Rather, it is not difficult: There, where Rabbi Yehoshua said that it is invalid ab initio, he was referring to the offering of an individual. Here, in the mishna, which states that it may be sacrificed even ab initio, it is referring to an offering involving the public.

The Gemara asks: Shall we say that the mishna is not in accordance with the opinion of Rabbi Yosei? As it was taught in a baraita: Rabbi Eliezer says that the frontplate appeases God for the impurity of portions of offerings that are supposed to be eaten. Rabbi Yosei says that the frontplate does not appease God for the impurity of portions of offerings that are supposed to be eaten; it appeases God only for the impurity of the parts of offerings that are burned on the altar.

The Gemara explains the question: It could enter your mind to say: From the fact that Rabbi Yosei said that the frontplate does not appease God for the impurity of portions of offerings that are supposed to be eaten, it can be inferred that he holds in accordance with the opinion of Rabbi Yehoshua, who said that we require the two parts of the offering, the blood and the meat, to be valid. If this were not the case, it would be sufficient for the frontplate to appease God for the impurity of the blood, and it would not be necessary for the frontplate to appease God for the impurity of the portions of offerings that are supposed to be eaten. Let us now say that the mishna is not in accordance with the opinion of Rabbi Yosei.

The Gemara rejects this assertion: No, Rabbi Yosei holds in accordance with the opinion of Rabbi Eliezer, who said that the blood of an offering is accepted although there is no meat.

The Gemara asks: If so, with regard to what halakha did Rabbi Yosei say that the frontplate does not appease God for the impurity of the portions of offerings that are supposed to be eaten? Even if it does not appease God for the impurity of these portions, the offering remains valid. The Gemara rejects the question: And according to your reasoning, with regard to Rabbi Eliezer himself, who said that the frontplate appeases God for the impurity of the portions that are supposed to be eaten, since he said that the blood may be sprinkled although there is no meat, with regard to what halakha did he make his other statement that the frontplate appeases God for the impurity of the portions of offerings that are supposed to be eaten? Clearly, whether the frontplate appeases God is significant for reasons other than ensuring that an offering is accepted.

Rather, the fact that they disagree about whether the frontplate appeases God for the impurity of the portions of offerings that are supposed to be eaten determines whether it is possible to establish the offering as one disqualified due to improper intent [piggul] and whether it is possible to exclude the offering from the prohibition of misuse of consecrated property. The dispute is to be understood in this light: Rabbi Eliezer holds that the frontplate appeases God for the impurity of the meat that is supposed to be eaten, and it renders it like pure meat that is not disqualified. Therefore, although the meat may not be eaten, it may be established as piggul. Similarly, because it is treated as though it were pure, the sprinkling of the blood of the offering excludes the meat from the prohibition of misuse of consecrated property.

And Rabbi Yosei holds that the frontplate does not appease God for the impurity of sacrificial meat that has become impure, and it does not render it like pure meat. Therefore, sprinkling the blood of the offering does not establish it as piggul and does not exclude it from the prohibition of misusing consecrated property.

Rav Mari strongly objects to this conclusion: Even granting that Rabbi Yosei holds in accordance with the opinion of Rabbi Eliezer that an offering is accepted through the blood alone, even if the meat has become ritually impure, there is still a difficulty. Granted, in the case of animal offerings, which have two permitting factors, the blood and the meat, there is at least one of them, the blood, for which the frontplate appeases God and causes the offering to be accepted. With regard to the omer, too, there is the handful, for which the frontplate appeases God and is thereby validated. With regard to the shewbread, too, there are the bowls of frankincense, which permit the bread in the same manner that the handful permits a meal-offering.

But with regard to the two loaves, what is there to say? They are completely eaten, and nothing is brought on the altar. How can they be brought in a state of ritual impurity, as the mishna has stated, according to the opinion of Rabbi Yosei?

And if you say that the two loaves are valid because the frontplate appeases God for the impurity of the two lambs that are sacrificed with them, this is the same as the communal peace-offerings that are mentioned separately in the mishna. If so, there are only four offerings listed in the mishna. But we learned in the mishna that there are five, because the two loaves and the communal peace-offerings are listed separately.

Rather, the previous suggestion is rejected. Instead, it is suggested that Rabbi Yosei holds that ritual impurity is permitted in cases involving the public, even without the frontplate. Therefore, the two loaves remain valid.

The Gemara asks: But wasn’t the following baraita taught concerning the purity of both the High Priest on Yom Kippur and the priest who burns the red heifer, each of whom is separated from his house for seven days to ensure his purity? The baraita states: In the case of both this priest and that priest, one sprinkles on him all seven days of his separation from all the purification offerings, i.e., the ashes of the red heifers, that are there in the Temple. If he had become impure through contact with a corpse, he will be purified through the sprinkling of the purification offering. This is the statement of Rabbi Meir. Rabbi Yosei says: One does not sprinkle upon him on any day except for the third and seventh days of his separation. This ensures his purification.

And if it enters your mind that Rabbi Yosei holds that ritual impurity is permitted in cases involving the public, why do I need sprinkling at all? The offerings of Yom Kippur are communal offerings and may be sacrificed even in a state of ritual impurity. Rather, it is clear that the mishna is not in accordance with the opinion of Rabbi Yosei.

With regard to Rabbi Yosei’s statement quoted earlier, Rav Pappa said to Abaye: Rabbi Yosei is like a document that awards something to two conflicting parties, as it was taught in a baraita that Rabbi Yosei said: I see as correct the statement of Rabbi Eliezer with regard to animal offerings, and the statement of Rabbi Yehoshua with regard to animal offerings, and the statement of Rabbi Eliezer with regard to meal-offerings, and the statement of Rabbi Yehoshua with regard to meal-offerings.

The statement of Rabbi Eliezer is correct with regard to animal offerings, as he would say that the blood brings atonement although there is no meat. The statement of Rabbi Yehoshua is correct with regard to animal offerings, as he would say that if there is no blood there is no meat, and if there is no meat there is no blood. The statement of Rabbi Eliezer is correct with regard to meal-offerings, as he would say that the handful is fit although there is no remainder. The statement of Rabbi Yehoshua is correct with regard to meal-offerings, as he would say that if there is no valid handful there is no remainder, and if there is no remainder there is no handful. Rabbi Yosei accepted several contradictory statements.

Abaye said to him: Rabbi Yosei did not intend to issue a halakhic ruling in favor of both opinions. Rather, he said what was reasonable. How so? When involved in studying the halakhot of animal offerings, he said: It is reasonable that just as they disagree with regard to animal offerings, they also disagree with regard to meal-offerings. When involved in studying the halakhot of meal-offerings, he said: It is reasonable that just as they disagree with regard to meal-offerings, they also disagree with regard to animal offerings.

Rav Pappa said to him: It works out well to say that when he was involved in animal offerings, he said: It is reasonable that just as they disagree with regard to animal offerings, they also disagree with regard to meal-offerings, as the essential verses written about this topic are written with regard to animal offerings. But it does not seem realistic to say that when he was involved in meal-offerings, he said: It is reasonable that just as they disagree with regard to meal-offerings, they disagree with regard to animal offerings. Aren’t the essential verses about this topic written with regard to animal offerings? Clearly, meal-offerings would not serve as a model for animal-offerings.

Rather, this answer has been refuted, and Rabbi Yosei’s statement is not difficult for a different reason. When he said: I see as correct the statement of Rabbi Eliezer, he was referring to cases in which part of the offering became impure. When he said that he agreed with the opinion of Rabbi Yehoshua, he was referring to cases in which part of the offering was lost or burned. In other words, Rabbi Yosei partially accepts the opinions of both Rabbi Eliezer and Rabbi Yehoshua.

The Gemara asks: In a case in which the offering became impure, what is the reason that Rabbi Yosei accepts the opinion of Rabbi Eliezer? It is because the frontplate appeases God for the impurity. But this is impossible, as you have heard that Rabbi Yosei said that the frontplate does not appease God for the impurity of the portions of offerings that are supposed to be eaten.

Rather, this answer should be rejected, and Rabbi Yosei’s opinion is not difficult for the following reason. When he said: I see as correct the opinion of Rabbi Eliezer, he was referring to a case in which an offering involves the public. When he said: I see as correct the opinion of Rabbi Yehoshua, he was referring to the offering of an individual.

The Gemara asks: With regard to an offering involving the public, what is the reason that Rabbi Yosei accepts the opinion of Rabbi Eliezer? It is because ritual impurity is permitted in cases involving the public. This explanation can be rejected for two reasons. One reason is that you have heard that Rabbi Yosei said that ritual impurity is merely overridden in cases involving the public; it is not wholly permitted. And furthermore, if Rabbi Yosei was referring to the offering of the public, is it only Rabbi Eliezer who validates the offering, and not Rabbi Yehoshua?