According to Abaye, why do I also need this mishna here? If you will suggest that this mishna is necessary, as one can infer from it that if one intended to partake of half an olive-bulk the next day and then intended to partake of another half an olive-bulk the next day, both from an item whose typical manner is such that one partakes of it, the mishna teaches us that they join together in order to render the offering piggul, this suggestion can be rejected: But you already learn the halakha in this case from the first clause of the latter clause of the previous mishna, as it teaches: Half an olive-bulk outside and half an olive-bulk the next day, the offering is unfit. One can infer from this that if his intent was to consume half an olive-bulk the next day and half an olive-bulk the next day, it is piggul.

If you suggest that the mishna is necessary for a case where one intended to consume and to burn, i.e., that the mishna teaches us the matter itself, that intent to consume does not join together with intent to burn, this too cannot be. The reason is that from the inference of the first clause of the mishna you can already learn the halakha in this case, as it teaches: If one intended to partake of an item whose typical manner is such that one partakes of it, the offering is rendered piggul. This indicates that if his intent was to consume an item whose typical manner is such that one does not consume it, the offering is not rendered piggul.

The Gemara explains how the halakha that intent to consume and burn do not combine can be inferred from the mishna: Now consider, if when one intended to partake of an item whose typical manner is such that one partakes of it and to partake of an item whose typical manner is such that one does not partake of it, you say that his intentions do not join together, despite the fact that both of his intentions referred to consumption, is it necessary for the mishna to teach that intentions to consume and to burn do not join together?

The Gemara responds: Yes; although the mishna teaches the halakha of a case where one intended to consume an item typically consumed and to consume an item typically not consumed, it was necessary for the mishna to teach the halakha of a case where one intended to eat and to burn. As it might enter your mind to say that there, where one’s intentions referred solely to consumption, the halakha is that his intentions do not join together, as he intended to act not in accordance with its typical manner, since he intended to consume that which is not meant to be consumed.

The Gemara continues: But here, where his intent was to consume half an olive-bulk and to burn half an olive-bulk, where with regard to this half he intends in accordance with its typical manner, and with regard to this half he intends in accordance with its typical manner, one might say that they should join together, despite the fact that each intention concerns only half an olive-bulk. Therefore, the mishna teaches us that such intentions do not join together, and the mishna can be explained even in accordance with the opinion of the Rabbis.

MISHNA: In the case of a priest who removes a handful from the meal offering with the intent to partake of its remainder or to burn its handful on the next day, Rabbi Yosei concedes in this instance that it is a case of piggul and he is liable to receive karet for partaking of it. But if the priest’s intent was to burn its frankincense the next day, Rabbi Yosei says: The meal offering is unfit but partaking of it does not include liability to receive karet. And the Rabbis say: It is a case of piggul and he is liable to receive karet for partaking of the meal offering.

The Rabbis said to Rabbi Yosei: In what manner does this differ from an animal offering, where if one slaughtered it with the intent to sacrifice the portions consumed on the altar the next day, it is piggul? Rabbi Yosei said to the Rabbis: There is a difference, as in the case of an animal offering, its blood, and its flesh, and its portions consumed on the altar are all one entity. Consequently, intent with regard to any one of them renders the entire offering piggul. But the frankincense is not part of the meal offering.

GEMARA: The Gemara questions the terminology of the mishna: Why do I need the tanna to teach that Rabbi Yosei concedes in this instance? Let the tanna simply state: If one removes the handful from a meal offering with the intent to partake of its remainder or to burn the handful on the next day, Rabbi Yosei says that the offering is piggul and one is liable to receive karet for partaking of the remainder.

The Gemara responds: It was necessary for the tanna to teach that Rabbi Yosei concedes, because he wants to teach the latter clause of the mishna, that if his intent was to burn its frankincense the next day, Rabbi Yosei says that the meal offering is unfit, but partaking of it does not include liability to receive karet.

The Gemara elaborates: The reason the tanna links the two cases of the mishna is lest you say that the reason that Rabbi Yosei does not render the meal offering piggul is because he holds that one cannot render an offering piggul with intent that concerns only half of its permitting factors. And consequently, since the burning of the handful and the frankincense render the remainder of a meal offering permitted for consumption, then even in the first clause of the mishna, where one intends to burn the handful the next day, Rabbi Yosei should hold that the offering is not rendered piggul, as the intent does not refer to the frankincense as well.