Hullin, Chapter Four, Mishnah Four
If a fetus sticks a limb out when being born and someone cuts off that limb before slaughtering the mother, the limb causes impurity as would a nevelah, as do all limbs taken from living animals. Our mishnah teaches that in this case the fetus that remains in the mother does not have the status of nevelah and it is clean. The rabbis in our mishnah debate whether the same is true if they slaughtered the mother first and then cut the limb off of the fetus.
1) If an animal was having difficulty in labor and the fetus put forth its limb and a person immediately cut if off and then slaughtered the mother, the flesh [of the fetus] is clean.
2) If he slaughtered the mother first and then cut if off, the flesh [of the fetus] is unclean like that which had touched nevelah, the words of Rabbi Meir.
3) But the sages say, it is like that which had touched a slaughtered terefah,
4) For just as we find that the slaughtering of a terefah animal renders it clean, so the slaughtering of the animal renders the limb clean.
5) Rabbi Meir said to them: No, for when you say that the slaughtering of a terefah [animal] renders it clean you are concerned with [the animal] itself, but can you say that it will render clean the limb which is not part of [the animal] itself?
6) From where do we learn that the slaughtering of a terefah animal renders it clean?
7) [For we could have argued to the contrary:] An unclean animal may not be eaten, and a terefah also may not be eaten; just as slaughtering does not render an unclean animal clean so slaughtering should not render a terefah animal clean?
8) No, if you said this of an unclean animal for at no time was it fit [for slaughtering]; can you also say this of a terefah animal which had a time when it was fit [for slaughtering]?
9) Take away with this argument that you brought forth! For where would we know this of an animal that was born terefah from the womb?
10) [Substitute therefore this argument]: No, if you said this of an unclean animal for none of its kind may be validly slaughtered; can you also state this of a terefah for whose kind there is valid slaughter?
11) [Accordingly], the slaughtering of a live eight months birth does not render it clean, since there is no slaughtering of its kind.
Section one: In this case, the fetus in its mothers womb remains clean because it is considered to be a limb of its mother, while its mother is still alive. Even if the fetus dies it is still clean. Even if the unclean limb touches the fetus, the fetus is still clean because animals cannot become unclean while alive.
Section two: If after the fetus sticks out its limb, its mother is slaughtered, and then he cuts off the limb, we now have a case of a cut-off limb touching a dead fetus. Rabbi Meir holds that the fetus is rendered unclean by virtue of contact with the unclean limb. The limb has the status of nevelah and meat which has contact with nevelah is unclean.
Section three: The other sages do not accord the limb the status of nevelah but rather terefah, and as we shall see below in the mishnah, a slaughtered terefah does not cause impurity.
Section four: The rabbis say that just as slaughtering renders a terefah clean (and saves it from ever becoming an unclean nevelah) even though the meat is forbidden, so too slaughtering renders the limb clean, even though it cannot be eaten.
Section five: Rabbi Meir rejects their argument. Slaughtering can render the terefah animal itself clean, but how can it render clean a part of the fetus, the limb, that was not attached to the fetus when its mother was slaughtered? Rather, the limb has the status of nevelah and renders the fetus unclean.
Section six: The mishnah now begins a prolonged argument trying to prove that a slaughtered terefah is clean, even though its meat cannot be eaten.
Section seven: However, in a most rabbinic fashion, the rabbis do not begin with the proof but rather with a counter-proof, what one might have argued. Seemingly one might have compared the terefah with the unclean animal. Both an unclean animal and a terefah cannot be eaten. Therefore, one might have argued that just as shechitah (slaughtering) does not render an unclean animal clean, for its meat transmits impurity, so too the slaughtering of a terefah renders it unclean and able to transmit impurity.
Section eight: That argument can be refuted. An unclean animal is not rendered clean by slaughtering because it never had the opportunity to be made permitted/clean through slaughtering. In contrast, if the terefah animal had been slaughtered before it became a terefah, it would have been rendered clean. Therefore, even if it is slaughtered after it becomes a terefah, it is clean (although not edible).
Section nine: The mishnah, employing graphic language found in a few other midrashim but no where in the Mishnah, says that the distinction drawn between the terefah and the unclean animal must be removed. There is a terefah which would never have been permitted by shechitahthe terefah that was born as such. This is similar to the unclean animal, which also never would have been permitted by shechitah. Therefore, our original question returns: How can the inedible terefah be rendered clean by slaughter?
Section ten: The mishnah now adjusts the distinction between the terefah and the unclean animal. A terefah comes from a species of animal that is edible. Other such animals can be eaten after shechitah. Therefore, it is rendered clean by shechitah, just as other animals of its kind are. This would be true even for a terefah that was born as such. In contrast, an unclean animal is by definition from a species that can never be edible. Therefore, it is not rendered clean by shechitah.
Section eleven: The rule that we posited in the previous section is that any animal whose kind can be permitted/edible by having been slaughtered, is also clean if it is slaughtered. An eight months birth refers to an animal born prematurely, one which is deformed and we know will die. The mishnah uses the term eight months because a human baby born at eight months is assumed not to be viable. An eight months birth is like a terefahit is an animal that is now alive, that we know will die shortly. Because of the general rule explained above, an animal born prematurely cannot be made clean by shechitah because none of its kind can be made permitted through shechitah. Such an animal that is slaughtered will have the status of nevelah.