Gemara

135b (Beraisa - R. Shimon ben Gamliel): Any child who lives 30 days is viable - "u'Fduyav mi'Ben Chodesh Tifdeh";

Inference: Before this time, it is a Safek.

136a - Questions: Do Chachamim argue with R. Shimon ben Gamliel? If they do, does the Halachah follow him?

Answer: Rav Yehudah taught that the Halachah follows R. Shimon.

If he yawned and died (soon after birth), all assume that he was a Nefel. They argue about a baby who fell from the roof or was eaten by a lion [within 30 days]. R. Shimon is concerned lest he was a Nefel. Chachamim assume that he was alive.

The son of Rav Kahana died within 30 days. He was mourning over him.

Rav Ashi: Rav Yehudah taught that the Halachah follows R. Shimon!

Rav Kahana: I know that he was born after nine months.

A similar case occurred with Rav Dimi bar Yosef's son, and he gave the above answer to Rav Dimi.

(Ravina citing Rava): If Reuven died, and then his only child died within 30 days of birth, and David (a stranger) was Mekadesh the widow:

If David is a Yisrael, she must do Chalitzah. If he is a Kohen, she does not need Chalitzah.

(R. Hoshaya brei d'Rav Idi): Chachamim assume that a baby was viable even if he died within 30 days. Since there is no solution for a Kohen to keep his wife if she does Chalitzah, we rely on Chachamim (to be lenient).

Nidah 43b (Mishnah): A one-day old obligates his brother's widow (to wait until he matures) to do Yibum [or Chalitzah], he exempts his mother from Yibum,... he inherits and bequeaths, and one who kills him is liable

He is like a grown man with respect to his relatives.

44b (Rav Papa): This teaches that if he dies, they mourn over him.

Suggestion: This is unlike R. Shimon ben Gamliel, who says that a baby who lives 30 days is not a Nefel;

Inference: If he died within 30 days, he is a Safek Nefel!

Rejection: The case is, we know that he had a full term pregnancy. Even R. Shimon is not concerned for a Nefel in this case.

Bava Basra 142a (Rav Sheshes): A one-day old baby inherits his mother's property to bequeath it to his paternal brothers, but a fetus does not.

This is because the fetus always dies before the mother.

Question: A case occurred in which a fetus quivered two times after its mother died!

Answer (Mar bar Rav Ashi): Quivering does not show that it is alive. If a rodent's tail is cut off, also it quivers!

Rishonim

Rif and Rosh (Yevamos 22b and 7:7): The Halachah follows Chachamim, who say that a fetus does not acquire until birth.

Rambam (Hilchos Nachalos 1:13): If the mother died, and afterwards her son died, even if he died the day he was born and he was premature, since he lived for a moment, he inherits his mother and bequeaths to his paternal heirs.

Rebuttal (Ra'avad): This is wrong. He bequeaths to his paternal heirs only if he was born after a full term pregnancy. If not, he (his heir) is Safek, and the baby's maternal brothers are Vadai, and a Safek cannot take from a Vadai.

Magid Mishneh: The Rambam learns from Nidah 44b. Rav Papa taught that a baby is like a grown man to his relatives (only) regarding mourning. The Gemara suggested that this is like R. Shimon ben Gamliel, and rejected this. (We know that he had a full term pregnancy.) Since the Gemara asked only about mourning, this shows that all other laws apply even if he was premature. This is not necessarily so. Also, perhaps for other laws we need not know that his months were completed, but if we know that he was premature, he does not inherit. Also, in Nidah it says that one who kills him is liable, and the Rambam exempts one who kills a premature baby within 30 days. Perhaps the Rambam derives this from the Gemara, which says that a fetus does not inherit. He infers that a born baby inherits, even if it was premature. This is not necessarily true. This requires investigation.

Magid Mishneh (Hilchos Yibum 1:5): The Rambam holds that if we do not know whether a baby was born after seven months or eight months, and his Simanim are not finished, if he did not live 30 days, it is a Safek. We are stringent for mid'Oraisa laws. However, one may circumcise on day eight. (Even if it is a Nefel, there is no Isur.) The Rambam rules like Rebbi, who says that a full term pregnancy shows viability, and like R. Shimon ben Gamliel, that living 30 days shows viability, even if Simanim are not finished. This is Torah law. Chachamim were stringent about some laws. They were not stringent about inheritance. Therefore, the Rambam says that even if he was premature, if he lived for a moment, he inherits and bequeaths. This is when his Simanim are finished. If his Simanim are not finished and he was premature, he is a Nefel. Chachamim did not enact about inheritance, for in monetary matters, a stringency for one is a leniency for the other. Chachamim were lenient about a murderer, since we do not consider it viable for all laws. We are lenient about Safek Nefashos.

Rosh (Yevamos 4:5): The Halachah follows R. Shimon ben Gamliel. We do not rely on the majority of children, who are viable, because the minority of Nefalim is common. We are concerned for a common minority, like (one who fell into) water from which one cannot see the shore (in at least one direction. We may not assume that he died.) The Halachah follows Ravina. If the widow became Mekudeshes to a Kohen, she does not do Chalitzah. Since Rabanan argue with R. Shimon ben Gamliel, we rule like them regarding a Kohen's wife, so she can stay with her husband. Even though now it is a Safek mid'Oraisa lest she is forbidden to her husband due to Yevamah l'Shuk (one who remarried without Chalitzah or Yibum), and if she did Chalitzah it would be only a Safek mid'Rabanan of a Chalutzah to a Kohen, it is better that she not do Chalitzah. If she did, people will say that Rabanan clarified that the baby was a Nefel, and therefore told her to do Chalitzah, and they will permit a Chalutzah to a Kohen. Now that she does not do Chalitzah, people will say that Rabanan clarified that the baby was viable, and therefore they did not require Chalitzah, and they will not permit a Yevamah l'Shuk.

Achiezer (1 EH 35) and Minchas Yitzchak (1:32): The Rosh means that there is a minority chance that she is forbidden. (We follow the majority, so it is not truly a Torah Safek.)

Chut ha'Meshulash (3:29): The Rosh means that according to R. Shimon ben Gamliel, there is a Torah Safek.

Poskim

Shulchan Aruch (CM 276:5): If the mother died, and afterwards her son died, even if he died the day he was born and he was premature, since he lived for a moment, he inherits his mother and bequeaths to his paternal heirs.

Rema: This is only if he was born. A fetus does not inherit his mother, who died while pregnant, to bequeath to his paternal heirs.

SMA (7): If the mother was killed, or the fetus began to leave, it can live after the mother dies. There is such a case in which a fetus inherits. The Mishnah taught that a baby inherits, for this is always true. The Ir Shushan says that in every case it is a Nefel. This is wrong. Tosfos says so. The Magid Mishneh says that when his Simanim were finished, the Rambam says that even if he was premature, if he lived for a moment, he inherits and bequeaths. If so, the same applies to a fetus.

Maharshach (2:196): A case occurred in which Reuven died, then his wife gave birth. She died days later, and the baby died days later. Why does the Magid Mishneh assume that the law about mourning is like R. Shimon? Rashi says that it refers to the entire Mishnah! Really, the Rambam is not difficult. The Magid Mishneh says that the Rambam (Hilchos Milah 1:13) holds that if the hair and nails of an eight-month baby are finished, or he lived 30 days, mid'Oraisa he is not a Safek Nefel. He is a seven-month baby who delayed coming out. In some cases Chachamim were stringent, e.g. we do not kill one who killed a premature baby less than 30 days old, for we are lenient about Safek capital cases. We follow the lenient opinion in mourning, so we mourn only if the hair and nails were finished, or it lived 30 days. Therefore, in Nidah we asked only about mourning and murder, that it is unlike R. Shimon.

Maharshach: There is no question regarding inheritance, since his Simanim were finished. A case occurred in practice. The baby's heirs can say 'we hold like the Rambam.' Even though Rashi connotes like the Ra'avad, the Tur and R. Yerucham hold like the Rambam. The Tur (CM 286) requires only that the baby lived a moment after the mother. He did not specify that it cannot be premature. We are lenient about money, for a stringency for one is a leniency for the other. We do not take from one who is Muchzak. However, the Gemara connotes that R. Shimon ben Gamliel requires a Vadai eight-month baby to have finished Simanim and live for 30 days (to remove Safek Nefel). If we do not know the term of pregnancy, it must live 30 days. This is whether or not the Simanim were finished. Shabbos 135b connotes that R. Shimon and Chachamim argue about a baby that died through an accident, but if it yawned and died, it is a Vadai Nefel. The Rambam and Ba'al ha'Ma'or hold that death due to illness is like an accident. Others say that it is like death after yawning.

Shulchan Aruch (EH 156:4): If a man died when his wife was pregnant, if she miscarried, she does [Chalitzah or] Yibum. If the baby was born alive, even if he died the moment [after] he was born, she is exempt from Chalitzah and Yibum. Mid'Rabanan, we must know that his months were complete, and he was born at the end of nine full months.

Gra (12): The Gemara rules like R. Shimon ben Gamliel. He discusses Stam children. If he had complete months, R. Shimon agrees. The Rambam holds that mid'Oraisa, R. Shimon agrees that we follow the majority. Most babies are viable. The Gemara asked that the law of Avelus is unlike R. Shimon. It did not ask about the entire Mishnah, for we could have said that the Mishnah teaches the Torah law, but Avelus is mid'Rabanan. This answers the Rosh's question. Since in every case (whether or not she does Chalitzah) it is a Safek Isur mid'Rabanan, it is better not to do Chalitzah, lest she become despised in her husband's eyes.