Keilim, Chapter 25, Mishnah 2. This chapter is built around a rabbinic decree that distinguishes between the inside of a utensil and its outside. When something tamei comes into contact with the inner side of a keli, the whole utensil becomes tamei. But when tamei liquid touches only the outer surface, the decree limits the tumah: the outside alone becomes tamei, and the inside remains tahor. Note carefully that this distinction was legislated with regard to liquids touching the utensil, and it is in that framework that our mishnah continues.
The keli under discussion here is the mardea, the ox goad, a tool used in plowing. Picture a long wooden pole with metal fitted at both ends. At one end sits a small blade, whose job is to cut through roots lying in the path of the plow. At the other end sits a prod, a sharp metal point with which the farmer pokes the animal and keeps it moving in a straight line.
Rebbi Yehuda: even a pole has an inside and an outside
Rebbi Yehuda's position is recorded in the words "Hamardea," the ox goad, "yesh lo achorayim v'toch": it is regarded as possessing both a back side and an interior. The statement sounds strange on first hearing, since a shaft encloses nothing and has no hollow space anywhere along its length. The halachah is nevertheless extended to it by way of comparison.
Which parts play the role of the inside? The two metal ends, the blade and the prod. They are the parts that accomplish the essential work of the tool, just as the inside of a container is where the container does its work, and therefore they take the status of the inside. The rest of the tool, the wooden shaft, functions like the outside of a utensil: it serves the working ends and enables a person to wield them, so it is genuinely part of the keli, but it carries the status of the outer surface.
Here the mishnah gives measurements: "Mishiv'ah lacharchur u'me'arba'ah ladorvan." The stretch of pole extending seven tefachim from the blade up to the blade itself, and the stretch extending four tefachim from the prod up to the prod, are the portions treated as the outside. These lengths are what support and serve the two working ends, and so they are included in the keli, with the halachic standing of the outside. "Divrei Rebbi Yehuda," this is the opinion of Rebbi Yehuda.
Rebbi Meir: this tool has no inside at all
"Rebbi Meir omer: Ein lahem." Rebbi Meir disagrees entirely. In his view the ox goad simply is not subject to this law. The decree of inside and outside was framed for vessels that hold something, utensils that actually possess an interior and an exterior. An ox goad is a prod and a blade on a stick; there is nothing here to compare to a container, and so the analogy cannot be drawn.
A difficulty now presents itself. The tradition handed down from the chachamim about the mardea contained the figures seven and four, and each of the two Tannaim had received it. On Rebbi Yehuda's approach those figures sit comfortably in place, marking out the sections of the shaft that carry the halachic standing of the outer surface. Rebbi Meir, however, removes this implement from the category of inside and outside altogether. What, then, did he take those two measurements to be conveying?
The measurements as a law of remnants
His own understanding is supplied by the mishnah in his name: "Lo hizkiru arba'ah v'shiv'ah," the chachamim never spoke of four and of seven, "ela l'shirayim," except concerning shirayim, the pieces left over when a goad has broken apart.
The point is this. Suppose the goad snaps in two. Each of the resulting pieces can still receive tumah, provided it remains large enough to serve a purpose, that is, provided the blade or the prod can still be used. And usability depends on how much of the wooden shaft came away with each metal end. The blade end remains serviceable only if at least seven tefachim of wood remain attached to it, and the prod end remains serviceable only if it retains four tefachim of wood. With those lengths the broken piece can still be handled and put to work, and therefore it is still a keli capable of becoming tamei. Without them, the fragment has no practical use.
So we come away with two very different readings of one received tradition. For Rebbi Yehuda, seven and four define where the "outside" of the ox goad begins. For Rebbi Meir, the numbers have nothing to do with the decree of achorayim v'toch at all; they are a measure of utility, telling us when a broken piece of an ox goad still qualifies as a keli.