Keilim, Chapter 22, Mishnah 2. This mishnah takes us to the dining room, and to a piece of furniture that we all know: a table standing on three legs. The question the Mishnah explores is what happens to such a table, in terms of tumah and taharah, as its legs are broken off one by one.
The first case in the Mishnah reads: "hashulchan shenitla achat meraglav, tahor." Take away one of the three supports, and the table is now tahor. What is the reasoning? A surface propped up on nothing but two legs does not function as a table at all. It tilts, it will not hold steady, and no one could lay out a meal on it. Having lost the ability to perform the task it was built for, it forfeits its standing as a kli, and an object that is broken beyond its use cannot contract tumah.
The Mishnah continues: "nitla hashniya, tahor." Take away a second support, and the ruling is unchanged: still tahor. The logic here requires no effort. If the loss of a single leg already emptied the table of its usefulness, then with two of them gone it stands even less securely and serves even less of a purpose.
"Nitla hashlishit, tamei." But now comes the surprising turn. Once the third leg is also removed, and all that is left is the flat tabletop lying on its own, the object becomes able to receive tumah once again. The reason is that it has stopped being a broken table and has become something useful in its own right: a board that one can carry and eat off of, a serving tray.
The Mishnah immediately qualifies this: "kesheyachshov alav." This new status depends on his machshavah, his intention. The tabletop, now stripped of all its legs, has the potential to serve as a tray, but potential alone is not enough. The owner must decide in his mind that this is what the board is going to be from now on. Once he thinks that thought, the object takes on its new identity as a kli, and from that moment it can become tamei.
"Rebbi Yose omer, ein tzarich machshavah." Rebbi Yose disagrees. In his view no new intention is needed at all, because nothing has really changed about how this object is being used. When it was a table, the surface on top was the part that people ate upon. Now that same surface is still being eaten upon, only that it is a tray rather than a table. Since the function was never interrupted, the board is a kli automatically, without any need for the owner to redirect it in his mind.
The Mishnah ends with the words "vechein hadilufki." A dilufki is a small auxiliary table on which food is brought out, and everything taught here applies to it as well. We might have assumed it would be treated differently, seeing as people do not normally take their meal directly from its surface. The Mishnah rules otherwise: a dilufki that has broken is judged by precisely the standard we applied to the table, remaining tahor while one or two of its legs are missing, and becoming capable of contracting tumah once none of the legs remain and it does the work of a tray.
The lesson of this mishnah is that tumah follows usefulness. An object damaged halfway is nothing at all, while the very same object damaged completely can be reborn as a different kli, either through the owner's machshavah or, according to Rebbi Yose, through the simple continuity of the use it always served.