1) THE DISPUTE WITH REGARD TO "SEMICHAH" FOR "SHALMEI CHOVAH"
QUESTIONS: The Gemara records two different traditions among the Tana'im with regard to the dispute between Beis Shamai and Beis Hillel about Semichah. Some Tana'im explain that the dispute is whether Semichah is permitted on Yom Tov or whether it is prohibited on Yom Tov because it involves a transgression of the prohibition against using a live animal ("Mishtamesh b'Ba'alei Chayim"). Others say that the dispute is whether or not there is an obligation to perform Semichah at all for Korbanos of Shalmei Chovah (obligatory Korbenos Shelamim, as opposed to voluntary ones) even on a weekday.
RASHI (DH Beis Shamai Hi) explains that according to the second opinion (that the dispute is whether or not there is an obligation of Semichah at all), Beis Shamai maintains that the obligation to perform Semichah with a Korban Chovah does not override the laws of Yom Tov.
Rashi's words are difficult to understand.
(a) When Rashi writes that Semichah does not override the laws of Yom Tov, he implies that on an ordinary weekday Semichah for an obligatory Korban is permitted. However, Semichah should be prohibited on an ordinary weekday as well, because leaning on the animal when there is no Mitzvah to do so is considered Avodah b'Kodshim, using a sanctified animal for one's own purposes (as the Gemara says in Chagigah 16b). If Rashi means that these Tana'im maintain that Semichah does not need to be done with all of one's strength (and thus the act does not constitute Avodah b'Kodshim), then why should the act be prohibited even on Yom Tov? Semichah which is not done with all of one's strength does not constitute "Mishtamesh b'Ba'alei Chayim" (as the Gemara in Chagigah says), just as it does not constitute Avodah b'Kodshim, and thus it should be permitted on Yom Tov.
(b) The Gemara in Chagigah (16b) quotes Rebbi Yochanan who says that the rabbinical enactments of Shevus should not be taken lightly, because we find that (according to Beis Shamai) the Rabanan enacted a prohibition of Shevus against performing Semichah on Yom Tov even though Semichah is a Mitzvah d'Oraisa. The Gemara there asks what new teaching Rebbi Yochanan intends to convey; we know that Beis Shamai prohibits Semichah on Yom Tov, because the Mishnah explicitly says so. The Gemara answers that Rebbi Yochanan is teaching that the Mishnah should be understood like the first approach mentioned above, that the dispute about Semichah is whether or not Semichah may be done on Yom Tov, and not whether or not there is any obligation to do Semichah in the first place (even on a weekday).
It is clear from the Gemara in Chagigah that if the dispute is whether or not there is ever an obligation to perform Semichah, the opinion of Beis Shamai would not teach anything about the severity of Shevus (i.e., that it overrides a Mitzvah d'Oraisa). Why, then, does Rashi write that even according to the opinion that the dispute is whether or not there is ever an obligation of Semichah, Semichah is prohibited on Yom Tov because of Shevus? (REBBI AKIVA EIGER in GILYON HA'SHAS and in DERUSH V'CHIDUSH to Chagigah 16b, and TOSFOS REBBI AKIVA EIGER on Mishnayos)
ANSWERS: The SHA'AR HA'MELECH (Hilchos Ma'aseh ha'Korbanos 3:13; see RASHASH) suggests illuminating answers to these questions.
(a) Rashi was bothered by a basic question on the Gemara's discussion. The SHITAH MEKUBETZES here (in the name of TOSFOS) and the PNEI YEHOSHUA ask that if the dispute between Beis Shamai and Beis Hillel involves the general issue of whether or not there is an obligation of Semichah for an obligatory Korban, then why is this dispute recorded here in Maseches Beitzah? It has no relevance to the Sugya at all. This is the question which bothered Rashi. (The Pnei Yehoshua leaves this question unanswered. Tosfos, cited by the Shitah Mekubetzes, answers that the Mishnah's intent is to teach that Beis Hillel, who argues and permits Semichah, permits it even on Yom Tov.)
In order to answer this question, Rashi understands that it must be that even if there is no obligation to perform Semichah for a Korban Chovah, if one does perform Semichah he fulfills a Mitzvah. (This is also the view of the ME'IRI in Chidushim, DH Hu d'Amar and DH d'Amar Lach.) (A similar concept is expressed in Eruvin 96b, where Rebbi Yosi and Rebbi Shimon rule that women, although exempt from the obligation of Semichah, are nevertheless permitted to do Semichah and their act does not constitute Avodah b'Kodshim.) The owner of any Korban (and only the owner) is allowed to do Semichah even though there is no obligation to do Semichah for that particular Korban, and his act is not considered Avodah b'Kodshim.
Accordingly, on an ordinary weekday Semichah for Shalmei Chovah is permitted and is not Avodah b'Kodshim, because one fulfills a Mitzvah when he does it. On Yom Tov, however, when one does Semichah (even when Semichah for that Korban is obligatory) he transgresses the Isur d'Rabanan of "Mishtamesh b'Ba'alei Chayim." Since, in this case, there is no obligation to do Semichah, the Rabanan did not permit one to perform an optional Semichah on Yom Tov.
(Rashi's approach -- that Rebbi Yosi and Rebbi Shimon permit one to perform an optional Semichah -- contrasts with the approach of TOSFOS in Chulin (85a, DH Nashim) who says that even according to Rebbi Yosi, a woman is permitted to perform Semichah only without all of her strength, for such an act involves only an Isur d'Rabanan of being "Mezalzel b'Kodshim" (demeaning Kodshim) and not an Isur d'Oraisa of Avodah b'Kodshim. Rashi disagrees with Tosfos and says that according to Rebbi Yosi a woman may perform Semichah with all of her strength, even though leaning on an animal of Kodshim is normally prohibited because of the Isur d'Oraisa of Avodah b'Kodshim.)
(b) To answer the second question, the SHA'AR HA'MELECH explains the Gemara in Chagigah as follows. The reason for the Gemara's assertion -- that the fact that Beis Shamai prohibits Semichah on Yom Tov does not show that Shevus is severe enough to override a Mitzvah d'Oraisa -- is not because there is no obligation of Semichah whatsoever, but because Semichah is not an obligation but is only permitted to be done. According to the other opinion which says that there certainly is an obligation of Semichah for Shalmei Chovah, the fact that the Rabanan decreed that Semichah not be done on Yom Tov shows the severity of Shevus (in that it overrides even a Mitzvah d'Oraisa of Semichah).
Rebbi Akiva Eiger apparently does not accept this answer because, as the Sha'ar ha'Melech points out, Rashi in Chagigah implies that according to the opinion that Beis Hillel and Beis Shamai argue about whether there is a Mitzvah of Semichah altogether for Shalmei Chovah, Beis Shamai maintains that one may not perform Semichah on an ordinary weekday just as one may not perform Semichah on Yom Tov (see RASHASH).
(See, however, Insights to Chagigah 7b. See also KEHILOS YA'AKOV, who suggests another answer to Rebbi Akiva Eiger's question based on the Yerushalmi cited by TOSFOS in Pesachim 66b, DH v'Ha: According to Rashi, there exists a rabbinical obligation to perform Semichah with Shalmei Chovah; the Rabanan's enactment of Semichah is not considered Avodah b'Kodshim.)

20b----------------------------------------20b

2) THE REASON TO PERMIT "SHECHITAH" OF KORBANOS ON YOM TOV
QUESTION: Beis Shamai and Beis Hillel argue whether one may slaughter obligatory Korbenos Shelamim, such as the Shalmei Chagigah, on Yom Tov. Each one proposes logical arguments for his position. The Gemara records two different traditions among the Tana'im with regard to their dispute about Shechitah. According to the first Tana, Beis Hillel maintains that since Shechitah is permitted for one's personal consumption, it certainly should be permitted for the sake of Gavo'ah (offering a Korban to Hash-m). According to the second Tana (Aba Shaul), Beis Hillel maintains that it is not proper that one's own table is full when Hash-m's table, so to speak, is lacking.
Beis Shamai argues that Beis Hillel's Kal v'Chomer is not valid. Everyone agrees that Nedarim and Nedavos may not be offered on Yom Tov even though the logic of Beis Hillel's Kal v'Chomer should permit them. Since the Kal v'Chomer is not valid, the Shechitah of Shalmei Chovah should also be prohibited.
Beis Shamai continues and proves his opinion from the verse which says "Lachem," implying that one is permitted to do Melachah only "for you" but not for purposes of Gavo'ah, and therefore one is prohibited to slaughter Shalmei Chovah on Yom Tov.
Beis Hillel responds with a verse that supports his opinion. The verse says "la'Hashem," which teaches that Melachah may be done for the sake of Gavo'ah.
Why does Beis Shamai base his opinion on the case of Nedarim and Nedavos and the verse of "Lachem"? Beis Shamai should simply say that he maintains that there exists no principle of "Mitoch" and thus Shechitah of a Korban should be prohibited on Yom Tov because the act is not necessary for Ochel Nefesh (food preparation). (Beis Shamai maintains that one may perform a Melachah on Yom Tov only for the purpose of Ochel Nefesh, and one may not perform a Melachah -- which is normally done for Ochel Nefesh -- for any other purpose. See 12a.)
In addition, the Gemara earlier (12a) expresses a doubt whether or not Beis Hillel maintains that a principle of "Mitoch" exists. Why does the Gemara there not prove from Beis Hillel's opinion here that Beis Hillel applies the principle of "Mitoch"?
ANSWER: Apparently, the Gemara maintains that the Shechitah of a Korban is permitted not because of "Mitoch" but because the Korban itself is considered Ochel Nefesh. Since a Jew may eat part of the Korban, it is considered Ochel Nefesh. Moreover, the Mizbe'ach's consumption of the Korban is considered "Ochel Nefesh" for Gavo'ah, as the Gemara in Chulin (81b) refers to the burning of the Korban as "Achilas Mizbe'ach." (Alternatively, offering a Korban is considered Machshirei Ochel Nefesh, because it is not proper that one's own table is full when Hash-m's table, so to speak, is lacking.) (See following Insight.)
3) THE LOGIC OF "MITOCH"
QUESTION: Beis Shamai and Beis Hillel argue whether one may slaughter obligatory Korbenos Shelamim, such as the Shalmei Chagigah, on Yom Tov (see previous Insight). Each one proposes logical arguments for his position. The Gemara records two different traditions among the Tana'im with regard to their dispute about Shechitah. According to the first Tana, Beis Hillel maintains that since Shechitah is permitted for one's personal consumption, it certainly should be permitted for the sake of Gavo'ah (offering a Korban to Hash-m). According to the second Tana (Aba Shaul), Beis Hillel maintains that it is not proper that one's own table is full when Hash-m's table, so to speak, is lacking.
The Gemara earlier (12a) concludes that Beis Hillel applies the principle of "Mitoch."
(a) According to Aba Shaul, Beis Hillel permits Shechitah for all types of Korbanos (including Nedarim and Nedavos) and does not accept the Derashah of "Lachem" (Melachah of Ochel Nefesh is permitted only "for you" and not for Hash-m). Beis Hillel argues that "it is not proper for your table to be full and your master's to be empty." If Aba Shaul's intent is to defend the reasoning of Beis Hillel, why does he not simply say that Beis Hillel permits Shechitah of Korbanos because he applies the principle of "Mitoch"? Why does Aba Shaul need to give logical arguments?
(b) Moreover, why does the Tana who argues with Aba Shaul assert that Beis Shamai and Beis Hillel agree that the Shechitah of Nedarim and Nedavos is not an act of Ochel Nefesh and is prohibited? According to this Tana, Beis Hillel should permit the Shechitah of Nedarim and Nedavos because of "Mitoch."
ANSWERS:
(a) TOSFOS (12a, end of DH Hachi Garsinan) explains that "Mitoch" only permits an act which is needed for Yom Tov itself ("Tzorech Yom Tov"). Nedarim and Nedavos do not involve any "Tzorech Yom Tov," and therefore "Mitoch" cannot permit their Shechitah. This is why Aba Shaul must mention the additional logic (that it is not proper for one's table to be full while the table of one's master is empty) in order for Korbanos of Nedarim and Nedavos to be "Tzorech Yom Tov."
(b) The reason why Beis Hillel prohibits offering Nedarim and Nedavos on Yom Tov according to the first Tana is because of "Lachem." "Lachem" teaches not only that Melachah for the purpose of Ochel Nefesh of Gavo'ah is prohibited, but also that the principle of "Mitoch" does not permit Melachah for Gavo'ah, as Tosfos earlier writes (12a, DH ha'Shochet).
However, TOSFOS and TOSFOS RABEINU PERETZ (19a) give a different answer. They explain that if not for the verse of "la'Hashem," one might have thought that all Korbanos are prohibited to be offered on Yom Tov except for the Korban Chagigah, because of the verse that Ula cites in defense of Beis Shamai (19a), "v'Chagosem Oso" (the Chagigah may be brought, but not any other Korban).
The MAHARSHA wonders why Tosfos does not write simply that one might have thought that all Korbanos are prohibited to be brought on Yom Tov because the verse says, "Lachem" (for you and not for Hash-m), which Beis Shamai here uses as proof against Beis Hillel. Why does Tosfos here mention the verse of "v'Chagosem"?
The answer might be that in the first Beraisa cited in this Sugya, Beis Hillel agreed that Nedarim and Nedavos may not be offered on Yom Tov. Why, then, did Beis Shamai assume that he had a proof against Beis Hillel's opinion from "Lachem" when he knew that Beis Hillel himself derived from "Lachem" the prohibition against offering Nedarim and Nedavos on Yom Tov? It must be that Beis Hillel had a second reason for prohibiting Nedarim and Nedavos other than "Lachem." What is that reason? It must be the verse of "v'Chagosem."

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