(a) RASHI (DH b'Holachah Rabasi) defines a Holachah Rabasi as any Holachah that is done with one's feet, while Holachah Zutrasi refers to any Holachah that is not done with one's feet. The Gemara's first explanation of the argument between Rebbi Shimon and the Rabanan is that they both agree that when the Kohen is moving during the Holachah, his thoughts can invalidate the Korban. Their argument applies only when the Kohen is not moving. The Rabanan maintain that this is still considered Holachah, and, therefore, the Kohen's thoughts during the procedure can invalidate the Korban. Rebbi Shimon maintains that this is not considered an act of Holachah, and, therefore, the Kohen's thoughts during this procedure cannot invalidate the Korban.
Rav Papa and Rav Huna do not agree with this explanation, because Rebbi Shimon in the Mishnah explicitly states that his reasoning is "because it is possible not to do Holachah." This means that even when the Kohen must walk a long distance to transport the blood, the Kohen's thoughts during that act of Holachah cannot invalidate the Korban because it was not necessary to slaughter the Korban so far from the Mizbe'ach in the first place. When the Holachah is done while the Kohen remains standing in one place, and there are no unnecessary steps, even Rebbi Shimon agrees that the Kohen's thoughts can invalidate the Korban during the Holachah (see Rashi DH Ela).
The SHITAH MEKUBETZES (Hashmatos #3) questions Rashi's explanation. How is it possible that the Gemara's initial explanation assumes that Rebbi Shimon in the Mishnah refers to a case in which the Kohen is not walking at all during the Holachah? Rebbi Shimon specifically says that his reasoning is "because it is possible not to do Holachah." Rebbi Shimon clearly refers to a case in which the Kohen is walking! Even though, according to Rashi, this is the question of Rav Papa and Rav Huna, it is such an obvious question that it is not reasonable to suggest that the Gemara even entertained such an explanation in the first place.
(b) The Shitah Mekubetzes explains that a Holachah Rabasi is when the Korban is slaughtered so far away that it is impossible to do the Zerikah without coming closer to the Mizbe'ach by walking. A Holachah Zutrasi is when it is possible to do the Zerikah without coming closer, but the Kohen nevertheless walks closer to the Mizbe'ach to facilitate the Zerikah. The Gemara initially assumes that Rebbi Shimon maintains that such a Holachah is not considered a Holachah because it is not necessary. The question of Rav Papa and Rav Huna is that Rebbi Shimon's statement in the Mishnah, "because it is possible not to do Holachah," implies that the case is when there is a lot of Holachah which can be avoided. This is why they explain that Rebbi Shimon argues only in a case of a Holachah Rabasi.
(c) The MISHNEH L'MELECH (Hilchos Pesulei ha'Mukdashin 1:23) records a third explanation, which involves an entirely different discussion. Both Holachah Rabasi and Holachah Zutrasi are procedures done without walking. The Gemara says that the status of a Holachah that is done without walking ("Holachah she'Lo b'Regel") depends on the argument between Rebbi Shimon and the Rabanan. Rebbi Shimon, who says that Holachah is not an Avodah, maintains that the Kohen does not have to move his feet for the Holachah, while the Rabanan maintain that if the Kohen does not move his feet, then the Holachah -- which, they maintain, is an Avodah -- was not done and the Korban is Pasul. The Gemara then says that in a case of Holachah Rabasi, in which the Kohen needs to walk in order to do the Zerikah, everyone agrees that if the Kohen does the Zerikah from where he is standing, without walking towards the Mizbe'ach (that is, without any Holachah), then the Korban is Pasul. This is because such a distance requires Holachah, and the Holachah was not done. In a case in which the Kohen is standing at a point from which he is able to do the Zerikah without walking towards the Mizbe'ach (Holachah Zutrasi), the Rabanan argue that since he does not need to walk, the Holachah is valid without him walking, and thus a wrongful thought during this time can invalidate the Korban. Rebbi Shimon maintains that Holachah always must involve walking, and therefore the Kohen who does not walk has not done an act of Holachah, invalidating the Korban due to the lack of the Avodah of Holachah.
The Mishneh l'Melech asks, however, that this explanation is not consistent with the next part of the Gemara. How can Rav Papa and Rav Huna say that it is clear from the Mishnah that the argument between Rebbi Shimon and the Rabanan applies in a case of Holachah Rabasi? The Mishnah obviously is discussing a case in which the Kohen did walk, as Rebbi Shimon says that the Korban is valid "because it is possible not to do Holachah," implying that Holachah was done. How, then, can one say that the Mishnah is discussing a case in which the Kohen did not move during the Holachah?
The PANIM ME'IROS, who gives an explanation similar to the one recorded by the Mishneh l'Melech, explains the question of the Gemara. It is true that the Mishnah is discussing a case in which the Kohen walked. Rebbi Shimon says that a wrongful thought does not invalidate the Korban at this point, because the Holachah was unnecessary. This shows that when the Kohen is not doing any unnecessary movement (Holachah Zutrasi), Rebbi Shimon would agree that a wrongful thought invalidates the Korban, even if no movement is done. This view is shared by the Rabanan, who say that a wrongful thought during Holachah always invalidates a Korban. Rav Papa and Rav Huna agree that the case of the Mishnah is one in which the Kohen needed to walk. They ask that since Rebbi Shimon is referring only to a case in which the Kohen needed to walk, it is evident that Rebbi Shimon agrees with the Rabanan that in a case where the Kohen does not need to walk (i.e. Holachah Zutrasi) that a wrongful thought can invalidate the Korban! This clearly shows that the act is considered Holachah according to everyone. Consequently, there is only one possible case in which Rebbi Shimon and the Rabanan argue about whether or not walking is necessary during Holachah, and that is the case of the Mishnah, a case of Holachah Rabasi. (Y. MONTROSE)
2) DERIVING THE LAW OF A "ZAR" WHO PERFORMS AN AVODAH FROM THE LAW OF A "BA'AL MUM" WHO PERFORMS AN AVODAH
QUESTION: The Gemara discusses the source for the law that a Zar (non-Kohen) who performs an Avodah of a Korban (such as the Kabalah) invalidates the Korban. Tana d'Vei Rebbi Yishmael derives the source from a Kal va'Chomer. If the Avodah of a Kohen who is a Ba'al Mum is Pasul even though he is permitted to eat the meat of Korbanos, then certainly the Avodah of a Zar, who is not permitted to eat the meat of Korbanos, is Pasul.
TOSFOS REBBI AKIVA EIGER (Mishnayos, #13) questions why the Gemara does not ask a serious question on this teaching. A Chalal, the child of a union between a Kohen and a divorcee, is not permitted to eat the meat of Korbanos, but nevertheless the Avodah that he performs is valid b'Di'eved. This clearly shows that the Kal va'Chomer of d'Vei Rebbi Yishmael is a fallacy. Instead of learning from a Ba'al Mum that a Zar's Avodah is Pasul, one can learn from a Chalal that a Zar's Avodah is valid!
In fact, TOSFOS in Ta'anis (17b, DH Davar) uses this very argument. Tosfos asks why we do not learn that a Kohen who is an Arel cannot perform the Avodah from the law of a Ba'al Mum. If a Ba'al Mum, who is permitted to eat Korbanos, invalidates the Korban if he does the Avodah, then certainly an Arel, who is not permitted to eat Korbanos, invalidates the Korban if he does the Avodah. Tosfos answers that we cannot learn the law of an Arel from the law of a Ba'al Mum, because we find that a Chalal cannot eat Korbanos and yet his Avodah is not invalid. Why does the Gemara here not use the law of a Chalal to refute the Kal va'Chomer of d'Vei Rebbi Yishmael?
(a) The SHA'AR HA'MELECH (Hilchos Bi'as ha'Mikdash 6:10) quotes the SHITAH MEKUBETZES in Sanhedrin (22b) who gives an answer to this question in the name of the grandson of the RASH MI'SHANTZ. There is a characteristic of a Chalal which makes it impossible to derive the law of a Zar from the law of a Chalal. A Chalal is a descendant of Aharon. By virtue of his ancestry, he does not invalidate a Korban when he performs the Avodah. Accordingly, it is obvious why the law of a Zar cannot be derived from that of a Chalal; a Chalal's Avodah is valid because he is descended from Aharon, while a Zar is not. Therefore, the law of a Zar can be derived only from a Ba'al Mum.
The Sha'ar ha'Melech is not satisfied with this answer. Although it explains why the law of a Zar is not derived from the law of a Chalal, and why Tosfos in Ta'anis does learn the law of a Kohen who is an Arel from the law of a Chalal, it does not explain the teaching of d'Vei Rebbi Yishmael later (16a-b), where he derives the law of a Kohen who is an Onen from the law of a Ba'al Mum. Tana d'Vei Rebbi Yishmael teaches that if the Avodah of a Kohen who is a Ba'al Mum is Pasul, even though he is permitted to eat the meat of Korbanos, then certainly the Avodah of an Onen, who is not permitted to eat the meat of Korbanos, is Pasul. Why does the Gemara there not point out the fallacy of learning the law of an Onen from the law of a Ba'al Mum? Instead of learning the law of an Onen from the law of a Ba'al Mum, we should learn from the law of a Chalal that an Onen's Avodah is valid. The answer of the Shitah Mekubetzes does not apply, since both an Onen and a Chalal are descendants of Aharon.
(b) In a preface to his answer, the KEHILOS YAKOV (#14) suggests that Tosfos in Ta'anis maintains that in contrast to the laws of an Onen and a Zar, there is no Isur of a Lo Sa'aseh against a Chalal doing the Avodah. The only reason why a Chalal may not do the Avodah is that he is not considered a fully qualified Kohen. By doing the Avodah, he negates the positive commandment that only fully qualified Kohanim must do the Avodah. Tosfos in Ta'anis explains that the law of an Arel cannot be derived from the law of a Ba'al Mum because an Arel can be learned from a Chalal. The logic of Tosfos is that since both the Arel and the Chalal are descendants of Aharon and are not called Zarim, the law of Arel can be learned from the law of Chalal to teach that an Arel's Avodah does not invalidate a Korban. However, a Zar and an Onen are different. The law of a Zar obviously is more stringent, since there is an Isur Lo Sa'aseh that prohibits him from performing Avodah: "v'Zar Lo Yikrav Aleichem" (Bamidbar 18:4). An Onen also has a specific prohibition against doing the Avodah. This is why the Gemara does not refute d'Vei Rebbi Yishmael's teachings for Zar and Onen. Since those cases are more stringent than the case of a Chalal (because they have specific verses which prohibit them from performing Avodah), there is no basis to compare them to a Chalal instead of to a Ba'al Mum. (Y. MONTROSE)