The beginning of the sixth perek of Pesachim discusses when erev Pesach falls out on Shabbat. It lists the processes involved in offering the korban pesach which would ordinarily be considered melachot but nevertheless can be performed on this Shabbat – they “docheh” (override) Shabbat.
There is an argument between Rebbi Eliezer and Rebbi Akiva about certain preparatory procedures. Rebbi Akiva maintains that one may not carry a korban pesach from outside of the techum on Shabbat and that one may not cut off a mum from the korban on Shabbat, while Rebbi Eliezer permits these actions. Their argument can be summed up as follows - Rebbi Eliezer permits these actions to be done on Shabbat in order to ensure that the mitzvah of korban pesach will be fulfilled, while Rebbi Akiva holds that since these actions could have been done before Shabbat, we do not allow one to perform them on Shabbat itself.
In the Mishnah, Rebbi Akiva brings support for his argument from the case of haza’ah - the sprinkling of purification waters over someone, as the final stage of the seven day purification process after coming into contact with a dead body. If the seventh and final day of this process coincides with Shabbat, R’ Akiva argues that haza’ah does not override Shabbat.
According to his reasoning however, this seems to be problematic because this person is not able to do the sprinkling before Shabbat, as he must wait until the seventh day, which in the Mishnah’s case will fall out on the fourteenth of Nissan which is a Shabbat. So this person is unable to do the haza’ah before Shabbat, unlike the other two cases cited in the Mishnah. Therefore the logic of Rebbi Akiva’s reasoning does not apply, so why should haza’ah be prohibited on Shabbat?
The Maharsha cites one answer - haza’ah is different to both the other examples cited by the Mishnah. The first two examples are essential to the korban pesach, however they can both be done before Shabbat and therefore does not docheh Shabbat. However, haza’ah cannot be done before Shabbat, as it is not its time but it also does not docheh Shabbat, because it is not an essential part to the korban pesach itself. Rather, it is an external limiting factor, and consequently cannot be docheh Shabbat. Only those things that are essential to the korban pesach itself, which cannot be done before Shabbat, are able to override Shabbat.
The Rambam however, has a different explanation of the Mishnah. The Rambam (Hilchot Korban Pesach 6:2,6) is of the opinion that one who is tamei during the day of the fourteenth, even if it is not Shabbat, is not able to eat of the korban pesach that night. This is because, since he was tamei during the day that the korban was brought, he is not able to eat of the korban that night, whether haza’ah was performed on him or not.
Consequently the Rambam holds that the Mishnah is referring to a case where the seventh day of the purification process fell on the thirteenth of Nissan which was also a Shabbat. In this case, Rebbi Akiva does not hold that haza’ah is docheh Shabbat. The Mishnah is teaching us that even in this case, where a person must do haza’ah on the thirteenth in order to be able to offer and eat the korban the next day, it is still not docheh Shabbat.
The Rambam maintains that this case is the same as the previous examples cited in the Mishnah (carrying, and cutting off a mum). Just as those examples are not docheh Shabbat, because one may do them before Shabbat, so too haza’ah is not permitted to be docheh Shabbat (on the 13th) as it can be done after Shabbat. The Rambam does not pay consideration to the fact that by doing haza’ah on the next day (14th/Sunday) that this person will be invalidated from eating the korban pesach, as this person is able to make up the korban on Pesach Sheni.
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