Gemara

Chachamim hold that part of a day does not count like an entire day. R. Shimon holds that it is like an entire day.

Alternatively, we can say that all count part of a day like an entire day.

21b (Beraisa - R. Shimon): A Bechor becomes Kodesh (when it is born,) before it may be offered (on the eighth day).

Shabbos 135b (Beraisa - R. Shimon Ben Gamliel): Any child that lives 30 days is viable - "u'Fduyav mi'Ben Chodesh Tifdeh." Any animal that lives eight days is viable - "umi'Yom ha'Shemini va'Hal'ah Yeratzeh l'Korban."

Inference: Before these times, it is a Safek.

Question: Do Chachamim argue with R. Shimon ben Gamliel?

Answer (Beraisa): A calf born on Yom Tov may be slaughtered that same day.

Rejection: The case is, we know that Kalu Chadashav (it had a full term pregnancy).

Rav Papa and Rav Huna brei d'Rav Yehoshua visited Rav Idi bar Avin. He prepared for them a third-born calf on its seventh day. They told him, had you waited until evening to slaughter it, we would have eaten it. Since you slaughtered it now, we will not eat it.

Rishonim

Rambam (Hilchos Isurei Mizbe'ach 3:8): It is a Mitzvah to offer all Korbanos from the eighth day and onwards.

Question (Mishneh l'Melech): If we know that an animal is not a Nefel (e.g. Kalu Chadashav), may it be offered before eight days? The Torah forbids Hakravah before eight days because it is a Safek Nefel, just like a baby before 30 days. Why doesn't the Rambam discuss this?

Answer #1: Kalu Chadashav proves viability for babies, but not for animals.

Rejection: Shabbos 136a permits to slaughter on Yom Tov a calf born that same day, if Kalu Chadashav.

Answer #2 (Mishneh l'Melech): It is a Gezeras ha'Kasuv that Korbanos may not be offered before eight days, even if it is not a Safek Nefel.

Question: If so, what is R. Shimon ben Gamliel's source that an animal is a Safek Nefel until eight days?

Answer #1 (Mishneh l'Melech): Indeed, the Torah forbids before eight days because it is usually Safek Nefel. The Torah forbids in every case, even when it is not a Safek.

R. Yom Tov Algasi (Hilchos Bechoros 1:14 DH v'Hinei Achti): The Torah does not allow Pidyon within 30 or eight days (for people and donkeys, respectively), due to Safek Nefel. Rashi (136a DH Lo Nitzrecha) says that we know that Kalu Chadashav only if the mother did not have relations the entire pregnancy. It is rare that we know this, therefore the Torah does not let us rely on it.

Answer #2 (Mishbetzos Zahav YD 15:3 DH Da): Reasoning teaches that it is a Safek Nefel before eight days.

Note: Presumably, he means that we have no source that it is viable, therefore it is a Safek to us. The Rashba (Bava Kama 11b DH Bechor) explains that it is a Gezeras ha'Kasuv to wait 30 days before Pidyon ha'Ben. It is not due to Safek Nefel. Nevertheless, we may infer that after 30 days it is viable, for the Torah would not command to redeem (or offer) a Safek Nefel.

Rambam (Hilchos Bechoros 1:8): A Bechor must be eaten within its year. If it is Tam we count the year from day eight, when it was Kosher to be offered. If it was born with a Mum, and Kalu Chadashav, we count the year from its birth, for it was permitted immediately. If we do not know that Kalu Chadashav, we count the year from day eight.

Rambam (Hilchos She'ar Avos ha'Tum'ah 2:6): If an animal was slaughtered within seven days, it is Tamei like a Nevelah, for it is like a Nefel.

Rosh (Shabbos 19:7): We rely on Chachamim to permit a Yevamah who became engaged to a Kohen (and the child died within 30 days. Chalitzah would forbid her to him). We are stringent like R. Shimon ben Gamliel to require Chalitzah if she became engaged to a Yisrael, and to forbid an animal slaughtered within seven days. We learn from Rav Papa and Rav Huna that one may slaughter on the night before the eighth day.

Dagul me'Revavah (YD 15:2): Regarding Yibum, we are lenient b'Di'eved. Why are we stringent about animals? We must say that people are different, for we see that the baby's hair and fingernails were finished. (This implies that it was not a Nefel.) This is difficult; it requires investigation. The Rashba is lenient about Chalitzah even without finished hair and fingernails. All the more so we should be lenient about a slaughtered animal, for it did not die by itself! Tevu'os Shor (12) says that we are stringent about animals, for it is merely monetary. This is difficult. Tosfos (Nidah 44b DH d'Kim) says that the minority of Nefalim is sizable and common, therefore we are stringent. I.e. for every animal born, the question arises when one may slaughter it. The case of Yevamah is very rare. Also, we cannot ignore animal Nefalim, for it is a sizable minority and there is Chezkas Isur. A Yevamah had Chezkas Heter, for most babies are viable. Rosh Hashanah 7a forbids eating a Ba'al Mum Bechor within seven days. It connotes that this is mid'Oraisa, due to Safek Nefel.

Rashba (1:253): If one bought kids from a Nochri, he may not trust him to say that they are eight days old. We rely on a Nochri to be lenient only for Edus Ishah. If we are unsure if they are eight days old because they are small, the Nochri's words do not settle the doubt, especially here, since he says so to praise what he sells.

Tosfos (20b, last lines): Letter of the law, the Halachah follows Chachamim, who assume that a Stam baby within 30 days (or an animal within eight days) is viable. They were stringent about Yibum (unless a Kohen was Mekadesh her), and also for animals, for if we would be lenient about animals, people would be lenient about Yibum. Also, if we permit slaughtering a healthy animal within eight days, people will slaughter sick animals within eight days.

Pleisi (YD 15:3): Tosfos holds unlike the Ran, who says that we do not follow the majority regarding Davar she'Yesh Lo Matirim. If he held like the Ran, he would not need to find a reason to be stringent about animals. We do not rely on the majority of viable animals, since we can slaughter after eight days!

Rebuttal (Minchas Yitzchak 5:55 DH v'Lo): Granted, before Shechitah it is Davar she'Yesh Lo Matirim. However, Chachamim were stringent even b'Di'eved if it was slaughtered before eight days. This is not Davar she'Yesh Lo Matirim. Tosfos explained why we never rely on the majority, i.e. even after Shechitah.

Poskim

Shulchan Aruch (YD 15:2): If we know that an animal was Kalu Chadashav, i.e. nine months for a big (work) animal or five months for a small animal, it is permitted the day it was born. If we are unsure, it is a Safek Nefel until the eighth night begins.

R. Akiva Eiger: The Taz (2, b'Sof) connotes that we need seven 24-hour periods. We do not count part (the end) of the day of birth like a full day. The Pri Megadim agrees. Tevu'os Shor is lenient. I agree. R. Shimon ben Gamliel supported himself from the verse "Shiv'as Yamim Yihyeh Im Imo." Tosfos (Erchin 18b DH mi'Shenaso) proves that we do not need seven 24-hour periods. He proved that the year to offer a Korban (that must be a yearling) is from the day of birth, and not from the day when it could be offered, since we say that hours disqualify Kodshim. I.e. it is possible to enter its second year between Shechitah and Zerikah. If we count from when it could be offered, this law could not apply! (It would enter its second year exactly one year from the eighth day, at the earliest time of the day to offer a Korban. This cannot be between Shechitah and Zerikah.) We may learn from Tosfos. If we required seven 24-hour periods, the second year could begin in the middle of the day (at the time it was born), which could be between Shechitah and Zerikah!

Noda bi'Yehudah (2:YD 7, from his son) brings R. Akiva Eiger's proof, but concludes that if a case occurred, he would not be lenient against great Poskim (the Taz and Pri Megadim). However, one who is lenient does not lose.

Shulchan Aruch (3): If one bought kids from a Nochri, he may not trust him to say that they are eight days old.

Shach (4): He is not believed even if he spoke l'Fi Tumo (unaware of the consequences), for a Nochri is believed only about Edus Ishah, and there he is believed only l'Fi Tumo. This shows that he is not believed about other matters even l'Fi Tumo.

Taz (4): We should be lenient due to a Sefek-Sefeka! Perhaps Kalu Chadashav, and even if it was not, perhaps the animal is eight days old! We can say that the Mechaber holds like the opinion brought in 110:8 that Sefek-Sefeka does not permit Davar she'Yesh Lo Matirim (something that is permitted in another situation). However, the Rema said there, and in Toras Chatas 74 in the name of the Ran, that one may be lenient for a need. If so, he should have been lenient here, even without the Nochri's testimony! I answer that this is not a Sefek-Sefeka, for there is surely a Safek whether it is a Nefel, so one cannot say 'if you will say that it is a Nefel...'This is unlike the Sefek-Sefeka in Tosfos Kesuvos (9a DH v'Iy) 'even if she was Mezanah (perhaps this was before Kidushin).'

Rebuttal #1 (Nekudas ha'Kesef): Here it is not guaranteed to become permitted, so this is not Davar she'Yesh Lo Matirim. Really, there is no question at all. It is not a Sefek-Sefeka, for if it is a Nefel, even if it is eight days old it is forbidden! Also, if it is a Nefel it will not live to be eight days old, for eight days removes the Safek of Nefel. Perhaps this was the Taz' answer. The answer is so obvious that there was no need to write it.

Rebuttal #2 (Birkei Yosef 2, citing Chidushei ha'Gershoni): The Rashba taught this law, and he holds that a Sefek-Sefeka permits even a Davar she'Yesh Lo Matirim!

Birkei Yosef (3, citing Radvaz 726): Nowadays people eat young kids. They do not rely on Nochrim, rather, on the rule that they do not have teeth before eight days. If this rule is substantiated, one may rely on it. If Nochrim testify about the rule, one may rely on them, for it is prone to become known. (People do not lie about such matters.)

Birkei Yosef (4): If a kid was slaughtered and some say that it seems that it was (at least) eight days old, and some say that it seems that it was less than eight days, we permit due to a Sefek-Sefeka. This is unlike what the Rashba discussed.