הָרוֹאֶה אוֹמֵר לְאַפּוֹשֵׁי מַיָּא הוּא דְּקָא עָבֵיד anyone watching would say that he did it to increase the water flow, and he did not intend to change the halakha. Rather, they would think that he widened the water trough only because there was not enough water flow.
תָּא שְׁמַע דְּאָמַר רַבִּי אֶלְעָזָר בַּר צָדוֹק כְּשֶׁהָיִיתִי לוֹמֵד תּוֹרָה אֵצֶל רַבִּי יוֹחָנָן הַחוֹרָנִי רָאִיתִי שֶׁהָיָה אוֹכֵל פַּת חֲרֵיבָה בְּמֶלַח בִּשְׁנֵי בַצּוֹרֶת בָּאתִי וְהוֹדַעְתִּי אֶת אַבָּא אָמַר לִי הוֹלֵךְ לוֹ זֵיתִים וְהוֹלַכְתִּי לוֹ רָאָה אוֹתָן שֶׁהֵן לַחִין אָמַר לִי אֵין אֲנִי אוֹכֵל זֵיתִים § The Gemara cites another relevant source. Come and hear, as Rabbi Elazar bar Tzadok said: When I studied Torah with Rabbi Yoḥanan the Ḥorani, who was a disciple of Beit Shammai, I saw that he would eat dry bread in salt in years of drought. I went and informed my father of his meager meal, and he said to me: Take olives for him, and I took for him some olives. Rabbi Yoḥanan saw that they were moist with the liquid that oozes from olives, which renders them susceptible to ritual impurity. Concerned that they had already become ritually impure, he said to me: I do not eat olives. He spoke politely and stated that he did not eat olives because he did not wish to embarrass his benefactor by disclosing that he feared they had become ritually impure.
בָּאתִי וְהוֹדַעְתִּי אֶת אַבָּא אָמַר לִי לֵךְ וֶאֱמוֹר לוֹ חָבִית נְקוּבָה הָיְתָה אֶלָּא שֶׁסְּתָמוּהָ שְׁמָרִים וּתְנַן חָבִית שֶׁל זֵיתִים מְגוּלְגָּלִים בֵּית שַׁמַּאי אוֹמְרִים אֵין צְרִיכָה לִנָּקֵב Rabbi Elazar bar Tzadok continued his account. I went and informed my father. He said to me: Go and say to him that the barrel containing the olives was perforated, but it was clogged by sediments in the oil and therefore some moisture remained inside. However, due to the presence of the hole, the olives were not rendered susceptible to ritual impurity. And we learned this in a mishna: With regard to a barrel of preserved olives, Beit Shammai say it does not need to be perforated, as the juice issuing from the olives does not render them susceptible to ritual impurity.
וּבֵית הִלֵּל אוֹמְרִים צְרִיכָה לִנָּקֵב וּמוֹדִים שֶׁאִם נִיקְּבָה וּסְתָמוּהָ שְׁמָרִים שֶׁהִיא טְהוֹרָה And Beit Hillel say that it does need to be perforated, as they maintain that the juice of olives is considered oil and it therefore renders the olives susceptible to ritual impurity. And Beit Hillel concede that if the barrel was perforated and subsequently clogged by sediments it is ritually pure, despite the moisture on the olives. Since liquids render food susceptible to ritual impurity only if they were placed on them intentionally, the hole in the barrel clearly shows that one did not intend for the juice to be there. By boring a hole in the barrel he has rendered it obvious that he did not desire the presence of the olive juices, and therefore it does not matter that the hole became blocked.
וְאַף עַל פִּי שֶׁתַּלְמִיד שַׁמַּאי הָיָה כׇּל מַעֲשָׂיו לֹא עָשָׂה אֶלָּא כְּדִבְרֵי בֵּית הִלֵּל אִי אָמְרַתְּ בִּשְׁלָמָא עָשׂוּ הַיְינוּ רְבוּתֵיהּ אֶלָּא אִי אָמְרַתְּ לֹא עָשׂוּ מַאי רְבוּתֵיהּ The baraita adds: And although Rabbi Yoḥanan the Ḥorani was a disciple of Shammai, he always acted only in accordance with the statements of Beit Hillel. The Gemara infers: Granted, if you say that Beit Shammai acted in accordance with their opinions, this is Rabbi Yoḥanan the Ḥorani’s greatness, i.e., he is praised for acting in accordance with the opinion of Beit Hillel. However, if you say that Beit Shammai did not act in accordance with their own rulings, what is the greatness and uniqueness of Rabbi Yoḥanan the Ḥorani? From here it can be inferred that Beit Shammai generally did act in accordance with their opinions.
תָּא שְׁמַע שָׁאֲלוּ אֶת רַבִּי יְהוֹשֻׁעַ צָרַת הַבַּת מַהוּ אָמַר לָהֶם מַחְלוֹקֶת בֵּית שַׁמַּאי וּבֵית הִלֵּל וַהֲלָכָה כְּדִבְרֵי מִי אָמַר לָהֶם מִפְּנֵי מָה אַתֶּם מַכְנִיסִין רֹאשִׁי בֵּין שְׁנֵי הָרִים גְּדוֹלִים בֵּין שְׁתֵּי מַחְלוֹקוֹת גְּדוֹלוֹת בֵּין בֵּית שַׁמַּאי וּבֵין בֵּית הִלֵּל מִתְיָירֵא אֲנִי שֶׁמָּא יָרוֹצּוּ גֻּלְגׇּלְתִּי § The Gemara adds: Come and hear a different proof. They asked Rabbi Yehoshua: What is the halakha with regard to the rival wife of a daughter? He said to them: It is a matter of dispute between Beit Shammai and Beit Hillel. They continued to ask him: And in accordance with whose statement is the halakha? He said to them: Why are you inserting my head between two great mountains, i.e., between two great disputing opinions, between Beit Shammai and Beit Hillel? I fear lest these two mountains break my skull.
אֲבָל אֲנִי מֵעִיד לָכֶם עַל שְׁתֵּי מִשְׁפָּחוֹת גְּדוֹלוֹת שֶׁהָיוּ בִּירוּשָׁלַיִם מִשְׁפַּחַת בֵּית צְבוֹעִים מִבֶּן עַכְמַאי וּמִשְׁפַּחַת בֵּית קוֹפַאי מִבֶּן מְקוֹשֵׁשׁ שֶׁהֵם בְּנֵי צָרוֹת וּמֵהֶם כֹּהֲנִים גְּדוֹלִים וְשִׁמְּשׁוּ עַל גַּבֵּי הַמִּזְבֵּחַ However, I shall testify to you about two great families that were in Jerusalem, the Beit Tzevo’im family who came from the town of Ben Akhmai, and the Beit Kofai family from the town of Ben Mekoshesh: They were the descendants of rival wives who married others, in accordance with the opinion of Beit Hillel, and from them came High Priests who served on the altar. Accordingly, I can testify that this was the accepted halakhic practice throughout the generations.
אִי אָמְרַתְּ בִּשְׁלָמָא עָשׂוּ הַיְינוּ דְּקָאָמַר מִתְיָירֵא אֲנִי אֶלָּא אִי אָמְרַתְּ לֹא עָשׂוּ אַמַּאי קָאָמַר מִתְיָירֵא אֲנִי וּנְהִי נָמֵי דְּעָשׂוּ מַאי מִתְיָירֵא אֲנִי The Gemara infers from this statement: Granted, if you say that Beit Shammai acted in accordance with their opinions, this is why Rabbi Yehoshua said: I fear, since a conclusive halakhic ruling would mean that certain children are mamzerim, and the descendants of that family might take vengeance upon him. However, if you say that they did not act in accordance with their opinions, why did he say: I fear? The Gemara retorts: And even if Beit Shammai did act in accordance with their rulings, what is the reason that he said: I fear?
הָא אָמַר רַבִּי יְהוֹשֻׁעַ אֵין מַמְזֵר אֶלָּא מֵחַיָּיבֵי מִיתוֹת בֵּית דִּין נְהִי נָמֵי דְּמַמְזֵר לָא הָוֵי פָּגוּם מִיהָא הָוֵי Didn’t Rabbi Yehoshua say that in his opinion a mamzer is only someone born from a union of those liable to receive the court-imposed capital punishments, not from those liable to receive karet. If so, in the opinion of Rabbi Yehoshua, the children of rival wives who entered into levirate marriage would not be mamzerim at all, and therefore he had no reason to fear reprisals. The Gemara answers: Even if this is the case, nevertheless, he had something to fear, as, although the child of a rival wife would not be a mamzer, he would nevertheless be of flawed lineage and disqualified from the priesthood.
מִקַּל וָחוֹמֶר מֵאַלְמָנָה מָה אַלְמָנָה שֶׁאֵין אִיסּוּרָהּ נוֹהֵג בַּכֹּל בְּנָהּ פָּגוּם זוֹ שֶׁאִיסּוּרָהּ שָׁוֶה בַּכֹּל כּוּ׳ The Gemara adds that this can be derived by an a fortiori inference from the case of a widow: Just as in the case of a widow, whose prohibition does not apply to all, as she is forbidden in marriage only to a High Priest and not to any other man, and yet the lineage of her son is flawed, as he is disqualified from the priesthood, the son of this rival wife should certainly be disqualified from the priesthood, as her prohibition applies equally to all, even regular Israelites.
קָבְעוּ מִינֵּיהּ צָרוֹת וְקָפָשֵׁיט לֵיהּ בְּנֵי צָרוֹת תַּרְתֵּי קָא בָּעֵי מִינֵּיהּ צָרוֹת מַאי וְאִם תִּמְצֵי לוֹמַר צָרוֹת כְּבֵית הִלֵּל בְּנֵי צָרוֹת דְּבֵית הִלֵּל לְבֵית שַׁמַּאי מַהוּ § Incidentally, the Gemara notes a problem with the above discussion: They asked Rabbi Yehoshua about rival wives, and he answered them about the children of rival wives. He did not refer to the rival wives themselves. The Gemara explains: They asked him questions on two matters: First, what is the halakha with regard to rival wives? And if you say that the halakha in the case of rival wives is in accordance with the opinion of Beit Hillel and they are exempt, what is the halakha according to Beit Shammai in the case of the children of rival wives who, following Beit Hillel, married others without ḥalitza?
לְמַאי נָפְקָא מִינַּהּ לְמִיפְשַׁט וְלַד מַחֲזִיר גְּרוּשָׁתוֹ לְבֵית הִלֵּל The Gemara asks: What difference does this question make? Since Rabbi Yehoshua maintains that the halakha is in accordance with the ruling of Beit Hillel, why even discuss Beit Shammai’s opinion on this matter? The Gemara explains: His answer enables one to resolve a different issue, the case of a child of one who remarries his divorcée according to the opinion of Beit Hillel. Is the child of a divorcée who remarried her previous husband after she had been married to another man fit or disqualified from the priesthood?
מִי קָאָמְרִינַן קַל וָחוֹמֶר וּמָה אַלְמָנָה לְכֹהֵן גָּדוֹל שֶׁאֵין אִיסּוּרָהּ שָׁוֶה בַּכֹּל בְּנָהּ פָּגוּם זוֹ שֶׁאִיסּוּרָהּ שָׁוֶה בַּכֹּל אֵינוֹ דִּין שֶׁבְּנָהּ פָּגוּם The Gemara elaborates: Do we say the following an a fortiori inference: And just as with regard to a widow married to a High Priest, whose prohibition does not apply to all, as she is prohibited in marriage only to a High Priest, and yet the lineage of her son is flawed as he is disqualified from the priesthood, so too, in the case of this rival wife, whose prohibition applies equally to all men, is it not right that her son should be of flawed lineage?
אוֹ דִלְמָא אִיכָּא לְמִיפְרַךְ מָה לְאַלְמָנָה שֶׁהִיא עַצְמָהּ מִתְחַלֶּלֶת וַאֲמַר לְהוּ צָרוֹת מִתְיָירֵא אֲנִי Or perhaps this comparison can be refuted: What about the fact that a widow is different, as she herself is disqualified from marrying a priest, i.e., if a High Priest has intercourse with her she is disqualified from marrying any member of the entire priesthood, including common priests, whereas a remarried divorcée herself is not disqualified from marrying into the priesthood? And Rabbi Yehoshua said to them: I fear that if I issue a decisive ruling concerning rival wives this might lead to a conflict,