Keilim, Chapter 14, Mishnah 7. Here the mishnah picks up a principle already familiar from the laws of tum'ah, and then records a disagreement over how far that principle extends. The baseline rule runs as follows: a keli that has become tameh and afterward breaks, so thoroughly that it can no longer do the job for which it was made, sheds its tum'ah and is tahor. And should someone collect the pieces and build a fresh utensil out of them, that utensil is tahor as well, since it truly is a different object from the one that was defiled.
Kelim of metal, though, do not follow this pattern. Chachamim legislated that when a tameh metal utensil shatters and its remains are worked into something new, the tum'ah of the earlier utensil transfers to the product, as if no breakage had intervened at all. Our mishnah begins with that halachah and then lays out a machloket concerning its details.
Two ideas in the opening line
The mishnah states: "Kelei matachot mitam'in umit'taharin shevurin," metal kelim contract tum'ah when broken and are purified when broken. Two distinct halachot are compressed into these few words, and each requires its own unpacking.
The first, that they contract tum'ah in a broken state, works like this. When the utensil shatters, the tum'ah it was carrying does leave it. Still, a trace of that tum'ah lingers in the shards, so that anything manufactured from them comes into existence already tameh, exactly as described above.
The second, "umit'taharin shevurin," that they are purified when broken, tells us that a utensil built out of shards can reach taharah through an easier route than a regular tameh keli must travel. What that easier route consists of will emerge from the case the mishnah now brings.
All of this is how Rabbi Eliezer reads the halachah. Rabbi Yehoshua grants the first clause and quarrels only with the second: "Rabbi Yehoshua omer einan mit'taharin ela shelemin." As he sees it, these kelim reach taharah by precisely the same procedure as any ordinary intact utensil, with no concession whatsoever.
Keitzad: locating the actual case
The mishnah asks "keitzad," where does this machloket actually arise? To follow the answer, keep in mind the procedure for purifying from tum'at met. An object defiled through a corpse requires two sprinklings of the waters of the parah adumah, one on day three from when the tum'ah was contracted and a second on day seven.
Now follow this sequence. "Hiza aleihen," the parah adumah waters were sprinkled upon the utensil on day three. "Venishberu bo bayom," it then broke on that same day. "Hitichan," its owner smelted the pieces and shaped a new utensil out of them. "Vechazar vehiza aleihen shenit bo bayom," whereupon he sprinkled upon it a second time, still within that same day. Rabbi Eliezer rules "harei eilu tehorin," the utensil is already tahor, and nobody need wait for day seven to sprinkle again. The mishnah labels this position "divrei Rabbi Eliezer," attributing the ruling to him.
Ordinarily sprinkling of the parah adumah waters is tied to a third day and a seventh day, yet chachamim were accommodating in this instance and waived the seventh-day sprinkling. What justifies the leniency? As noted at the start, the whole tum'ah in question is derabanan. On the level of Torah law, a metal utensil built from the debris of a shattered tameh keli is simply a new object and is tahor; it is chachamim who ruled that we regard it as tameh. Rabbi Eliezer therefore reasons that a tum'ah of rabbinic origin may be handled with a somewhat gentler hand than tum'ah in the usual sense.
So whereas any other utensil, whether newly made or long in use, that was defiled by a corpse needs sprinkling both on day three and on day seven, in our case the item standing before us is an entirely different object from the one that became tameh, and a single sprinkling on the day of the smelting and refashioning is enough. The defilement of the earlier utensil does migrate into its replacement once the replacement is made, but not with full severity, and we do not require him to hold out until day seven.
Rabbi Yehoshua's position
Rabbi Yehoshua rejects this: "Rabbi Yehoshua omer ein haza'ah pechot mishelishi ushvi'i." Sprinkling, in his view, counts only when performed on day three and on day seven, and even here the second sprinkling has to be deferred to the seventh day. Sprinkling again within the same day accomplishes nothing.
Rabbi Yehoshua concedes that the tum'ah before us is rabbinic, and one might have expected that fact to open the door to some flexibility. Even so, he holds that when chachamim established this tum'ah they gave it the identical rules that apply to a keli that is tameh in the fullest sense. Consequently, just as with tum'at met on the Torah level, the second sprinkling belongs on day seven.
Rabbi Eliezer, for his part, is content with two sprinklings all told: one administered before the breakage and one after the utensil was rebuilt. Once both have taken place, waiting for a third and a seventh day is unnecessary. We are lenient, given that this tum'ah is a rabbinic institution from the outset.