Keilim, Chapter 22, Mishnah 3. The next several mishnayot in this chapter turn our attention to wooden benches, chairs and stools. Ordinarily we learn that a wooden utensil becomes susceptible to tum'ah only if it forms a receptacle, a vessel that holds something inside it. The items discussed here are, for the most part, flat surfaces with no cavity at all. Nevertheless they can contract impurity, because of a different category entirely: tum'at midras, the impurity that comes to an object designed for a person to sit upon, lie upon, or otherwise rest his weight upon. A seat is a seat, even when it has no hollow.
Our mishnah deals with a seat whose height comes from broad boards serving as its legs, lifting the surface to a comfortable level for sitting. The question is what happens as those supports are removed one at a time.
"Safsal shenitlah achas mera'shav, tahor." A bench from which one of its supporting boards was taken away is tahor. Once it has lost that support it cannot be sat upon, and a seat that cannot be used for sitting is no longer a seat at all.
"Nitlah shniyah, tahor." Should the remaining board be pulled away as well, the bench still stays tahor. All that is left now is a plank resting flat on the ground, and whoever sits there gains nothing beyond what he would gain from sitting directly on the earth. Serving no purpose as a seat, it has no seat status at all.
"Im yesh bo govah tefach, tamei." If, however, the plank that remains measures a tefach in thickness, it is subject to tum'ah. Wood of that depth holds a person above ground level, so settling onto it is not the same as settling onto the floor. People will readily use it, and it therefore retains a genuine function as a seat.
"Arafraf shenitlah achas mera'shav", a footstool from which one of its legs was removed, can still become tamei, since a person is able to rest his feet on the raised side. Picture the footstool as two supports with a board across the top. When one of the supports breaks away, the board tilts and the whole thing takes on the shape of a triangle. A person can still put his weight on the higher end and get genuine use out of it, so it keeps its status as an object made for resting upon.
"Vechein hakisei shelifnei kasedra." The identical ruling governs the low seat set in front of a kasedra. The kasedra was the chair on which women sat while riding in a wagon, and the small stool placed before it let them step upward and reach their place. Its halachah matches the footstool's precisely: even with one of its props missing, it still holds a person's weight, and so it remains capable of receiving tum'ah.
The principle running through the whole mishnah is straightforward and very human: the determining factor is not the object's original design but whether a person would still actually use it for sitting or standing upon. As long as it offers real support, it carries the status of a seat. The moment it offers no more than the floor beneath it, it is simply a piece of wood.