1) THE "KAL VA'CHOMER" OF REBBI YISHMAEL
OPINIONS: The Gemara (40b) quotes an apparently vague Kal va'Chomer in the name of Rebbi Yishmael: If, where two Korbanos are not equated with each other, their actions are equated with each other, then certainly where two Korbanos are equated with each other, their actions are equated with each other.
The Gemara explains the Kal va'Chomer: If the Avodah of the Par He'elem Davar and the Se'ir Yom ha'Kipurim is the same, even though these Korbanos are not brought from the same type of animal, then certainly two similar Korbanos, such as the Par Yom ha'Kipurim and the Par Kohen Mashi'ach, or the Se'ir Yom ha'Kipurim and the Se'ir Avodah Zarah, should have the same Avodah. The Gemara compares the Par Yom ha'Kipurim to the Par Kohen Mashi'ach, and applies the laws of "Es b'Dam v'Tevilah" (as explained on 40b) to the Par Yom ha'Kipurim. It also concludes that the laws of the Se'ir Yom ha'Kipurim are learned from the Se'ir Avodah Zarah, but it does not state what laws are derived.
How exactly does this Kal va'Chomer function?
(a) RASHI (40b-41a) understands that the Gemara's intention is to derive the laws of "Es b'Dam v'Tevilah" for the Se'ir Yom ha'Kipurim in the follow manner. If the Avodah is the same for the Par He'elem Davar and Se'ir Yom ha'Kipurim despite the fact that they are brought from different types of animals, then certainly the laws of a Se'ir Yom ha'Kipurim may be derived from a Korban which is brought from a similar type of animal, namely the Se'ir Avodah Zarah.
RAV ELAZAR MOSHE HA'LEVI HOROWITZ has great difficulty with this explanation. The typical Kal va'Chomer in the Gemara states that if a certain requirement exists in a category which is not strict, then certainly that requirement should exist in a category which is strict. Here, however, the Kal va'Chomer does not work this way. This Kal va'Chomer essentially states that since two Korbanos which are brought from different animals have the same laws, the laws of one Korban should be derived from another Korban which is brought from the same type of animal, even though those laws are not explicitly stated with regard to the second Korban. In other words, if the laws of two dissimilar Korbanos are the same, then certainly the laws which are not stated explicitly for one Korban should be able to be derived from another, similar Korban. However, in the first half of this "Kal va'Chomer," no laws are being derived from one Korban to the other. Rather, we merely find that their laws are the same! How, then, can that be a logical basis to derive (in the second half of this "Kal va'Chomer") laws from one Korban to another?
Moreover, the Gemara (Bava Kama 25a and elsewhere) records a dispute about whether a Kal va'Chomer may be applied to teach a more stringent Halachah, or whether it may be used to teach only the exact status as the source Halachah. This is known as "Dayo la'Ba Min ha'Din Liheyos ka'Nidon." According to the opinion that maintains "Dayo," the difficulty with Rebbi Yishmael's Kal va'Chomer is strengthened. Even according to the opinion that does not maintain "Dayo," it remains difficult to understand what is being derived through this Kal va'Chomer from the two Korbanos of Par He'elem Davar and the Se'ir Yom ha'Kipurim.
(b) In light of his questions on Rashi's explanation, Rav Elazar Moshe ha'Levi understands the Gemara differently. He explains that in fact there is no Kal va'Chomer through which the Se'ir Yom ha'Kipurim is derived from the Se'ir Avodah Zarah. Rather, the laws of the Se'ir Yom ha'Kipurim are derived through a Hekesh which compares the two Korbanos. The Torah says "ha'Chatas" with regard to both Korbanos, which teaches that these Korbanos are brought due to a sin, and gives grounds to compare their laws to each other.
When the Gemara says that the laws of "Es b'Dam v'Tevilah" for the Par Yom ha'Kipurim are derived from the Par Kohen Mashi'ach, and the Se'ir Yom ha'Kipurim from the Se'ir Avodah Zarah, "through a Kal va'Chomer," it means that after a Hekesh compares the two Se'irim, the laws of the Par Yom ha'Kipurim can be derived through a Kal va'Chomer. Just as the Se'ir Yom ha'Kipurim and Par He'elem Davar have the same laws of "Es b'Dam v'Tevilah" even though they are different animals, the Par Yom ha'Kipurim can be derived from the Par Kohen Mashi'ach since they are the same type of animal.
This resolves the question that in the Kal va'Chomer, in the first set of Korbanos, the laws for both Korbanos are taught explicitly, while they are not taught explicitly in the second set of Korbanos. According to Rav Elazar Moshe ha'Levi Horowitz, this is not the case. It is only through a Hekesh that the laws of the Se'ir Yom ha'Kipurim are derived. Therefore, the laws of the Par Yom ha'Kipurim should be derived through a Hekesh from the Par Kohen Mashi'ach. (Mordechai Zvi Dicker, Y. MONTROSE)
41b----------------------------------------41b
2) AN APPARENTLY EXTRA "HEKESH"
QUESTION: The Gemara (41a) derives the requirement to burn the Yoseres ha'Kaved (diaphragm of the liver) and Shtei ha'Kelayos (two kidneys) of the Se'ir Avodah Zarah on the Mizbe'ach from the laws of the Par He'elem Davar, as implied by the verse, "Chatasam... Al Shigegasam" -- "their sins... for their accidents" (Bamidbar 15:25).
The Gemara (41a-b, see also RASHI DH Amar Rav Papa) explains that although a verse already compares the Se'ir Avodah Zarah with the Par He'elem Davar with regard to other laws, this second Hekesh is still needed to teach the law of the Yoseres and the Kelayos. This law, that the Yoseres and Kelayos must be burned on the Mizbe'ach, is not stated explicitly even for the Par He'elem Davar. Rather, this requirement for the Par He'elem Davar is derived from the Par Kohen Mashi'ach. Accordingly, one might have thought that the Par He'elem Davar may not be used as a source to teach this requirement for the Se'ir Avodah Zarah. Hence, a second Hekesh of "Chatasam... Al Shigegasam" is needed.
TOSFOS (41b, DH Aval) and the SHITAH MEKUBETZES are perplexed by the Gemara's answer. The Gemara (41a) says explicitly that when the verse states, "v'Asah la'Par Ka'asher Asah l'Far" regarding the Par He'elem Davar, the second word "l'Far" refers to the Par Kohen Mashi'ach. Rav Papa explains that this Hekesh enables the Par He'elem Davar to be the source that teaches that the Yoseres and Kelayos of the Se'ir Avodah Zarah are burned on the Mizbe'ach, since "this Hekesh makes it as though the law is explicitly stated [for the Par He'elem Davar]." How, then, can the Gemara here say that "Chatasam... Al Shigegasam" is necessary to make it as though it is explicitly stated? There is already a Hekesh that serves this purpose!
ANSWERS:
(a) TOSFOS answers that perhaps the Hekesh of "Chatasam... Al Shigegasam" is the Gemara's source that the first word "la'Par" refers to the Par He'elem Davar, and the second "l'Far" refers to the Par Kohen Mashi'ach.
(b) The SHITAH MEKUBETZES suggests that there are three levels of non-explicit law in the Torah. There is a law derived from another topic in a manner which does not make it as though the Torah states the law explicitly with regard to this topic. This derivation is not clear and obvious. On another level, a law derived from another topic is considered as though it is written explicitly in the Torah, but one still would not think to teach this law through a Hekesh to another topic, since it is not actually written. The third level is a law derived from another topic which is considered as though it is written explicitly in the Torah, and it may be taught through a Hekesh to another topic. In the case of the Gemara here, only because the verse says, "v'Asah la'Par Ka'asher Asah l'Far ha'Chatas" (implying that everything done to the Par Kohen Mashi'ach must be done to the Par He'elem Davar), are all aspects of the service of the two Korbanos the same. This is why both Hekeshim are needed.
(The Shitah Mekubetzes later retracts this answer and concludes with the answer of Tosfos.) (Mordechai Zvi Dicker, Y. MONTROSE)