as in all situations of impurity imparted by corpses in cases involving the public, the Merciful One permits those who are impure to perform the Temple service.

The Gemara analyzes the rationale behind the two opinions. Rav Sheshet said: From where do I derive to say that impurity is overridden in cases involving the public? It is as it was taught in a baraita: If a priest was standing and sacrificing the omer meal-offering and it became impure in his hand, the priest, who was aware of what transpired, says that it is impure and the priests bring another meal-offering in its stead. And if the meal-offering in his hand is the only meal-offering available there, the other priests say to him: Be shrewd and keep silent; do not tell anyone that it is impure.

In any case, it is teaching that he says that it is impure and the priests bring another meal-offering in its place. Apparently, when it is possible to perform the service in a state of purity, even in cases involving the public, it is preferable to do so, and the prohibition of ritual impurity is not permitted. Rav Naḥman rejected the proof and said: I concede that in a case where there are remnants of the offering designated for eating it must be performed in purity wherever possible. Although it is permitted to sacrifice an offering when impure, the mitzva to eat portions of the offering must be performed in a state of purity. Therefore, in cases where portions of the offering are eaten, the preference is to sacrifice the offering in a state of purity.

The Gemara raises an objection to the opinion of Rav Naḥman from the Tosefta: If a priest was sacrificing the meal-offering accompanying the sacrifice of bulls, rams, or sheep, and the meal-offering became impure in his hand, the priest says that it is impure and the priests bring another meal-offering in its stead. And if the meal-offering in his hand is the only meal-offering available there, the other priests say to him: Be shrewd and keep silent; do not tell anyone that it is impure.

What, is it not referring to the bulls, rams, and sheep of the festival of Sukkot, which are communal offerings that are not eaten? Apparently, even in cases of communal offerings, the priests seek to perform the service in a state of purity and the prohibition of impurity is not permitted but merely overridden.

Rav Naḥman could have said to you: No, the bulls mentioned in the Tosefta are not standard communal offerings. Rather, the reference is to the bull sacrificed when the entire community engages in idolatry unwittingly. Although this offering is a communal offering, since it has no specific time fixed for its sacrifice, we seek out a pure meal-offering in its stead.
Similarly, the rams mentioned in the Tosefta are not additional offerings of the Festival. Rather, the reference is to the ram of Aaron sacrificed on Yom Kippur. Although it has a specific time fixed for its sacrifice, since it is an offering brought by an individual, the High Priest, we seek out a pure meal-offering in its stead, as service in a state of impurity is permitted only for communal offerings.
The sheep mentioned are not those for the daily offerings or the additional offerings of the Festival. Rather, the reference is to the sheep that accompanies the omer meal-offering, as in that case, there are remnants designated for eating. Therefore, the meal-offering must be offered in purity.

The Gemara raises an additional objection to the opinion of Rav Naḥman: With regard to blood that became impure and a priest sprinkled it on the altar, if he did so unwittingly, the offering is accepted. If he sprinkled the blood intentionally, the offering is not accepted. Apparently, even in cases involving the public, performing service in the Temple in a state of impurity is not permitted. This objection is rejected: When that baraita was taught, it was with regard to the offering of an individual, where the prohibition of impurity is certainly in effect.

The Gemara continues: Come and hear a different argument based on that which was taught in a baraita. For what does the frontplate worn by the High Priest effect acceptance? It effects acceptance for the blood, for the flesh, and for the fat of an offering that became impure in the Temple, whether it became impure unwittingly or whether it became impure intentionally, whether it was due to circumstances beyond his control or whether it was done willfully, whether it was in the framework of an individual offering or whether it was in the framework of a communal offering. And if it enters your mind that impurity is permitted in cases involving the public, why do I need the frontplate to effect acceptance? If the prohibition of impurity is permitted, no pardon is necessary.

The Gemara responds that Rav Naḥman could have said to you: When the baraita teaches that the frontplate effects acceptance it is not referring to the entire list of items cited in the baraita; it is referring to an individual offering brought in impurity, not to a communal offering. The communal offering is mentioned only in the sense that in that case too, impurity is permitted, albeit for a different reason. Or if you wish, say instead: Even if you say that the frontplate effects acceptance for a communal offering, it is only for those offerings that lack a fixed time. Rav Naḥman concedes that with regard to those communal offerings that have no specific time fixed for their sacrifice, the prohibition of performing the service in impurity remains in effect and requires the acceptance effected by the frontplate.

The Gemara raises an objection. It is stated: “And Aaron will gain forgiveness for the sin committed in the sacred things that the children of Israel shall hallow in all their sacred gifts, and it shall be always upon his forehead that they may be accepted favorably before the Lord” (Exodus 28:38). And for which sin does the frontplate gain forgiveness? If it is for the sin of piggul, an offering disqualified by the intention to sacrifice or eat it after the permitted time, it has already been stated: “And if it is eaten at all on the third day, it is piggul; it shall not be accepted” (Leviticus 19:7). There is no acceptance of an offering that became piggul. And if it is for the sin of notar, meat of an offering left after the permitted time for eating it passed, it has already been stated: “And if any of the flesh of the sacrifice of his peace-offerings is eaten on the third day, it shall not be accepted, neither shall it be credited to he who offered it” (Leviticus 7:18).