Ohalos, Chapter 5, Mishnah 1. Our Mishnah presents a case in which tumah reaches an oven not through its own mouth, but through the pipe that carries off its smoke, and the Tannaim disagree about how far that tumah travels.
What Their Oven Looked Like
Before we can picture the case, we have to picture the oven. Their tanur was shaped roughly like an ice cream cone standing upside down. It did not narrow to a point at the top; rather there was an opening up there, and that is where the dough was placed in and the finished bread was removed. Lower down there was a second opening, through which the wood was fed in and the fire was tended.
Every oven needs somewhere for the heat and smoke to escape, just as an oven or a dryer in our own homes does. Their ovens too had a pipe leading out of the top, and that pipe fit into an opening in the oven, so that the smoke could be carried away. This pipe is what the Mishnah calls the ayin of the tanur.
The Case
The Mishnah opens: "Tanur she'omeid besoch habayis ve'eino kemurah lachutz." An oven is standing inside the house, positioned near a wall, and its vent pipe protrudes through the wall to the outside. If you stand outdoors you see a pipe emerging from the wall; if you step inside the house you see that the very same pipe leads into the oven.
Now: "vehe'eelu alav kovrei hameis." A group was carrying a meis out to be buried, and as they walked along outside the house, the meis passed directly over the protruding pipe. For that moment the meis served as an ohel spread over the ayin of the oven. What is the halachah?
Beis Shammai: Everything Is Tamei
"Beis Shammai omrim hakol tamei." According to Beis Shammai, everything becomes tamei: the oven itself and everything inside the house. Their reasoning is that the tumah enters the oven by way of the pipe, and once it is inside the oven it does not stop there. Recall that the oven has an opening facing into the house at its lower end, so the tumah continues out of the oven and spreads through the entire house. The tanur is tamei, and so are the keilim standing in the house.
Beis Hillel: The Oven Only
Beis Hillel respond: "U'Beis Hillel omrim, hatanur tamei vehabayis tahor." On the opening step they concur: the tumah does descend through the pipe, and the tanur becomes tamei. But what claim does the rest of the house have on this tumah? At the oven the tumah comes to rest. In Beis Hillel's understanding it makes no further journey outward from the tanur, and therefore the house, together with the keilim standing in it, stays tahor.
Rebbi Akiva: Even the Oven Is Tahor
A third opinion is recorded: "Af hatanur tahor," says Rebbi Akiva. He carries the leniency one step past Beis Hillel. Not only is the house untouched; the oven is unaffected as well. His logic is straightforward: the meis never hovered above the tanur in the first place. It hovered above a pipe. And in Rebbi Akiva's view, tumah of that kind never arrives at the oven at all.
A Parallel Mishnah in Maseches Keilim
This ruling of Rebbi Akiva echoes something taught in Maseches Keilim, Chapter 8, Mishnah 7. That Mishnah discusses a kezayis min hameis resting within the ayin hatanur, the smoke pipe, in a case where the pipe has no posei'ach tefach (its interior does not measure a cubic tefach: a tefach in length, a tefach in width, and a tefach of height). Under those conditions the tumah is blocked from descending into the oven below, and the tanur remains clean of it.
The principle behind that ruling is one we return to again and again: without a posei'ach tefach, the space is not treated as a separate entity, and it is not an ohel in its own right. And when tumah sits in a place that is not an ohel of its own, where does it go? It breaks straight upward through the covering above it and does not spread off to the sides.
Where the Machlokes Lies
Beis Shammai and Beis Hillel have no quarrel with that Mishnah in Keilim; there they do not argue at all. They agree that when the tumah is inside the pipe and the pipe lacks a posei'ach tefach, the tumah rises straight up and goes no further. But our case, they hold, is different. Here an actual meis is spread over the pipe from above, and that form of tumah does spread: it travels through the pipe and into the oven. From there, Beis Shammai say it continues into the house; Beis Hillel say it stops at the oven.
Rebbi Akiva, by contrast, draws no distinction between the two situations. If tumah situated within a pipe that lacks a posei'ach tefach cannot make its way down to the oven, then a meis stretched above that very same pipe should likewise be unable to send its tumah downward into it. Hence his ruling that the tanur, no less than the house, escapes tumah.