Terumos, Chapter 2, Mishnah 1. Our mishnah deals with two separate vessels, A and B, each containing produce of a different status. Unlike the previous mishnayos, there is no difference here in the Terumah obligations: both batches of produce are on the same level, and the only difference between them is that one is tamei and one is tahor. Under ordinary circumstances, there is no reason at all, on a Torah level, why a person should not separate Terumah from one for the other.
Terumah from the tamei for the tahor:
It is worth noting that one who separates Terumah from the tamei for the tahor shortchanges the kohen, since a kohen can do nothing with tamei Terumah other than burn it and derive some benefit at the time of its burning. Olive oil can at least be used for kindling and light, but tamei grapes are of no particular use to him. We will deal with this subject in the next mishnah.
Terumah from the tahor for the tamei:
Our mishnah deals with taking from the tahor produce on behalf of the tamei: vessel B contains tahor grapes, and from them Terumah is separated for B and also for A, while vessel A contains tamei grapes. On the face of it, this is a good deal for the kohen: if there were fifty grapes in each vessel, tamei in A and tahor in B, he is owed two grapes. If he were given one grape from the tamei and one from the tahor, that would be his fair share, but he would have only a single grape available to eat; whereas when two grapes are taken from the tahor batch, he ends up receiving two grapes that are fit to be eaten.
Nevertheless, the mishnah rules that this may not be done, for a reason entirely external to the halachos discussed until now. There is a separate halachah here: when separating Terumah, and likewise maaser, the vessels, piles or groups being tithed together must be adjacent to one another - what is called 'min hamukaf', from the term meaning surrounded or adjacent. The technical details of this law, what counts as close and connected enough, are quite involved, and we will discuss them in Maseches Challah with Hashem's help. For our purposes it is enough to know that in this situation the grapes would have to be placed next to one another.
The concern is that if they are placed too close, the grapes will touch one another in a way that transfers tumah from the tamei to the tahor, and it is forbidden to render Terumah grapes tamei. For that reason the Sages were concerned that a person would distance them too much and thereby fail to fulfill the requirement of 'min hamukaf'. It may be, then, that we have here a rabbinic decree designed to protect a rabbinic law, although many Rishonim understood that the requirement of mukaf is a Torah requirement. Either way, out of concern that a person would not keep them close enough because they would render each other tamei, the Sages said that one should not take even from the tahor for the tamei.
These are the words of the mishnah: "Ein torimin min hatahor al hatamei" - one may not take tahor grapes, or any other produce, on behalf of the tamei. "V'im tarmu, terumatan terumah" - after the fact the separation takes effect, since on a Torah level it is completely valid.
"Be'emes amru":
Wherever the mishnah uses the phrase "be'emes amru", it means that what is now being stated is not subject to dispute and cannot be challenged; no proof is available and none is needed, for the matter is as clear as a halachah l'Moshe miSinai. In many cases it is indeed a genuine halachah l'Moshe miSinai, that is, a tradition we possess on a Torah level going back to Moshe at Har Sinai, for which there is no built-in hint or derashah in the verses from which to derive it. So, for example, the law that tefillin must be black: there is no verse requiring it, nor any derashah that could be derived from the verses, and yet we possess an absolute tradition that this is so.
Here too the mishnah comes to say that the matter is a truth that cannot be challenged, like a halachah l'Moshe miSinai, even though this is not necessarily a halachah l'Moshe miSinai in the literal sense, and certainly not when we are dealing with a rabbinic law. Indeed, as the Bartenura notes here, the mishnah sometimes uses this expression even with regard to a clear and straightforward rabbinic law, as in Maseches Shabbos.
And what is this matter that cannot be denied or disputed? "Igul shel develah shenitma miktzato" - a cake of pressed figs part of which became tamei. A collection of figs pressed together is not considered a single unit, and there is no legal connection between them that would impose an equal tumah upon all of them; if a dead mouse touched one of the figs, not all the figs become a rishon at once. Each fig stands on its own: the figs that are exposed and touch the mouse directly become a rishon, those touching them become a sheni, and those touching the latter remain tahor, since chullin (and this tevel is chullin, as it is not yet Terumah) does not become tamei as a shlishi.
Picture five figs pressed together in a row, with a dead mouse touching the one on the left:
The leftmost fig, the one touching the mouse, becomes a rishon (first degree).
The second fig from the left becomes a sheni (second degree).
The remaining three figs on the right stay tahor.
Structurally, then, we have an exact parallel to the previous case of the two vessels: here too there are two sides, right and left, the right side tahor and the left side tamei. And yet, in contrast to the opening clause, where we were told that one does not take from the tahor produce on behalf of the tamei, here it is permitted to take from the tahor figs of the cake of pressed figs on behalf of the tamei ones.
The reason is this: there is no room here for the decree of 'min hamukaf' and for the concern that he will separate the figs from one another, since as they stand they are already joined and pressed together. Nothing further can happen in terms of moving them apart or bringing them together, and once the concern falls away the decree falls away with it, so one may separate Terumah from the tahor on behalf of the tamei.
The same applies in all those cases where the produce is joined and intermingled from the outset:
A cake of pressed figs - a cake of figs pressed together, part of which became tamei.
A bundle of vegetables - for example, carrots tied together.
A pile of grain - a large heap of grain.
In all of these, if part is tamei and part is tahor, one takes from the tahor on behalf of the tamei, since as they stand they are already touching and intermingled with one another.
"Hayu shnei igulin, shtei agudos, shtei aremos" - if there were two cakes of pressed figs, two bundles, two piles:
This line contains no great novelty, but rather an intermediate case: two cakes of pressed figs, two bundles of vegetables or two piles of grain, "achas temei'ah v'achas tehorah - lo yitrom mizeh al zeh" - one tamei and one tahor, he may not separate Terumah from this one for that one. That is, one may not take from the tahor on behalf of the tamei, just as was stated at the beginning of the Mishnah. The only novelty is that instead of vessels we are dealing with these cakes of pressed figs, bundles of vegetables or piles of grain, and the halachah remains as explained until now.
Rabbi Eliezer, however, disagrees and says: "torminn min hatahor al hatamei" - one may separate Terumah from the tahor on behalf of the tamei. In his view it is permitted to take from the tahor in the second vessel on behalf of the tamei in the first vessel. In other words, he is not concerned at all about the matter of 'min hamukaf', that a person might refrain from bringing them close enough out of fear of spreading tumah; and since he has no such concern, there is nothing to prevent taking from the tahor on behalf of the tamei. The halachah, however, does not follow his view.
In summary: in this Mishnah we learned that one does not separate Terumah from tahor produce on behalf of tamei produce, and if he did so, his Terumah is valid Terumah, since by Torah law the separation takes effect. The reason for the prohibition does not lie in the laws of Terumah themselves but in the law of 'min hamukaf': the concern that he will distance the produce more than necessary, because bringing it close would transfer tumah from the tamei to the tahor. For this reason, in a cake of pressed figs, a bundle of vegetables and a pile of grain, part of which became tamei, one may separate Terumah from the tahor on behalf of the tamei, since they are joined and intermingled in any case; whereas with two separate cakes, two bundles or two piles, one does not separate Terumah from this one for that one. Rabbi Eliezer permits it even in this case, and the halachah does not follow his view.