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The Mishnah (1:3) in Eduyot mentions a debate between Hillel and Shammai regarding a law in mikvaot -- the volume of drawn water that would invalidate a mikvah. The Mishnah however ends by explaining that a third opinion was accepted. This opinion was presented based on the testimony of two weavers from sha'aar ha'ashpaut that presented the opinions of Shamaya and Avtalyon.1
The Melechet Shlomo (1:3) cites the Rash Sarilio who explains that despite Hillel and Shammai feeling that their opinions were more logical, once they heard the tradition related to this law, they accepted it.
The Rambam (1:4) however appears to understand that it was the Chachamim who accepted the position of the two weavers, setting aside the opinions of Hillel and Shammai.
The next Mishnah (1:4) then asks, why the Mishnah mentioned the opinions of the Shammai and Hillel, considering that their opinions were ultimately rejected. The Mishnah answers that that this was to teach people not to stubbornly stick to their opinion. Why? "Because the Avot Olam -- lo amdu al divereim" -- they did not stand by their words. How do we understand this Mishnah?
Recall that the Rash Sirilio explained that Shammai and Hillel retracted. Accordingly, the Mishnah is teaching that even these great Chachamim ultimately accepted the tradition of the two weavers and accepted the truth. Consequently, one should learn not to be stubborn, but rather be willing to admit when faced with the truth.
According to the Rambam, the opinions of Shammai and Hillel were overruled. The Rambam explains that the Mishnah is teaching that one should not try to force his position, considering that the opinions of these great sages were rejected. The Shoshanim LeDavid adds that despite one being convinced of his opinion, the Mishnah is teaching that one is fallible and prone to confirmation bias. Seeing that even the opinions of these giants were not accepted, should give one pause for the thought when engaged in a debate.2
The Shoshanim Le'David however addresses the question of why Shammai and Hillel are referred to as "Avot Olam" (fathers of the world). He cites the Maaseh Rokeach who explains that it is well known that Hillel exemplified that attribute of chessed while Shammai stemmed from gevurah. In this case the Chachamim adopted the halachic position between the two, which resembles that attribute of tifferet. Indeed the Avot, Avraham, Yitzchak and Yaakov each embodied these three attributes -- chessed, gevurah and tifferet. Since only Avraham, Yitzchak and Yaakov are referred to as the avot and in this case, all three of their attributes are found in their completeness, the term avot is appropriately used.
1 See volume 10 issue 32 for an analysis of the details of that Mishnah.
2 The Shoshanim Le'David notes that the difficulty with this explanation is that the term omed (al devarav) would have a different meaning in the two times mentioned in the Mishnah.
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