Taharos, Chapter 3, Mishnah 2. This chapter is occupied with liquids that congeal, and with the fundamental rule that tamei food conveys its tumah to a liquid only when the food amounts to a kabeitzah, an egg's volume, which is the minimum shiur for food to transmit tumah at all. Our mishnah has two halves: first a dispute over which liquids never truly lose their status as liquids even when they thicken, and then a case of tamei olives that give up their oil.
Liquids that stay liquids
Rabbi Meir's ruling is stated first: "Hashemen techilah le'olam." In his view oil never sheds its status as a liquid. Congealed oil has not genuinely dried up; a certain wetness remains in it, so it continues to satisfy whatever we require of something called a liquid. Halachically, then, oil is forever a techilah, ranked as a rishon in matters of tumah just like every other liquid.
"Vachachamim omrim: af hadvash." The Chachamim wish to add honey to that category. Anyone who has eaten honey that has crystallized knows how good it is, and it too is regarded as a liquid rather than as a solid.
Rabbi Shimon Shezuri broadens the category once more: "Af hayayin." Wine too, he holds, belongs among those liquids that never fully cross over into being solids.
A clump of olives in a hot oven
The mishnah now shifts to a connected topic. The subject is no longer a liquid stiffening into a solid, but a solid that carries liquid within it, a case in which tumah rests on the solid while the liquid emerging from it is clean.
An aside worth noting: this mishnah bears on a machlokes that surfaces elsewhere in the Gemara, not here, concerning the very nature of liquid trapped inside a solid. Is that liquid simply part of the solid, or does it have an independent identity of its own? In the Gemara's terms, is it mufkad, deposited there, or balua, absorbed into the solid? Our mishnah lines up neatly with one side of that debate, or at the very least serves as good ammunition for it, and the other side is left with the burden of explaining it.
"Gush shel zeisim shenaflah lesanur vehusak." Olives that were made susceptible to tumah and have actually contracted it are pressed together in a lump; the lump drops into an oven, and a fire is lit beneath it. Under the heat the olives release their oil. Nothing in the ruling depends on the oven as such: it merely creates the conditions under which oil separates from the fruit.
Now comes the question: how much olive do we have? "Kabeitzah mechuvan, tahor." If the olives are precisely a kabeitzah, no more, the oil that emerges is tahor. "Yoser mikabeitzah, tamei, shekeivan sheyatzas tipah rishonah nitmes bekabeitzah." If there was more than a kabeitzah, the oil is tamei.
The reasoning: the moment a drop of oil leaves the olives, the solid mass has become that much smaller. Where the olives were exactly a kabeitzah or less to begin with, they can no longer pass tumah on to the liquid, since food below a kabeitzah cannot transmit at all. But where there was more than a kabeitzah, the very first drop to emerge was made tamei while a full kabeitzah was still present, and once that first drop is tamei, every drop that follows picks up tumah from it. It makes no difference that the solid has by now dwindled below a kabeitzah and lost its power to transmit; the first drop already carries the tumah forward.
The closing clause: "Im hayu ferudin", if the olives were lying loose rather than compacted into one lump, then "afilu hen se'ah, tahor", the oil remains tahor even should the olives fill a se'ah, which is a considerable measure indeed. Some texts have instead "afilu hen me'ah", even a hundred olives. The halachah is identical in either version, and it rests on the same logic: no individual olive reaches a kabeitzah, so no individual olive has the shiur required to render its own oil tamei.