Keilim, Chapter 25, Mishnah 4. This chapter works out the relationship between the inside of a vessel and its outside, and how tumah that reaches one of them affects the other. Our mishnah applies that discussion to an unusual case: a single thick block of wood in which two hollows have been carved side by side, so that one piece of wood serves as two measuring receptacles. One of the hollows holds a rova (a quarter of a kav), and the hollow beside it holds only half of a rova.
The ruling concerns a wooden utensil in which a rova and a half rova have been hollowed out together: "Harova vechatzi harova". Suppose tamei liquid reached the larger cavity. The mishnah's words are "Nitma harova", the rova became tamei, and it adds: "lo nitma chatzi harova", meaning that the smaller cavity carved beside it stays tahor. The opposite case is stated as well. Should the tamei liquid come into contact with the half rova instead, the mishnah teaches "Nitma chatzi harova", and continues with the words "lo nitma harova": the larger cavity is unaffected and remains tahor.
Why should the two not be treated as one vessel that has become tamei? Because each hollow is regarded as a receptacle in its own right, with its own inside. Relative to each hollow, the neighboring hollow is nothing more than the outer surface of the block. Here the governing rule is that when the achorayim, the outside of a vessel, contract tumah from tamei liquid, the toch, the inside, does not become tamei along with it. So the tumah stays where it landed and does not carry over.
The Question of Rabbi Akiva's Students
Rabbi Akiva's disciples came to this case with a premise of their own. In their view, once a single utensil contains two cavities, one of them must be the dominant receptacle, the toch, while its companion is subordinate to it and therefore counts as achorayim. Working from that premise, they laid their objection before their teacher, "Amru lifnei Rebbi Akiva", they spoke before Rabbi Akiva, and their opening words were "Ho'il vechatzi harova achorayim larova": given that the half rova amounts to nothing more than the exterior surface belonging to the rova. Their logic rested on size: the rova is the roomier of the pair and hence the primary cavity, the toch of the utensil, which leaves the little half rova hollow beside it in the role of its outer wall.
Granting that, they pressed on: "kli shenitma tocho", a utensil whose inside has contracted tumah, "lo nitma achorav?", does its outside not become tamei along with it? This is the second clause of the halachah governing tamei liquids: tumah does travel outward from the inside, even though it never travels inward from the outside. Accordingly, once the rova, which they took to be the toch, was rendered tamei, the half rova ought to have been drawn into that tumah with it.
Rabbi Akiva's Answer
His reply opens with "Amar lahen", he told them, and continues "shel kat kodmin hee": this question belongs to an earlier group. The talmidim who came to learn from Rabbi Akiva were seated in rows before him, and he informed these questioners that those sitting in the forward rows had already put the identical difficulty to him, and that this was the response he had given them. Perhaps matters are exactly reversed: "Shema harova achorayim lechatzi harova", the rova may be nothing more than the outer side of the half rova.
In other words, even granting the students' assumption that one receptacle is primary and the other secondary, what entitles them to award the primary status to the larger hollow? Perhaps the smaller one is the essential receptacle. A person who needs to measure out half a rova cares about that hollow and nothing else, small as it is, and for him the roomier rova hollow is the secondary side of the utensil, its achorayim.
What the answer establishes is that no such determination can be made at all. Which of the two cavities counts as the primary one is dictated purely by what the user happens to need at a given moment, and precisely because either of them can be presented as the principal receptacle, neither can be locked in as principal. The mishnah's initial halachah therefore holds firm: the cavity that met the tamei liquid is tamei and its neighbor is not, for the operative principle here is "kli shenitme'u achorav", a utensil whose exterior became tamei, "lo nitma tocho", its interior does not follow it into tumah. Every cavity is an inside unto itself, and serves its fellow as nothing but an outer surface.