Mishnah 7 in chapter 7 of Maseches Eduyos brings the testimony of Rabbi Yehoshua and Rabbi Papyas on four different matters: the first two deal with tumah and taharah, and the last two with the leap year - the addition of an extra month to the Hebrew calendar. We will take up each one separately.
1. Bakers' boards:
The first testimony concerns the status of "aruchos shel nachtomin," and according to the version we have in Maseches Keilim, "aruchos." These were a kind of wooden tray on which the baker would shape the loaves before putting them into the oven. The rule regarding wooden vessels is that they do not become tamei unless they have a receptacle, a place in which something can be held, and this is derived from the exposition that compares wooden vessels to a sack, which holds things. A wooden vessel that has no receptacle does not become tamei by Torah law.
Nevertheless, flat wooden vessels - vessels that have no receptacle - do become tamei by rabbinic law, and the dispute here is whether bakers' boards are included in that decree. The reasoning for including them is that even though they have no receptacle, they are specially engineered and sophisticated implements. An ordinary householder also uses a sort of board to prepare his bread, but it is nothing more than a flat plank of wood, which does not become tamei at all; the bakers, by contrast, have a finished and precisely made tray, which, though it has no receptacle, has features that make it an efficient tool designed for its work. For this reason the Sages ruled that it is considered a vessel and does become tamei, even though by Torah law, lacking a receptacle, it would not.
The words of the Mishnah: "Hem he'idu al aruchos shel nachtomin shehen temei'os, sheRabbi Eliezer metaher" - Rabbi Yehoshua and Rabbi Papyas testified about those boards that bakers use, that they do become tamei. They needed to testify about this because Rabbi Eliezer held that since they are flat wooden vessels with no receptacle, they do not become tamei even by rabbinic law.
2. An oven cut into rings:
The second case is extremely well known. It involves a cone-shaped earthenware oven, a sort of kiln, of the type common in the era of the Mishnah. The question is its status when it was cut crosswise into rings, so that none of the pieces is particularly large and none contains the majority of the oven, and afterward the rings were stacked one on top of another, reconstructing the shape of the oven - with sand placed between each ring and the next. The sand separates the pieces, and perhaps even helps them sit straight, but it certainly prevents them from joining into one complete oven as it had been.
The common practice was that after the oven was set on the ground, it would be plastered all over with a layer of clay. Hence the question: once the oven has been plastered with clay, even though it is divided into rings with sand separating them, it looks like a single unified body wrapped in clay. Does the clay override the separation created by the sand, so that the oven once again becomes a functioning vessel that becomes tamei - or perhaps, since its parts do not have the required measure and they are separated by sand, it does not become reunified even though it is encased in clay, and it is therefore tahor?
Rabbi Eliezer ruled it tahor, while Rabbi Yehoshua and Rabbi Papyas testified that it is tamei. This is the famous case brought in Maseches Bava Metzia, page 59: Rabbi Eliezer was unwilling to retreat from his position that the oven is tahor, and he brought a series of miraculous proofs that culminated in a heavenly voice testifying from Heaven that the halachah follows him in every place. To this the Sages responded, "It is not in Heaven," and in the end they even placed him under a ban for not retracting. It is a fascinating story in its own right, and this is not the place to elaborate on it.
The law appears also in Maseches Keilim, chapter 5 mishnah 10. And the words of our Mishnah here: "Hem he'idu al tanur shechatacho chulyos venasan chol bein chulya lechulya, shehu tamei, sheRabbi Eliezer metaher" - the oven was cut crosswise into rings, sand was placed between each ring and the next when they were reassembled, and afterward it was plastered around with clay; in the view of Rabbi Yehoshua and Rabbi Papyas it once again coalesces into a single oven and becomes tamei, while Rabbi Eliezer held that it does not become reunified and does not become tamei. The halachah follows those who testified and not Rabbi Eliezer.
The leap year - background:
The final two testimonies deal with adding a month to the Hebrew calendar. It is obligatory to maintain alignment between the Hebrew calendar and the solar calendar, so that Pesach falls in the month of spring. The Hebrew calendar is based on lunar months, and each lunar month is about twenty nine and a half days; twelve such months come to three hundred fifty four days. The solar calendar, by contrast, is based on the earth's orbit around the sun, which takes three hundred sixty five and a quarter days. It emerges that every year a gap of eleven and a quarter days opens up between the solar calendar and the lunar calendar.
To keep the lunar calendar aligned with the astronomical reality of the solar cycle, an extra month was periodically added, creating a year of thirteen months. In the time of the Mishnah, the decision whether to declare a leap year was based on six factors, all of which revolve around a single question: are we ready for Pesach and for the Omer offering? For example, if the roads leading to the Beis HaMikdash were not passable because of the winter rains, so that the multitudes could not come up for the festival, they would push the date off by a month to allow people to prepare; and likewise if the grain needed for the Omer offering, the first of the barley crop, had not yet ripened.
In the time of the Mishnah, then, the decision was made each year according to the situation on the ground. Since the year 358 of the common era, more than sixteen hundred years ago, a fixed calendar has been in place, in which every nineteen year cycle contains seven leap years, and everything works out precisely. But in the time of the Mishnah a ruling was required every single year: will this year be a leap year, a year that, as it were, is pregnant with an additional thirteenth month that lengthens it.
3. Until when may the year be declared a leap year:
The third testimony deals with the question of how late the Sanhedrin may declare a leap year. The final month of the Hebrew calendar is Adar, the twelfth month, and that is when it is done. The question is how late in the month the intercalation may be announced. Originally they would not allow it to be delayed beyond Purim, which falls on the fourteenth of the month. The reason is a separate rule, that thirty days before a festival one begins to teach the laws of that festival, and the thirty days preceding Pesach begin on Purim. From Purim onward the Sages occupy themselves with the laws of Pesach in preparation for it, and therefore, if they were to inform the public that Pesach was still a full month away, people would not believe it. They would say: we have already begun learning the laws of the festival, a sign that we are within the thirty days.
Concerning this Rabbi Yehoshua and Rabbi Papyas testified that the public does understand the matter: people know that although ordinarily thirty days pass between Purim and Pesach, sometimes sixty days pass when the year is made a leap year. Therefore the announcement may be delayed until the end of the month, and the twenty ninth of Adar is the last opportunity. As a side point it is worth noting: even though Adar may have thirty days, since the thirtieth day may already be Rosh Chodesh Nisan and the beginning of the new year, no month may be added on that day, for it is too late an hour. But until the twenty ninth of Adar, according to them, it is still possible.
The words of the Mishnah: "Hem he'idu she'me'abrin es hashanah b'chol Adar, she'hayu omrim ad haPurim" - an additional month may be added to the year throughout the entire month of Adar, and they came to testify to this because originally it was said that the final date is Purim, the fourteenth of the month, for the reason explained.
4. Declaring a leap year conditionally:
The basic protocol of the Sanhedrin required the approval of the Nasi, the head of the Sanhedrin, in order to declare a leap year. Hence the question: may the members of the Sanhedrin convene and announce the additional month in the absence of the Nasi, with the announcement made conditional upon his approval, so that when he learns of it and approves, the intercalation takes effect retroactively? Rabbi Yehoshua and Rabbi Papyas testify that this may indeed be done.
The words of the Mishnah: "Hem he'idu she'me'abrin es hashanah al tenai" - the Sanhedrin may decide to add a month to the year, and afterward the Nasi gives his approval retroactively. And so it actually happened: "U'ma'aseh b'Rabban Gamliel she'halach litol reshus me'hegemon b'Surya". Rabban Gamliel was the Nasi in the era of Yavneh, the first Nasi after Rabbi Yochanan ben Zakkai established Yavneh, and it is there that all the testimonies of this tractate take place. He went to Syria, to the Roman governor there, in order to obtain permission regarding a certain matter. The word 'hegemon' means the leader, the person in charge of the place, and from it the foreign word 'hegemony' is derived.
"V'shahah lavo" - Rabban Gamliel was delayed in returning, and was still in Syria at the time when the Sanhedrin in Yavneh wished to declare a leap year. "V'ibru es hashanah al tenai lichsheyirtzeh Rabban Gamliel" - they declared the year a leap year and added a month, on the condition that when the Nasi returned he would confirm the matter and give his consent. "U'ksheba amar rotzeh ani" - when he returned from Syria he said: yes, this is my wish, that the year be made a leap year with an additional month. "V'nimtzeis hashanah me'uberes" - the year was retroactively made a leap year from the moment the Sanhedrin declared it, even though at that time the Nasi had not approved it, since they had done so conditionally and dependent upon his approval, which was ultimately given.
In summary: in this Mishnah Rabbi Yehoshua and Rabbi Papyas testified about four matters. In the area of tumah and taharah: bakers' boards are susceptible to tumah even though they are flat wooden vessels, contrary to the opinion of Rabbi Eliezer who declares them pure; and an oven that was cut into rings with sand placed between them and plastered over with clay is impure, here too against Rabbi Eliezer who declares it pure, and this is the famous case found in tractate Bava Metzia. Regarding the leap year: the year may be declared a leap year throughout the entire month of Adar and not only until Purim, and it may even be declared conditionally, pending the Nasi's retroactive approval, as in the incident with Rabban Gamliel, who was delayed in Syria and upon his return said "this is my wish".