Ohalos, Chapter 5, Mishnah 2. Our mishnah continues with the case of an arubah, an opening in a ceiling, what we would call a skylight: a chalon, a window, set into a roof. Here the arubah is not in an outer roof but in the ceiling that separates the house on the ground floor from the aliyah, the story above it. Something has been placed over that opening, and the question is whether it succeeds in stopping tumah from traveling from the lower floor to the upper one.
The case
"Arubah shebein habayis la'aliyah": an opening between the house below and the upper story above. "Ukedeira nesunah lah": and a pot has been set over that opening. The pot is a kli cheres, an earthenware vessel, and it is not a perfect one. "Shehi nekuvah k'konas mashkeh": it has a hole in it, and the hole is of the size through which liquid enters. That is a slightly larger hole than one through which liquid merely drips out; a small perforation will let mashkeh trickle out but will not let mashkeh in, while this hole is wide enough that if you were to lower the pot into liquid, the liquid would flow inside.
Now the three opinions. "Beis Shamai omer hakol tamei": if there is tumah in the house below, everything is tamei, the pot itself and everything in the aliyah as well. The pot will not serve as a cutoff. The tumah rises through the arubah, which is an opening of a poseiach tefach, easily large enough to carry tumah, and this damaged pot has no standing to stop it. "UBeis Hillel omer hakedeira tmei'ah veha'aliyah tehorah": Beis Hillel hold that the pot itself becomes tamei, but the upper story remains tahor. "Rebbi Akiva omer af hakedeira tehorah": Rebbi Akiva says that even the pot stays tahor.
The background from Mesechtes Keilim
To follow the machlokes we need two halachos that we learned in Mesechtes Keilim.
Begin with the special rule governing earthenware. Tumah that presses against the outer wall of a kli cheres accomplishes nothing; such a vessel is susceptible only mitocho, when the tumah gains access to the hollow inside it. Now picture an intact pot inverted over the aperture that separates the lower floor from the aliyah, its bottom pointing up toward the ceiling and its rim resting on the floor of the upper story. Tumah climbing from below reaches nothing but the pot's exterior surface, and so the vessel is immune. And a kli that has no way of receiving tumah acts as a chatzitzah, a divider, so the tumah downstairs never crosses into the room above.
Next, the shiurim of perforation that end a vessel's career as a kli. Where the owner set the vessel aside for liquids, the moment the breach is wide enough that liquid can pass inward, k'konas mashkeh, the vessel is finished and is tahor. Where the vessel was designated for dry food, more damage is required: the gap must be such that a zayis can drop through, kemotzi zayis. And what of a vessel that serves both roles, liquids and solids together? It retains its standing as a kli until the perforation reaches that olive shiur.
Our pot is exactly that kind of vessel: it is used both for milk, juice and wine, and also for cooked solid food. Practically speaking, with a hole of konas mashkeh you can no longer store milk in it, but you can certainly still cook and hold solid food in it. So this pot is damaged but not finished. It has a hole for liquid to come in, yet nothing near the size of a zayis, and therefore it is still a kli that is mekabel tumah.
Beis Shamai
For Beis Shamai the verdict is tumah across the board. The logic runs like this: a breach of konas mashkeh is modest enough that the vessel keeps its full standing as a kli, and yet it is not so modest that tumah is barred from passing through it. Take a sealed kli cheres left standing inside an ohel hameis. So long as it is shut tight, tumah has no entry and whatever lies within it stays tahor. Introduce any aperture, however, and the tumah works its way in. And earthenware, recall, is vulnerable precisely when tumah reaches its cavity, which is exactly what this perforation permits.
So this pot is caught in the middle. Had it been whole, Beis Shamai would agree that it blocks the tumah, since nothing could reach its inside. Had the hole been genuinely large, the pot would have stopped being a kli altogether, and a kli that is not mekabel tumah makes a hefsek, a separation. But the hole is big enough to let the tumah in and too small to strip the vessel of its status. The pot therefore becomes tamei, and a tamei pot cannot hold back tumah. Hence everything is tamei: the pot and the aliyah. There is a great deal more Torah in working out the precise shita of Beis Shamai, but this is the broad outline.
Beis Hillel
Beis Hillel take issue with the measurement. Their argument: this pot doubles as a container for dry food, so the breach does not suffice to declare the vessel finished as a kli; and if the gap falls short of that shiur, it equally falls short of admitting tumah. Test it: shut such an earthenware vessel, leave it in an ohel hameis with a konas mashkeh perforation in its wall, and the tumah will not reach inside. The conclusion follows by itself. Our pot is not susceptible at all, and since it cannot receive tumah, it stands as a divider and keeps the tumah from climbing into the upper story. Hence the aliyah is tahor.
Why then do Beis Hillel declare the pot itself tamei? A perforation of konas mashkeh makes no difference, and earthenware is untouched by tumah that meets only its outer surface, so by rights the vessel ought to be clean through and through. The resolution is that strict law would indeed leave the pot tahor; its tumah here is a gezeira deRabbanan, a rabbinic ruling that it be handled as though it were tamei.
Rebbi Akiva
Rebbi Akiva rules that the pot too is tahor. On the central issue he sides with Beis Hillel: a breach of konas mashkeh will not admit tumah. Close up such a vessel, set it inside an ohel hameis, and its contents survive intact despite the small hole. Our pot, then, is not susceptible, and it serves as a genuine chatzitzah dividing the tumah on the lower floor from the aliyah overhead. As for the vessel itself, it ought to be plainly tahor, since tumah on the outer surface of earthenware has no effect; and the rabbinic ruling that Beis Hillel applied here is one Rebbi Akiva does not adopt.
So the whole discussion turns on one small hole. Is a perforation of konas mashkeh an opening through which tumah travels, or is a vessel that still serves for solid food effectively intact? On that question hang the status of the pot, and with it the status of everything in the upper story.