard to a rapist: “He may not send her away all his days” (Deuteronomy 22:29), indicating that even if he divorces the woman whom he raped and was subsequently commanded to marry, all his days he stands commanded to arise and remarry her as his wife. Evidently, specifically there the husband is obligated to remarry his divorcée, as the Merciful One reveals as much. But here, what he did, he did.

Rav Mesharshiyya said to Rava: If he intends to divorce her and she is living with him and serving him, what is the halakha? Rava read the following verse about such a person: “Devise not evil against your neighbor, seeing he dwells securely by you” (Proverbs 3:29).

§ It is taught in a baraita (Tosefta, Sota 5:9) that Rabbi Meir would say: Just as there are different attitudes with regard to food, so too, there are different attitudes with regard to women. With regard to food, you have a person who, when a fly falls into his cup, he throws out the wine with the fly and does not drink it. And this is comparable to the demeanor of Pappos ben Yehuda with regard to his wife, as he would lock the door before his wife and leave so that she would not see any other man.

And you have a person who, when a fly falls into his cup, he throws out the fly and drinks the wine. And this is comparable to the demeanor of any common man, whose wife speaks with her siblings and relatives, and he lets her do so.

And you have a man who, when a fly falls into his serving bowl, he sucks the fly and eats the food. This is the demeanor of a bad man, who sees his wife going out into the street with her head uncovered, and spinning in the marketplace immodestly,