The first perek of Bechorot deals with the mitzvah of pidyon peter chamor – redeeming the first-born male donkey. The donkey is ideally redeemed with a young lamb or kid, which is given to a kohen. If however one did not want to perform this redemption, the donkey would require arifa – it is killed by taking an axe to the back of the neck
The Mishnah raises a number of cases of doubt regarding peter chamor. For example (1:3) a donkey, in her first birth, gave birth to a male and female but which are not sure which was born first. Since peter chamor only applies to a male first born, and there is a doubt which of the offspring was first, it is questionable whether pidyon peter chamor is required. The Mishnah continues that a lamb must still be separated, yet it can be retained by the owner.
The Bartenura explains that considering the doubtful status of the foal, the lamb must be separated to remove the potential sanctity if it is indeed the peter chamor. Once that issue is dealt with, since it is questionable whether it was necessary and whether the lamb should be given to the kohen, the owner can keep the lamb. This is based on the principle of hamotzi me'chaveiro alav ha'ra'aya. In other words, regarding financial matters, the burden of proof is placed on the one attempting to extract the funds from another.
The Gemara (9b) questions why the separation of the lamb is necessary in this case of doubt if the owner is going to retain it. It answers, much like we saw in the Bartenura above, that it is to remove the prohibition that exists if the animal is indeed a peter chamor. The Gemara comments that the Mishnah must then be according to the opinion of R' Yehuda who prohibits deriving any benefit from a peter chamor prior to the redemption. In contrast, R' Shimon maintains that there is no prohibition even then.
The Tosfot (9b s.v. le'afukei) explains, that if the sole interests in a case of doubt was just to exempt one from performing arifa, then no lamb would need to be separated. The reason is that the two are linked together. In other words, if giving the pidyon to the kohen is not necessary, then neither is arifa.
The Minchat Chinnuch (23:2) explains that the Tosfot's comment implies that R' Yehuda and R' Shimon have fundamentally different understands of the mitzvah of pidyon peter chamor.1 According to R' Yehuda, who understands that prior to redemption the peter chamor is prohibited, the mitzvah is one of redemption. After the redemption, the Torah gifted the lamb used to the kohen. Nevertheless, of prime importance is the redemption itself. If redemption is performed and was not given to the kohen, then the mitzvah has been fulfilled. Consequently, even in a case of doubt, the redemption would still be required. Furthermore, since the Torah states that arifa stands in the place of redemption if not performed, then even in cases of doubt, one would need to be concerned for the mitzvah of arifa and prefer to perform the pidyon. Yet, as explained above, once performed, the ownership of the lamb is a financial matter.
The Minchat Chinnuch continues that according to R' Shimon, who permits the chamor prior to redemption, the mitzvah is one of netina – giving the kohen a gift. If the chamor is permitted, then why does the Torah require that a lamb be separated? Simply to serve as (another) gift to the kohanim. He compares this mitzvah with pidyon ha'ben – "redeeming" the first-born male. Consequently, if the lamb was separated, but not given to the kohen, then the mitzvah has not been fulfilled. Since the entire mitzvah is one of netina and not one of redemption, in cases of doubt, the issue is purely financial and separating a lamb is unnecessary.
The Minchat Chinnuch uses this understanding of R' Shimon to explain the Tosfot above. The Gemara concluded that our Mishnah must be according to R' Yehuda. Considering the position of R' Shimon, since the "redemption" is purely financial, then in cases of doubt arifa would also be unnecessary. Redemption and arifa are link, and according to R' Shimon, since redemption is not necessary in cases of doubt, then we need not be concerned for the mitzvah of arifa either and no redemption would be required.
1 The distinction presented follows a similar pattern to the explanation of the debate between the Chachamim and R' Ilay regarding reishit ha'gez in last week's article.
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