Ohalos, Chapter 5, Mishnah 3. This chapter deals with an arubah, an opening in the ceiling of a lower room which is at the same time a hole in the floor of the upper story. Stand in the aliyah and look down through it and you can see the room below (and you had better watch your step). Tumah in the lower room would ordinarily rise through that opening and render everything in the upper story tamei. The question the Mishnah keeps returning to is what happens when a keli is set over the opening: does it seal the two floors off from one another, so that the tumah below stays below?
Here the case is as follows. A kedeirah, an earthenware pot, is lying over the arubah with its base facing downward toward the lower room, and there is tumah (a meis) in the room below. The Mishnah stresses about this pot: "hoysah shleimah", it was whole. There is no perforation in it at all: not a hole the size of a zayis, which is the measure that renders a k'li cheres used for dry foods unfit and therefore no longer able to receive tumah, and not even the smaller hole through which liquid would seep out. It is a perfectly intact vessel. What, then, is the status of the pot itself, and what is the status of the food, the drink and the keilim sitting in the aliyah above it?
The two opinions
Beis Hillel say "matzalas al hakol", the pot saves everything. Their logic runs as follows. Since the vessel has no breach anywhere in it, the tumah beneath has no route into its airspace. All the tumah meets is the exterior wall of a clay vessel, and clay takes on tumah exclusively through its inner cavity; contact from without leaves it entirely unaffected. The kedeirah therefore remains tahor, and once a tahor vessel lies spread across the opening it acts as a chatzitzah, halting the tumah right where it is. Nothing in the aliyah is touched: keilim, ochlin and mashkin all remain tahor.
Beis Shammai accept every step of that analysis of the pot, yet they reach a narrower conclusion: "einah matzalas ela al ha'ochlim v'al hamashkin v'al klei cheres", its protection reaches only foods, liquids and vessels of earthenware. Whatever food, drink or clay utensil stands upstairs remains tahor. Keilim of wood, of metal and the like, however, become tamei. The Mishnah then reports the final outcome: Beis Hillel withdrew from their position and went on to teach the halachah exactly as Beis Shammai had stated it.
Why should the ruling be selective?
The obvious difficulty cries out. If the pot is intact, if there is no opening for tumah to enter it, and if it therefore does not receive tumah at all, it should be a full barrier. And if it is not a barrier, nothing upstairs should be saved. Why pick and choose, saving ochlin, mashkin and k'lei cheres while abandoning wood and metal?
One might be tempted to answer simply that wooden and metal vessels have a remedy: they can be immersed in a mikveh and made tahor again, whereas a k'li cheres has no taharah in a mikveh (the only way to remove its tumah is to break it), and there is no such thing as immersing food or drink; you cannot dip a tamei orange in a mikveh and call it tahor. True enough as a fact, but that still does not explain why the pot saves one category and fails for the other.
The pot belongs to an am ha'aretz
The crux of the Mishnah lies in the identity of the pot's owner: this kedeirah resting across the opening is the property of an am ha'aretz. Such a person does not guard the taharah of what he eats, and the Chachamim ruled that his standing is that of an av hatumah. Once that is his standing, anything he handles, be it a keli, ochlin or mashkin, picks up tumah from him. Any vessel found in his possession must consequently be assumed tamei, since in all probability he took hold of it at some point. Our earthenware pot, which happens to be lying over the passage joining the lower room to the story above it, is accordingly b'chezkas tamei. All of this operates only m'd'Rabbanan: the Rabbanan are the ones who assigned him the standing of an av hatumah, and the presumed tumah of his keilim follows on its own from that. In practical terms, though, the pot counts as tamei. And the principle holds firm that a vessel can hold tumah back only when it is itself tahor. That is precisely why this pot cannot function as a chatzitzah.
Then why does it save anything at all?
Now to the second half of Beis Shammai's ruling, the half Beis Hillel eventually adopted. Chazal applied this decree with care. Imagine walking over to an am ha'aretz and announcing that all his vessels are tamei because he himself ranks as an av hatumah; he would never accept such a claim. "Me, an av hatumah? On what grounds? I am tahor and so are my keilim." Chazal had no interest in making his life miserable. Their worry was only this: a man unschooled in the laws governing tumah and taharah could easily have contracted the tumah of a meis without ever noticing. The decree was therefore enforced wherever it would head off a genuine mishap, and not pressed in situations where enforcing it would accomplish nothing.
Consider how the am ha'aretz himself reads the situation. A meis lay in the room below, but his pot was covering the gap, and as far as he is concerned everything above it was shielded. Suppose we allow him that assumption regarding the food, the drink and the clay vessels standing in the upper story. Who is hurt by it? Picture a chaver, someone meticulous in tumah and taharah, who has shown that he commands these halachos (and Keilim and Ohalos give some sense of how many there are, with plenty still ahead). Such a person already knows that food or drink handled by an am ha'aretz is off limits to him, as are earthenware vessels an am ha'aretz has touched, all of them presumed tamei however sincerely their owner believes otherwise. Nor is immersion any solution for him: dipping food or drink accomplishes nothing, and clay has no taharah in a mikveh. The chaver will keep clear of these items from the outset. Practically speaking, then, we can allow that this am ha'aretz's clay pot over the arubah does rescue the ochlin, the mashkin and the vessels of cheres above it. Nothing is lost by it, and life in his household continues exactly as before.
Where the real stumbling block lies
Vessels that can be purified in a mikveh stand on entirely different footing: wood, metal, hide. Here the risk is real, and here we hold firm to the decree: the pot counts as tamei, it does not interpose, and those keilim in the aliyah are tamei. Picture the scene. A chaver's wife sends him upstairs to borrow a pot from the neighbor, and the neighbor is an am ha'aretz. He says to himself, "No problem, I will take it to the mikveh and toveil it." Such a calculation is thoroughly realistic: he knows that an am ha'aretz pays no attention to these matters and bears the Rabbinic standing of an av hatumah, so a tevilah ought to settle the question.
And there lies the trap. The chaver has no idea that this vessel carries more than the tumah conveyed by an am ha'aretz's touch: it bears tumas meis. Against tumas meis, immersion on its own achieves nothing whatsoever. The keli requires sprinkling on the third day and again on the seventh with water containing ash of the Parah Adumah, a procedure spanning a full week, and only afterward does it enter the mikveh. Normally a vessel borrowed from an am ha'aretz raises no suspicion of having shared a roof with a meis, and a tevilah truly is the answer. Here, however, exposure to a meis is exactly what occurred: a meis lies in the room below, and the sole thing separating it from the upper story is that clay vessel of his, tamei m'd'Rabbanan and therefore incapable of serving as a barrier. The tumah has a Rabbinic source, yet in practice it is treated as tumas meis.
This, then, is the balance struck by Beis Shammai, and Beis Hillel came around to it. There is no difficulty in telling the am ha'aretz that his pot covered the opening and his food, his drink and his earthenware upstairs are fine, even though strictly speaking his pot is presumed tamei and should not have interposed at all, since no one will be led astray by it. But he must be told that his pot does not rescue the vessels that have taharah in a mikveh, and that they carry tumas meis, for here a chaver may well come to borrow one of them, immerse it, and never suspect that a tevilah is insufficient without haza'ah on the third and seventh day.