Menachos, Chapter 2, Mishnah 2. This Mishnah too deals with the laws of piggul and with the fine points of multiple matirin (permitting agents) and multiple items being permitted, just as we learned in the previous Mishnah. The two offerings this Mishnah discusses are the shtei halechem (two loaves) and the lechem hapanim (showbread).
Shtei halechem - the two loaves of bread brought on Shavuos together with the two lambs.
Lechem hapanim - twelve loaves arranged on the Table in the Heichal, in the vessel designated for that purpose, from Shabbos to Shabbos, in two arrangements: two rows of six loaves each. On top of the two rows rest two bazichin (spoon-like vessels), each holding a full handful of frankincense. The frankincense is burned on the altar, and the loaves are eaten by the kohanim.
The structure of the two offerings:
The structure of the two offerings is very similar. The Chumash calls both of them menachos, neither of them goes up on the altar, and both are eaten by the kohanim. And in both there is a matir:
By the shtei halechem: the slaughtering of the two lambs is what sanctifies the offering with kedushas haguf, inherent sanctity, and the sprinkling of the lambs' blood is what permits the eating of the two loaves.
By the lechem hapanim: the burning of the frankincense in the two bazichin, which rest on top of the two arrangements all week long, is what permits the eating of the twelve loaves of the showbread.
The question of the Mishnah:
Since we have here two separate loaves and two separate arrangements, with each arrangement of the showbread having its own bazich, and both arrangements being permitted by the two lambs, the question arises: a person can cause piggul through an intention of eating beyond the proper time at the moment the lamb's blood is sprinkled or at the moment the frankincense in the bazich is burned, by intending to eat the bread past its proper time. But what is the law when he had in mind specifically one loaf alone, or one row of the showbread - how does that affect the second loaf or the second row? Here too Rabbi Yose disagrees with the Sages, as in the previous Mishnah, although the reason is different, and once again Rabbi Yose distinguishes between the two loaves while the Sages do not.
"Shachat shnei kevasim le'echol achas min hachalos lemachar" - on Shavuos the kohen performed one of the essential services (slaughtering, receiving the blood, or sprinkling it) on one of the lambs or on both, whose blood permits the two loaves, and he intended specifically to eat loaf number one tomorrow and not today. These are piggul intentions, and loaf number one has certainly become piggul; the question is what the law is regarding loaf number two.
"Hiktir shnei bazichin le'echol echad min hasedarim lemachar" - he burned one of the bazichin of frankincense or both of them, which are the matir for the eating of the showbread, and he explicitly intended that one of the two rows be kept for tomorrow, after Shabbos. (It is worth noting that there is a dispute about the time for eating the showbread: from the language of the Bartenura it appears that the time is Shabbos alone, while most of the poskim, among them the Rambam, understood that its time for eating is like that of a Shabbos afternoon offering and the night that follows.) Either way, the question stands: what is the law regarding the second arrangement?
"Rabbi Yose omer: osah hachalah ve'oso haseder shechishev lah - piggul vechayavin alav kares, vehasheni pasul ve'ein bo kares" - Rabbi Yose distinguishes between them: that particular loaf, or that particular arrangement of six, about which he had the intention concerning half, becomes piggul, and one who eats it is liable for kares. But the second one is not piggul, only pasul - and even though this is a disqualification from the Torah, unlike the previous Mishnah where the disqualification was rabbinic - there is no kares for it, since he did not have it in mind. The reason for the distinction is that the loaves are kneaded separately, and there is even a requirement that each of the two loaves be kneaded in a separate bowl, so there is a separation between them, and likewise with the showbread each arrangement stands on its own.
"Vachachamim omrim: zeh vazeh piggul vechayavin alav kares" - the Sages disagree and hold that if he had an intention of eating beyond the proper time regarding one of the two loaves or one of the two arrangements, all the bread becomes piggul and one who eats it is liable for kares, even that portion which he did not directly have in mind. And this is the halachah.
The law of tumah in one of the loaves or in one of the arrangements:
A further point, somewhat connected to this, is another dispute, and here it is Rabbi Yehudah who disagrees rather than Rabbi Yosei: what is the law when one of the two loaves became tamei, or one of the two rows, but not the other?
"Nitmeis achas min hachalos o echad min hasedarim - Rabbi Yehudah omer: sheneihem yeitz'u l'veis hasereifah" - in Rabbi Yehudah's view everything is treated as tamei and goes out to the place of burning, since they are joined to one another. He had a tradition that "a communal offering is not divided": the communal shelamim of Shavuos, which the two loaves accompany, are a communal offering, and so too the lechem hapanim. Therefore, if one part became tamei, all of it became tamei. This is not based on a verse, nor even on logic, but on tradition alone.
"Vachachamim omrim: hatamei b'tumaso v'hatahor yei'acheil" - the Sages did not have this tradition, and therefore they rejected this principle: whatever became tamei is tamei and must be destroyed and burned, but whatever remained in its purity is eaten according to its law. They thus reject the idea that everything is joined together.
When did the tumah occur:
The Bartenura, following the approach of the Rambam: Rabbi Yehudah is speaking only of a case where the tumah occurred before the sprinkling of the blood of the lambs. Until the sprinkling they are united, and afterwards they are merely loaves of bread, each one standing on its own.
Rabbeinu Gershom (and Rashi, who follows the tradition of Ashkenaz): in Rabbi Yehudah's view, even after the sprinkling of the blood the loaves are still joined to one another, and if one of them became tamei both became tamei.
The halachah: the halachah does not follow Rabbi Yehudah but the Sages, and therefore each of the breads stands on its own: if one loaf or one row became tamei, that loaf or that row is not eaten, while the other is eaten according to its law. And this is the law whether the tumah occurred before the permitting factor or after it, whether at the sprinkling of the blood or at the burning of the bazich and the frankincense.