Granted, if you say that they notified them, it is due to that reason that they did not need to refrain from using their objects. However, if you say that they did not notify them, granted, it is logical that Beit Shammai did not refrain from handling items belonging to Beit Hillel, as ritually impure objects for Beit Hillel are ritually pure for Beit Shammai, and therefore no special care is necessary.

However, why didn’t Beit Hillel refrain from touching articles that belonged to Beit Shammai? After all, ritually pure objects for Beit Shammai are ritually impure for Beit Hillel. Rather, is it not the case that Beit Shammai notified Beit Hillel that these items were ritually pure only in their own opinion, and Beit Hillel separated themselves from them? The Gemara summarizes the discussion: Conclude from here that this is the correct interpretation.

The Gemara asks: In what way is this case stronger than that case? In other words, why is the statement with regard to ritual purity and impurity more conclusive than the one that deals with marriage? Since the practice of notification was not explicitly stated in the case of ritual purity but was merely inferred logically, the same reasoning applies equally to the case of marriage. The Gemara answers: Lest you say that since it is so unusual, a marriage to a rival wife generates publicity and is so widely known that no special notification is required, therefore, the Gemara teaches us that even in this case notification is required.

§ Since the statement of Rabbi Elazar was mentioned, the Gemara turns to discuss the matter itself. Rabbi Elazar said: Although Beit Shammai and Beit Hillel disagreed with regard to rival wives, they concede that a mamzer is only from a union whose prohibition is a prohibition of forbidden relations punishable by karet. The Gemara asks: Who concedes to whom? If we say that Beit Shammai concede to Beit Hillel, this is obvious, since if they acted in accordance with their own opinion that rival wives who married others without ḥalitza are liable only for violating a regular prohibition, their children are therefore fit and are not mamzerim at all.

Rather, one could say that Beit Hillel concede to Beit Shammai. But in that case she herself, the rival wife of a forbidden relative who married one of the yevamin, is liable to receive karet in the opinion of Beit Hillel, and the child is a mamzer, whereas Rabbi Elazar’s statement indicates that they concede with regard to a different case.

The Gemara explains: Actually, Beit Shammai concede to Beit Hillel, and this is not a novelty with regard to their basic dispute. Instead, the statement comes to exclude the opinion of Rabbi Akiva, who said: The offspring from forbidden relations for which one is liable for violating a prohibition is a mamzer. Rabbi Elazar teaches us that Beit Shammai and Beit Hillel agree that the offspring from forbidden relations for which one is liable for violating a prohibition is not a mamzer; rather, one is a mamzer only if he is born of a union punishable by karet.

§ The Gemara returns to the initial question of whether or not Beit Shammai acted in accordance with their own opinion. The Gemara suggests: Come and hear: Although Beit Shammai and Beit Hillel disagreed with regard to several cases, nevertheless, they did not refrain from marrying women from each other’s communities. The cases with regard to which they disagreed include rival wives, and sisters, i.e., if two sisters had been married to two brothers and simultaneously became obligated in levirate marriage, Beit Hillel prohibit both in levirate marriage, and if they violated the prohibition and married regardless, they require a divorce. By contrast, Beit Shammai permit them to remain married.

Furthermore, Beit Shammai and Beit Hillel disagreed with regard to an outdated bill of divorce that had been written but not delivered. Beit Shammai maintain that if the husband and wife continued to live together after the writing of the bill of divorce, the same bill of divorce can still be used later, whereas Beit Hillel dispute this. And they likewise disagreed with regard to an uncertain married woman, i.e., whether a minor who was actually married, and not merely betrothed, may perform refusal. And they also disagreed with regard to one who divorces his wife and later she lodged together with him at an inn, as to whether or not this is sufficient grounds for assuming that they remarried.

Additionally, they disagreed with regard to the issue of betrothal by money and with the equivalent value of money, and by a peruta or with the equivalent value of a peruta. According to Beit Shammai, the minimal amount of money effective for betrothal is a dinar or the equivalent of a dinar, whereas Beit Hillel maintain that even the less valuable peruta or its equivalent is sufficient.

Despite the fact that these halakhot entail important ramifications depending on whether or not these women were married or fit for marriage, or whether their offspring are fit for marriage, Beit Shammai did not refrain from marrying women from Beit Hillel, nor did Beit Hillel refrain from marrying women from Beit Shammai. This serves to teach you that they practiced affection and camaraderie between them, to fulfill that which is stated: “Love truth and peace” (Zechariah 8:19). Rabbi Shimon says: They did refrain in the certain cases, but they did not refrain in the uncertain cases. In other words, Beit Hillel were not worried that any ordinary woman from Beit Shammai might be one of those of uncertain status.

The Gemara infers from the opinion of Rabbi Shimon: Granted, if you say that Beit Shammai did act in accordance with their opinion, it is due to that reason that they refrained in the certain cases. However, if you say that they did not act in accordance with their opinion, why did they refrain from marriage? The Gemara replies: And how can you understand it that way, that Beit Shammai acted in accordance with their opinion? Even if they acted in accordance with their opinion, granted that Beit Hillel refrained from marrying into Beit Shammai, as those rival wives who entered into levirate marriage are liable to receive karet and their children are mamzerim according to the opinion of Beit Hillel.

However, why did Beit Shammai refrain from marrying the offspring of rival wives of Beit Hillel? The parents are liable for violating a regular prohibition, and therefore their children are fit. The Gemara answers as Rav Naḥman bar Yitzḥak said with regard to a different matter: This halakha was necessary not for the children of the rival wife, but only for the rival wife herself. Here too, it was necessary only for the rival wife herself. The halakha was not taught with regard to the children of the rival wives; rather, it is referring only to the rival wives.

The Gemara asks further: And in what way are uncertain cases different from the certain cases, such as forbidden rival wives? If you say that certain cases are undoubtedly prohibited in the opinion of Beit Hillel, the cases involving uncertain circumstances, e.g., one who divorced his wife and then stayed with her in the same inn, are also prohibited. Even if Beit Hillel render these cases prohibited only due to some uncertainty, the ruling is the same.

The Gemara answers: Do not say: In the uncertain cases, i.e., that the halakha involved doubtful circumstances. Rather, say: From the unspecified case. In other words, barring clear knowledge of an uncertain betrothal within a specific family, they would take women from that family in marriage. The reason is that Beit Shammai would notify Beit Hillel of the prohibition according to their opinion, and they would refrain from the marriage. If there was no notification, this was a clear sign that no doubt was involved in this case at all.

The Gemara asks: But if so, what does this come to teach us? Is it that they had relations of affection and camaraderie between them, i.e., that each trusted that the other side would never cause them to err with regard to something they held to be prohibited? This is the same as the first clause of the baraita. What is Rabbi Shimon adding by his statement? The Gemara answers: This comes to teach us that the entire baraita is the opinion of Rabbi Shimon. This is not a dispute between two Sages. Rather, Rabbi Shimon’s opinion elucidates the earlier statement.

§ The Gemara offers an alternative resolution: Come and hear, as Rabbi Yoḥanan ben Nuri said: How should one act with regard to this halakha of rival wives? In what form should it become widespread among the Jewish people? If we act in accordance with the statement of Beit Shammai and permit a rival wife in levirate marriage, the offspring will be a mamzer according to the statement of Beit Hillel. If we act in accordance with the statement of Beit Hillel and grant full exemption to the rival wives, the offspring will be of flawed lineage according to the opinion of Beit Shammai, as he is the child of a woman prohibited in marriage by a regular prohibition. Although he is not a mamzer, his lineage is nevertheless defective. Instead, let us enact a general decree for rival wives