Kinnim, Chapter 1, Mishnah 4. The final clause of the preceding mishnah laid down a principle, and our mishnah now supplies the illustrations. Once designated pairs of birds drawn from distinct designations have become intermingled, the resulting mixture may never be handled as one undifferentiated batch. That holds whether the two designations answer to a single category of chiyuv or to two different categories, and whether a single woman stands behind them or two women do. In each of these variations the pairs remain separate units. The mishnah proceeds to spell out exactly which situations those descriptions are describing.
One name, two names, one woman
"Keitzad mishem echad?" What does the mishnah mean by pairs belonging to one and the same name? It answers with two illustrations. "Leidah ve-leidah": a woman set aside pairs on account of a birth, and later set aside further pairs on account of another birth. Or "zivah ve-zivah": she set aside pairs on account of zivah, and afterward set aside additional pairs on account of zivah once again. Zivah describes a woman who saw a flow of blood at a time that falls outside her regular menstrual cycle, a status that carries with it its own korban of two birds.
These are pairs viewed as belonging to a single category. Yet as the previous mishnah taught, even when the very same woman designated multiple pairs for the very same type of obligation, the pairs still cannot be merged into one large group, unless she made both designations simultaneously.
"Mishnei shemot," from two names: "leidah ve-zivah." Here the first set of pairs was designated for childbirth and the second set for zivah. In this situation, even if one woman designated both at the same moment, we regard them as two separate groups, precisely because they answer to two different obligations.
Two women
"Keitzad shetei nashim?" What arrangement is the mishnah calling two women? It gives two illustrations. "Al zo leidah ve-al zo leidah": this one is liable for a birth and her fellow is liable for a birth as well. Or "al zo zivah ve-al zo zivah": each of the two carries an obligation stemming from zivah. Here the two obligations do fall under a single name, yet the birds still may not be pooled into one large group, because there are two separate owners standing behind them, the common category notwithstanding.
And "mishnei shemot, al zo leidah ve-al zo zivah": two women with two different types of obligation, one owing a korban for childbirth and the other for zivah. Here the pairs certainly cannot be combined, both because the owners are two separate women and because the obligations are of two separate kinds.
Rabbi Yose's exception
A different Tanna now teaches that there are circumstances in which two sets of birds may indeed be handled as one undesignated group, even when different women brought them and even when the obligations differ in kind.
Rabbi Yose describes two women "shelakchu kineihen be'eruv," who acquired their obligatory pairs as one blended purchase. Instead of each woman buying her own pair on her own account, they combined their funds and took possession of both pairs together. The mishnah offers a second version of the same arrangement: "o shenatnu demei kineihen lakohen," the two of them handed the price of their pairs to the kohen whose task was selling birds at the Mikdash, and that kohen then transferred four birds onward to the kohen who would bring them upon the mizbe'ach.
"Le'eizeh sheyirtzeh kohen yakriv chatat u-le'eizeh sheyirtzeh kohen yakriv olah." The decision now rests entirely with the kohen: this bird he brings as a chatat on behalf of whichever of the two women he prefers, and that bird he brings as an olah on behalf of whichever he prefers. All four birds hold the status of a single undesignated pool, so any one of them may serve as a chatat and any one as an olah for either of the two. Every combination is valid, so long as the final tally works out: each of the women must be credited with two birds, one brought as a chatat and one as an olah.
The mishnah adds that Rabbi Yose's ruling applies "bein mishem echad," that is, when both women put in their money for obligations falling under one and the same name, and equally "bein mishnei shemot," when their obligations belong to two different categories. In Rabbi Yose's view, the joint purchase itself functions as a stipulation between them that either pair is available to serve either woman. Once that condition is in place, no individual bird belongs to any particular woman until the very moment it is brought.