The Mishnah (5:3) teaches that if one slaughters a korban pesach exclusively for people that were not appointed to be part of that korban pesach, for areilim (uncircumcised men) or people that are tameh then the korban is invalid. We shall try to understand the law of the areilim.
An arel (uncircumcised male) is not allowed to partake in the korban pescach. There can however, be different situations in which one might be an arel. Either because that person deliberate refused to have a brit millah. Alternatively, it may be that he is not allowed to have one. That case would be if he had other brothers that died because of having a brit millah. Does the law prohibiting an arel from being part of a korban pesach apply to all areilim?
The Tosfot (Chagigah 4b, s.v. demerabe) cites a debate between Rashi and Rabbeinu Tam regarding this matter. According to Rashi, even an arel that is halachically forced to be so, is forbidden from having a korban pesach. Rabbeinu Tam however disagrees, arguing that such an arel would be allowed. How do we understand this debate?
The Atvan Deoraita explains that the debate relates to how we understand the case of oness. The exemption in the case of oness is learnt from the case of rape. The context there is the exemption relating to the violation of a negative mitzvah. With respect to a positive mitzvah however, how it works is not clear. It could either be that one is complete exempt from that mitzvah -- the mitzvah does not apply to that person. Alternatively, the mitzvah still exists, yet one is simply unable to perform it.
A practical difference is found in the debate between the Derisha and the Taz. Normally, if one misses a tefillah, then one must mashlim -- recited shemonah esrei in the next tefillah twice. If however one was in a situation of oness when they missed the tefillah, there is debate whether the obligation of tashlumin applies. If oness means that one was exempt, then there is no need for tashlumin. If however the obligation was still in place, then one would need to be mashlim.1
The Atvan Deoraita uses this distinction to explain the debate between Rashi and Rabeinu Tam above. According to Rabbeinu Tam one is completely exempt in the case of oness. Consequently, since there is no obligation for this arel, he may take part in the korban pesach. According to Rashi however, even though this arel is oness, the obligation is still there -- it is just that he is unable to fulfill it. Consequently, since the obligation is in place, he is an arel that is not allowed to partake in the korban pesach.
The Atvan Deoraita however continues by proving that Rashi appears to maintain that an oness for this arel is completely exempt. He however further suggests that there is a difference between this arel and a regular case of oness. In this case, the Torah explicitly exempts the arel due to the risk to his life (ve'chai bahem).
Perhaps we can suggest a different basis for the debate between Rashi and Rabbeinu Tam. Both can agree that the arel is completely exempt. Nevertheless, they might argue regarding why an arel is not allow to partake in the korban pesach. Rabbeinu Tam might understand that an arel in this context is one that is obligated to have a brit millah. Since he is not obligated, he can eat from the korban pesach. According to Rashi however it is a function of whether this person is physically an arel irrespective of whether he is obligated to have a brit millah. Consequently, he cannot have any of the korban pesach.2
1 See the Atvan Deoraita who answers that there is a difference regarding the type of mitzvah. If it is a mitzvah ben adam le'makom (between man and Hashem) then in a case of oness one is completely exempt. For mitzvot bein adam le'chaveiro, the obligation is still there even if one is not able to fulfil it at that moment (e.g. maake, paying off a loan, etc).
2 This distinction may help to explain the following point. An arel kohen is also not allowed to eat terumah. The Gemara (Yevamot 71a) discusses whether a new born baby kohen, less than eight days old, can have terumah oil rubbed on their skin. Interesting the Rambam rules like the Yerushalmi (Shabbat) that the baby for the first seven days is not considered an arel. On the night of the eighth, before the day on which he can have a brit millah he is considered an arel. Interestingly, even though there is no obligation for this child to have a brit millah until the morning, its body, is already defined as an arel.
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