Taharos, Chapter 4, Mishnah 13. This mishnah closes the fourth chapter, which has been devoted to lists of sfeikos: first the doubtful cases in which we rule stringently and declare tumah, and then a long list of doubtful cases in which we rule leniently. The final entry on the lenient list is safek korbanos: a doubt as to whether a person actually owes a korban.
The mishnah presents its case: "ha'ishah sheyeish aleha safek chameish leidos u'safek chameish zivos." A woman finds herself with five doubtful births, or five doubtful cases of zivah.
The Two Doubts
What is a doubtful birth? A woman who miscarried, where it is not clear whether the miscarriage was of the sort that obligates her in a korban or not. The details of these cases are worked out at length in Maseches Kerisus.
And what is a doubtful zivah? Those who have learned Maseches Niddah know that halachah distinguishes between the status of a niddah and that of a zavah, whatever our practice may be today. Here, five months went by, and in each of them this woman had bleeding on three consecutive days, without it being clear whether the bleeding fell during her days of niddah or during her days of zivah. I state it in deliberately open terms, because this whole area is a thicket of machlokos among the Rishonim. The upshot is that she may be a zavah, who would owe a korban, or she may be an ordinary niddah, whose status carries no korban obligation at all. Either way, the bottom line is a genuine doubt as to whether she owes these korbanos.
One Korban for All Five
The ruling: "meivi'ah korban echad," she brings a single korban. Note that these are five separate occasions on which she ran into the same doubt, one after another, and still we tell her to bring one korban and let it cover all five situations. "Ve'ocheles bizvachim": once that korban has been brought, she may eat from korbanos, since she is now regarded as clear and tehorah. "Ve'ein hashe'ar aleha chovah": the remaining four are not an obligation upon her.
Why the Others Are Not Merely Optional
And it is not simply that we do not require them. We do not permit them either. The Bartenura explains why. The chatas she brings is a bird offering, slaughtered by melikah, pinching the neck with the fingernail. If she does not in fact owe the korban, the bird is plain chulin, and performing melikah on chulin for the mizbe'ach is forbidden; it may be done only for the sake of a genuine korban obligation.
Therefore b'kushi hitiru: it was only with difficulty that the Sages permitted even the melikah of this one chatas, and they permitted it solely so that she should be able to eat zevachim. Once that single offering has accomplished that purpose, there is no reason to take on the risk again with the other four. Hence she brings one, and no more.
Ad kan the fourth chapter. Thank you for working through it together.