The Mishnah debates the status of a woman who gives birth via caesarean (yotze dofen) and whether it shares that same status as natural childbirth (derech rechem). The consequence, in the context of our Mishnah, is whether the mother is defined as a yoledet. If she is, then the periods of tumah and tahara that follow would apply, along with the korban she must to bring at the end of the tahara period. The Chachmim understand that the mother would not be considered as a yoledet, while R' Shimon disagrees.
The Gemara explains that both opinions are based on pesukim. The Chachamim explains that when the Torah teaches the law of the yoledet is writes, "When a woman conceives and gives birth..." (Vayikra 12:2), it connects the method of childbirth to the manner of conception1. R' Shimon however understands that the pasuk is expanding the definition of the yoledet to include certain cases of miscarriage.
R' Shimon however learns his position from the later pasuk "and if she gave birth to a girl..." (Vayikra 12: 5). In that context, the word "teled" (gave birth) is superfluous. He therefore understands it is there to include all manner of birth. The Chachamim however understand that since the pesukim only discuss a male or female child, teled is there to include other children -- the tumtum and angroginus.
The Ritva however finds the flow of the Gemara difficult. What would be the assumption without any pesukim? When the Gemara asks for the source of the Chachamim's position, it appears that the basic assumption is that a yotzei dofen would be no different unless there was a pasuk to exclude it from certain laws. Yet, the Gemara then continues by asking for a source for R' Shimon position. If the basic assumption is that it is no different, then a pasuk would be unnecessary.
The Ritva explains that the basic assumption is that leida is only derech rechem. The reason the Gemara asked for a source for the Chachamim is because it was aware that the Chachamim use the term "teled" to include a tumtum and androginus. That being the case, the Gemara was questioning why it would not also include a yotze dofen.
From the Tosfot however it appears that the basic assumption is the opposite -- a yotzei dofen is equivalent to derech rechem. The Tosfot also asks why the Chachamim required a pasuk. The Chachamim could have simply connected a yoledet to the laws of bechor, a first-born animal, where there it is clear that a yotzei dofen would not be brought as a korban. The Tosfot answers, that were it not for the pasuk cited in the Gemara, the Chachamim would have preferred to learn from the pasuk "teled" drawing the same conclusion as R' Shimon.
Interestingly, the Aruch LaNer understands we find these two understandings behind another debate. The Gemara (Bechorot 47b) records a debate whether a first born who was a yotze dofen is considered a bechor for the laws of inheritance (such that he receives a double share). The Chachamim understand that he is not since the Torah writes "yaldu lo..." (and they bear him sons). Rashi understands that the Chachamim maintain that since a yotze dofen is not considered leida (birth), the bechor yotze dofen does not qualify for yaldo lo. The Tosfot however ask that we learn from our Gemara, that it is only because the Torah used the term "tazria" that excluded a yotzei dofen for a yoledet. The Tosfot therefore understand that the Chachamim must exclude a bechor yotze dofen by way of a gezeira sheva -- common terms used -- that connected our Mishnah to the laws of bechor. How do we understand this debate?
The Aruch La'Ner explains that Rashi understands like the Ritva above that the basic assumption is that a yotze defen is not considered leida. That is why the term yaldu lo is enough to exclude a bechor yotzei dofen. The Tosfot are however consistent with their position in our Gemara. Since the basic assumption is that a yotze defen is considered leida, the term yaldu lo alone would not exclude a yotzei defen. Consequently, the Tosfot understand that a gezeira shava must have been employed.
1 R' Chananel (Chagigah 16a) learns that the manner of conception is also important for the definition of a yoledet. He understands that the word tazria teaches that to fall under the definition of yoledet the conception must be way of bi'ah. Accordingly, in a modern context, a child born through artificial insemination would not define the mother as a yoledet. See Ritva (Nidah 40a), Mosad HaRav Kook, footnote 5.
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