Can you help me understand some things about Beit Hillel and Beit Shammai?
When did BH and BS function? Was a Sanhedrin in operation at that time? If so, why were the disagreements not settled by the Sanhedrin?
Yehuda
RASHI in Bava Metzia (34a) writes that in the days of the students of Hillel and Shamai, three generations before Rabeinu ha'Kodesh, when the students were not as careful with absorbing their masters' teachings as they should have been (due primarily to the troubles befalling the Jewish people at that time), there was a great increase in the number of Halachic arguments (see also Tosafos in Chagigah 16a, DH Yosi). It is clear from several sources (see Beitzah 20b) that Hillel lived in the time of the Beis ha'Mikdash, and the arguments between Beis Shamai and Beis Hillel were in the time of the Beis ha'Mikdash, when the Sanhedrin was in operation, and indeed votes were issued to determine whom the Halachah should follow (see Beitzah there, and Shabbos 16a). Thus it seems that the Sanhedrin did play a part in determining which opinion was to be followed as Halachah.
As far as your question why the Sanhedrin itself did not settle the arguments altogether, the Acharonim discuss this question. RAV REUVEN MARGOLIOS (Yesod ha'Mishnah v'Arichasah) has a beautiful approach in explaining this.
Mordecai Kornfeld
My understanding is that Shammai did not accept voting as a means to deciding halacha. What is right is right, period, doesn't matter how many votes you have. See the famous dispute between R. Elaezar and the Chachomin (bas kol, etc.). R. Elaezar, a disciple of Shammai, was not impressed with their vote, and even Shomayim testifies that his hard line view is the correct one. We poskin like Hillel, the side of chesed, and not like Shammai, the side of din. Nevertheless, in the Moisee Mashiach, when we can function at the level of din, Shammai's rulings will be put into place.
Shammai and Hillel TOGETHER possess Torah! As a pair. See Pirkei Avot where individuals possess Torah in toto originally, then comes the pairs, chesed and gevurah. See also the discussions, should man have been created, what came first earth or shomayim, how many candles are lit the first day of Hanukah, etc. for further examples of this split. Shammai always holds we start with perfection and then deal with human "frailty", and Hillel always holds that we start with imperfection and build to perfection.
I find it hard to believe that Beis Shamai refused to follow the majority, for that would be ignoring what is written in a verse in the Torah. A Zaken Mamre is killed for ruling against the decision of the majority of Sanhedrin. And Rebbi Eliezer was indeed put into Cherem for the way he acted, so he could not have been following a "school of thought".
However, what you write about Beis Shammai considering the world a place for perfection and Beis Hillel considering it full of imperfection is very insightful. I personally heard Rav Moshe Shapiro Shlita talk about this recently, and he presented it in the same light. He explained to us that this is what lies behind the Machlokes Beis Hillel and Beis Shamai (Ohalos 12:3) over whether a person is considered "hollow", (B'H) or "solid" (B'S) as far as bringing Tum'ah from one place to another (if he is lying in a doorway). Beis Hillel looks at a person as a hollow, incomplete creation, who is brought to this world to struggle to complete himself.
Yasher Kochach!
-Mordecai
-except that in that case, R' Eliezer was paskening 'tahor' -- not a 'hard line view' -- as opposed to the other chachomim.