Gemara

(R. Avahu): If a baby was born after eight months of pregnancy, we do not consider him (to be viable) until 20 years.

Question: An eight-month baby cannot live!

(Beraisa): An eight-month baby is like a rock. One may not move him on Shabbos, but his mother may bend down to nurse him, due to danger (to both of them).

Answer: The case is, there are signs that he is viable.

(Beraisa) Question: What is an eight-month baby?

Answer #1: It is one who was not in the womb the proper time;

Answer #2 (Rebbi): There are signs of this. His hair and nails are unfinished. If they are finished, we assume that he is a seven-month baby that delayed a month before being born.

Question: A case occurred, and a woman gave birth 12 months after her husband went overseas. Rabah Tosfa'ah ruled that the child is Kosher.

Is this like Rebbi, who says that a fetus can delay in the womb (unlike Chachamim)?!

Answer: R. Shimon ben Gamliel agrees, so they are like a majority.

(Beraisa - R. Shimon ben Gamliel): Any child who lives 30 days is viable. (Even if he was born in the eighth month, we say that he was a seven-month baby that came out late.)

Shabbos 136a (Beraisa - R. Shimon Ben Gamliel): Any child who lives 30 days is viable - "U'Fduyav mi'Ben Chodesh Tifdeh";

(Shmuel): The Halachah follows R. Shimon ben Gamliel.

Rishonim

The Rif brings our Gemara until but not including the ruling of Rabah Tosfa'ah. In Shabbos (55a) the Rif brings Shmuel's ruling like R. Shimon ben Gamliel.

Ba'al ha'Ma'or: If a baby's Simanim are finished, even if he was Vadai born in the eighth month, he is viable. Surely, he is a seven-month baby that delayed in the womb. R. Avahu does not discuss Nefalim. Rather, he teaches that being born after eight months is a sure Siman of being a Seris. We do not act to consider him an adult until 20 years. A baby is Vadai viable if he lived 30 days or we know that he was born after nine months. If neither of these applies he is a Safek, even if his Simanim were finished.

Nimukei Yosef (DH Gemara): Even if he brought two hairs, they are Shuma (not hairs of adulthood), even if he is viable. This is when we know that he was born in the eighth month. If we are unsure, he is an adult after 13 years and two hairs. If not, we should be in doubt about Kidushin of most men (under 20), for usually we are not sure in which month a baby is born! Most Poskim rule like R. Avahu. (R. Avahu can hold even like R. Shimon ben Gamliel, who does not discuss adulthood.) Shmuel rules like R. Shimon ben Gamliel. It suffices that the baby lived 30 days, even if his Simanim were not finished. R. Shimon ben Gamliel agrees that Simanim are better than living 30 days, and they also prove viability. Some say that R. Shimon ben Gamliel also requires that the Simanim were finished.

Milchamos Hash-m: The Yerushalmi reveals what our Gemara discusses. We thought that R. Avahu does not treat a Vadai Ben Shemoneh like a Vadai Nefel even if its Simanim were not finished. We conclude that he admits then. He discusses when we are unsure of the month. In spite of the unfinished Simanim, he is a Safek. We are stringent, e.g. we must help him to live in case he is viable. Without R. Avahu we would have said that Rebbi and Chachamim argue about when we do not know his months. We would say that Chachamim follow (or are concerned for) the majority of women who give birth after nine months, even if the Simanim are unfinished, and Rabah Tosfa'ah is like Chachamim.

Rambam (Hilchos Milah 1:13): If a baby was born in the eighth month and his hair and nails are finished, he is a viable seven-month baby who delayed a month. One may move him on Shabbos. He is not like a rock. He is circumcised on (day eight, even if it is) Shabbos.

Kesef Mishneh: Shmuel rules like R. Shimon ben Gamliel; if an eight-month baby lived 30 days, we assume that he is a seven-month baby that delayed coming out. Similarly, the Halachah follows Rebbi against Chachamim. Alternatively, Simanim are better than living 30 days, so all the more so the Halachah follows Rebbi.

Rambam (Hilchos Yibum 1:5): If a woman gave birth after her husband died and the baby was born alive, even if he died right away his mother is exempt from Yibum. However, mid'Rabanan we must know for sure that he was born after nine full months. If we do not know the length of the pregnancy, if he lived 30 days he was viable and he exempts from Yibum and Chalitzah. If he died within 30 days, whether from sickness or an accident, he was a Safek Nefel, so Chalitzah is required mid'Rabanan.

Magid Mishneh: Mid'Oraisa, the Rambam rules like Rebbi, that Simanim prove viability. He rules like R. Shimon ben Gamliel, that living 30 days proves viability. Also knowing that the pregnancy was nine full months proves viability. However, Chachamim were stringent in some matters.

Rosh (8:6): If the hair and nails of an eight-month baby are finished, we say that he is a seven-month baby who delayed coming out. According to Rebbi, after 30 days he is not a Safek Nefel, just like according to R. Shimon ben Gamliel. R. Avahu taught that according to Chachamim he is a Safek Nefel until 20 years. The Halachah follows Rabah Tosfa'ah who ruled like Rebbi and R. Shimon ben Gamliel. The Halachah does not follow R. Avahu.

Poskim

Shulchan Aruch (OC 330:7): If a baby was born in the eighth month, or it is a Safek whether it was the seventh or eighth month, we are not Mechalel Shabbos for him unless his hair and nails are finished.

Beis Yosef (DH v'Hani): If his hair and nails are finished, even if we are sure that he was born in the eighth month, e.g. his father was home eight month ago and then left, we assume that he is a seven month baby who delayed in the womb

Rebuttal (Gra DH Ela): The Gemara (Yevamos 80b) connotes that we follow Rebbi and rely on Simanim only when we can join the opinion of R. Shimon ben Gamliel, i.e. the baby also lived 30 days! This is the opinion the Rema brings (EH 4:4). It seems that even Tosfos and the Rosh say that we rely on R. Shimon ben Gamliel himself only to move the baby and circumcise him (which is not a Melachah even if he is a Nefel), but not to Mechalel Shabbos for him.

Defense (Bi'ur Halachah Sof DH O Safek): If a pregnant woman sat on the Mashber (birthing stool) and died on Shabbos, we may Mechalel Shabbos to remove the fetus (Erchin 7a; Shulchan Aruch Sa'if 5). BaHaG derives that we may Mechalel Shabbos for a fetus. (The Ramban argues and says that once she sits on the Mashber the fetus is considered born.) A Safek Ben Shemoneh is no worse than a fetus.

Kaf ha'Chayim (46): The Magen Avraham holds that we would not Mechalel Shabbos for a fetus if we knew that he was born after eight months. The Eliyahu Rabah (10) permits, unless we know that his Simanim are unfinished.

Shulchan Aruch (YD 266:11): If it is known or possible that a baby was born in the eighth month we circumcise him on Shabbos only if his hair and nails are finished.

Rema: Some say that if it is possible that he was born in the seventh month we circumcise him on Shabbos, but we do not Mechalel Shabbos for him for other matters. It seems that this is the primary opinion.

Shulchan Aruch (EH 156:4): If a woman gave birth after her husband died and the baby was born alive, even if he died right away his mother is exempt from Yibum. However, mid'Rabanan we must know for sure that he was born after nine full months.

Rema: Nowadays nature has changed, and it suffices if he was born even one day into the ninth month.

Shulchan Aruch (ibid.): If we do not know the length of the pregnancy, if he lived 30 days this shows that he was viable and his mother is exempt.

Beis Yosef (DH uvi'Teshuvos): We hold like R. Shimon ben Gamliel, that even Simanim do not remove the Safek if the baby died within 30 days.

Rema: Some say that living 30 days suffices only if his Simanim were finished; this seems correct.

Taz (2): Even the Tur is stringent only l'Chatchilah to require checking the Simanim, for perhaps R. Shimon ben Gamliel requires this. If the baby died after 30 days and they did not check his Simanim, we assume that they were complete. Most babies are viable, and mid'Oraisa it suffices to be born alive.