For the source text click/tap here: Chagigah 17
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In the Mishnah on our daf, Beit Shammai and Beit Hillel disagree about whether various sacrifices can be brought on Yom Tov. According to Bet Shammai, a korban olah, which is totally burned up, cannot be brought.
A korban shelamim, however, can be brought, since parts of it will be eaten by the kohanim and by the owner, making it not only a sacrifice, but also food preparation, which is permitted on Yom Tov. Nevertheless, they forbid performing semikha on the animal.
Bet Hillel permit both olot and shelamim to be brought since they are connected to the holiday, even though there is no obligation to bring them on the actual Yom Tov.
We explore the literature about Bet Hillel vs Bet Shammai from different literary perspectives including the use of their hermeneutic approaches in the recent divide in response to COVID19, between charedim and religious zionists, with an insightful article by Rabbi Aryeh Meir.