Before us is Mishnah 3 in chapter 8 of Maseches Eduyos. This Mishnah is rich in content, far beyond what its plain words suggest. Let us first lay out the foundations on which it is built, and afterward examine its actual wording.
The laws of a chalal and a chalalah:
A kohen is forbidden to marry certain women, among them a divorcee. If a child is born to him from a divorcee, the son is called a chalal and the daughter a chalalah. Even though the child's father is a kohen, the child is emptied of his status of kehunah: he does not serve in the Beis HaMikdash, he does not eat Terumah, and so on. Moreover, a Yisraelis who has relations with a chalal herself becomes a chalalah, and by virtue of that very fact she is forbidden to marry a kohen.
The rules of doubt:
A doubt in a Torah prohibition - we rule stringently, and we assume the more severe possibility of the doubt.
A doubt in a rabbinic prohibition - we may rule leniently.
A double doubt (sfek sfeika) - two doubts built one upon the other, so that even if the first doubt is resolved stringently, there still remains the second possibility that the second case is the lenient scenario. With such a double doubt one may be lenient even in a matter of Torah law.
The case in the Mishnah:
A woman who married into a family known to contain a man of doubtful chalal status, and now she is a widow. We have two doubts before us:
Perhaps she never married that possible chalal at all, but rather one of the other members of the family, a cousin of his and the like.
And even if she did marry precisely the man whose lineage is questionable - perhaps he is not a chalal at all, since from the outset this was never more than a doubt. How the doubt arose is not relevant to our discussion at this point.
It emerges that this woman has a double doubt, and the question is whether she may marry into an ordinary family of kohanim. By the letter of the law the answer is yes: perhaps her husband was not that possible chalal, and even if he was - perhaps he was not truly a chalal. She should therefore be permitted to a kohen, and the concern that she might be a chalalah can be disregarded. However, the Mishnah teaches of a rabbinic decree that was enacted close to its own time.
The Mishnah recalls the period at Yavneh: Rabban Gamliel is the Nasi, and his predecessor was Rabban Yochanan ben Zakkai. Rabban Yochanan ben Zakkai decreed, because of 'maalas yuchsin' - an extra stringency in preserving the purity of lineage and the cleanliness of the family tree - that kohanim may not marry a woman who carries even a double doubt of chalalus. Therefore, even though by the letter of the law it is permitted, the halachah follows Rabban Yochanan ben Zakkai: initially we do not arrange matters so that they can marry, but after the fact, if they have already married, we do not force them to divorce. This is the content of the Mishnah.
Explanation of the Mishnah's wording:
The Mishnah uses the term "almanas isah". 'Isah' means dough, and the hint is that dough is a mixture of several things. Whenever 'isah' is mentioned, it is a kind of code word for a double doubt, for the problem of the twofold uncertainty in lineage.
The Mishnah therefore states: Rabbi Yehoshua and Rabbi Yehudah ben Beseira testified about "almanas isah" - a woman who is the widow in a case of double doubt, like the case described above: perhaps her husband was not the man whose status as a chalal was in question, and even if he was, perhaps he is truly not a chalal, so that nothing more than a doubt exists here. Their testimony is "shehi kesheirah likehunah" - that she is permitted to marry into an ordinary family of kohanim even at the outset, since her status as a chalalah is no more than a double doubt (sefek sefeika), and in a case of double doubt we are lenient even in a Torah prohibition.
"kesheirah letamei uletaher, lerachek ulekarev":
A family that has a possible chalal mixed into it is entirely fit in every sense. This means that the doubt in the family tree - perhaps the grandmother is that woman who may have been a chalalah - may not be used to rule leniently or stringently in other matters. The doubt is neutralized completely, and the family is required to conduct itself consistently and stringently in every direction, with no flexibility, as though the doubt is disregarded entirely and they are treated as an ordinary family of kohanim.
According to one reading: "letamei" - when a man who is forbidden to marry into the family comes along, they are "lerachek", and they do not marry him; "uletaher" - a man who is permitted by the letter of the law, they are "ulekarev", and they may draw him near. Whatever the precise translation of these four words may be, the overall message is one: we do not treat them more leniently, we treat them stringently, and all the stringencies of an ordinary family of kohanim about whom there is no doubt are maintained. The double doubt is set aside entirely.
"amar Rabban Gamliel: kibalnu eduschem":
Many versions of the Mishnah read "Rabban Shimon ben Gamliel," but Rabban Gamliel was the Nasi at the time this took place, as emerges from the beginning of Maseches Eduyos, and he is the fitting figure here. He did indeed have a son named Shimon and also a father named Shimon, but apparently the version here is not correct, and these words should be removed.
Rabban Gamliel says: we accept your testimony and believe it fully. This is a tradition you received from your teachers, and it may well reach back to Har Sinai; we do not cast any doubt upon it at all, and we accept that a woman whose status as a chalalah is a double doubt is permitted to marry kohanim. Nevertheless, this is not the practical ruling.
"aval mah na'aseh sheggazar Rabban Yochanan ben Zakkai shelo lehoshiv batei dinin al kach":
What can we do? There is no choice. Rabban Yochanan ben Zakkai, his predecessor in the office of Nasi, issued a separate decree. The plain meaning of the words: a beis din is not convened for this purpose, and his intent in practice is that we do not arrange matters at the outset so that even a woman who is a double doubt of chalalah should marry a kohen, all because of the high standard demanded in matters of lineage. The halachah follows Rabban Yochanan ben Zakkai, but this means that after the fact, even though we do not arrange it at the outset, if a woman who is a double doubt of chalalah did marry a kohen, the marriage is allowed to stand.
"hakohanim shom'in lachem lerachek aval lo lekarev":
If the kohanim are told to keep their distance from that woman of double doubt and not to marry her, they will listen. But if they are told that she is permitted to them, they will not listen. In other words, even if the matter is technically correct and correct by the letter of the law, the kohanim will disregard it, and it is better not to say it at all.
The Rambam in his Commentary on the Mishnah understands this as reflecting the attitude presented in the previous Mishnah. In the previous Mishnah we saw a family of kohanim that wished to believe the witnesses that their daughter-in-law was not fit to remain married, since they accepted the testimony that she had been taken captive and rejected the testimony that she had not been defiled. It emerges from there that the kohanim were extremely stringent with themselves, even beyond what was reasonable and beyond what the law required.
Here too Rabban Gamliel says that the kohanim will be stringent. From the decree of Rabban Yochanan ben Zakkai it emerges that they must set aside the strict letter of the law and follow the special standard of lineage, being unusually careful and exacting about their pedigree. Therefore, even though this is a case of a double doubt and she is permitted to them by the letter of the law, the Sages will say regarding this halachah: the kohanim do not marry a woman forbidden to them even in a case of double doubt.
In summary: in this Mishnah we learned the laws of a challal and a challalah, the rules of doubt - stringency in a Torah law, leniency in a rabbinic law, and leniency even in a Torah law in a case of double doubt - and the case of the 'widow of a mixed family', which is a double doubt with regard to challalah status. Rabbi Yehoshua and Rabbi Yehudah ben Beseira testified that she is fit for the priesthood and that the doubt is neutralized for every purpose, to declare tamei and to declare tahor, to distance and to draw near. Rabban Gamliel accepted their testimony as far as the letter of the law is concerned, but set against it the decree of Rabban Yochanan ben Zakkai on account of the special standard of lineage - that such marriages are not arranged at the outset, and after the fact the couple is not separated - and concluded that the kohanim, whose way it is to be stringent with themselves, listen to distance and do not listen to draw near.