Keilim, Chapter 5, Mishnah 7. Earlier in Masechet Keilim we learned a fundamental rule about earthenware: a clay vessel that has become tamei has no path back to purity through water. Immersing it in a mikveh accomplishes nothing. The only way it sheds its tum'ah is by being broken, since once it is no longer a vessel there is nothing left to carry the tum'ah. Our Mishnah applies that principle to a large item, an earthenware oven, and asks the practical question: how much breaking is enough?
The Mishnah opens: "Tannur shenitma, keitzad metaharo?" An oven of earthenware became tamei. By what means is it purified? In other words, to what extent must it be broken up before it stops being an oven?
Dividing it into three
"Cholko lishlosha." He splits it into three. In practice this means making three vertical cuts through the wall of the oven, each one running the full height of the wall, from its upper rim straight down.
At first glance this seems like more than necessary. Two cuts would already split the oven apart, so why insist on three sections? The answer lies in a rule we know regarding broken vessels: if one piece contains the majority of the original vessel, that piece is still treated as the vessel itself and retains its properties, and with them its tum'ah. Cutting an oven in only two places is likely to produce an uneven split, with one piece larger than the other, and that larger piece would remain tamei. Dividing into three guarantees the result automatically: no single piece of three can be the majority, so nothing is left that still counts as the original oven.
The outer coating and the depth of the cut
"Vegored es hatefilah." The plaster must be removed as well: that smeared layer of clay covering the oven's outer surface has to be scraped off. Leave it in place, and the segments stay bonded to one another even after the cuts have been made, so the oven has not genuinely come to pieces.
"Ad sheyehei ba'aretz." The cuts in the wall must run all the way down to the ground. If any portion of the wall at the bottom remains uncut, that strip continues to hold the sections together, and the oven is not considered broken at all.
The opinion of Rabbi Meir
Rabbi Meir eases both requirements. "Rabbi Meir omer": in his view "eino tzarich", one is under no obligation "ligror es hatefilah", to scrape off the coating where the cuts pass through it. And "velo ad sheyehei ba'aretz": neither is there any demand that each cut be carried down as far as the floor.
What does suffice? "Ella me'ato mibifnim", he chips away at the walls working from within, "arba'a tefachim", until under four tefachim of the oven are left whole. Once that much has been removed, Rabbi Meir treats the oven as a broken one, and it is of no consequence that the outer clay is still holding the fragments in place.
The opinion of Rabbi Shimon
"Rabbi Shimon omer: tzarich lehasi'o." Rabbi Shimon takes the opposite direction and is stricter even than the first Tanna. In his view it is not enough to scrape the coating and cut through to the ground; one must also physically move the sections apart from one another. For the first Tanna, once the cuts are complete and the plaster has been removed, the job is done and the oven is tahor. For Rabbi Shimon, the pieces must actually be separated and drawn away from each other before purity takes effect.
An uneven division into two
"Chalako lishnayim, echad gadol ve'echad katan": he cut it in two, and the two resulting pieces came out unequal, one bigger and one smaller. The ruling is "hagadol tamei vehakatan tahor", the bigger piece stays tamei while the smaller becomes tahor.
Precisely this outcome is what made a threefold division necessary in the first place. The bigger fragment holds most of what had been there, and halachah therefore refuses to view it as broken at all. It inherits the standing of the oven together with the tum'ah that oven already bore. The smaller fragment, by contrast, can no longer be called an oven, so its tum'ah falls away and it emerges tahor.
Three sections, one of them a majority
"Chalako lishlosha, echad gadol kishnayim, hagadol tamei ushnayim haketanim tehorim." Suppose the cutting yielded three pieces, but one of them equals the two others put together: that oversized piece remains tamei, while the pair of smaller ones are tahor.
Three pieces were produced, yet the split came out so unbalanced that one of them holds over half of what the oven had been, each of the remaining two amounting to under a quarter. Because the large piece carries the majority, it keeps the status of an oven and stays tamei. Neither of the small pieces holds a majority, so both forfeit the character of an oven altogether; they simply cannot be called one any longer, and they are tahor.
The Mishnah thus leaves us with a clear measure. Earthenware departs from tum'ah only by ceasing to be a vessel, and an oven ceases to be an oven only when no surviving fragment can claim to be the majority of what stood there before. Whether the coating must be scraped, how deep the cut must run, and whether the pieces must be pulled apart are the points on which the Tanna'im differ, but the underlying principle is shared by all of them.