Gemara

2a - Mishnah - Beis Shamai: One may eat an egg laid on Yom Tov;

Beis Hillel forbid.

Gemara - Question: What is the case?

If the owner is ready to eat the hen (i.e. he is not saving it to lay eggs), why would Beis Hillel forbid? The egg is like part of a food that separated!

If he keeps the hen for eggs, why would Beis Shamai permit? The egg is Muktzah!

We are thinking that even the opinion that permits Muktzah forbids Nolad.

Answer #1 (Rav Nachman): Really, the hen is for eggs. The opinion that forbids Muktzah forbids Nolad, and the opinion that permits Muktzah permits Nolad. Beis Shamai permit Muktzah, like R. Shimon. Beis Hillel forbid Muktzah, like R. Yehudah.

Question: Rav Nachman contradicts himself!

Mishnah - Beis Shamai: We may remove bones and peels from the table;

Beis Hillel say, we shake the entire tabletop (to cast them off).

Rav Nachman: (The opinions in our Mishnah must be switched.) Beis Shamai forbid Muktzah like R. Yehudah, Beis Hillel permit like R. Shimon.

Answer: Regarding Shabbos, a Stam Mishnah is like R. Shimon, therefore Rav Nachman establishes Beis Hillel to be like R. Shimon;

Mishnah: (On Shabbos) we may cut gourds in front of animals, and a carcass in front of dogs.

Regarding Yom Tov, a Stam Mishnah is like R. Yehudah, therefore he establishes Beis Hillel to be like R. Yehudah:

Mishnah: One may not chop wood (e.g. for cooking) from beams (designated for building) or from a beam that broke on Yom Tov.

Question: Rebbi codified the Mishnah. Why did he make the Stam Mishnah like R. Shimon regarding Shabbos and like R. Yehudah regarding Yom Tov?

Answer: Shabbos is severe. We are not concerned lest people disgrace it, therefore Rebbi was lenient like R. Shimon. Yom Tov is lenient. We are concerned lest people disgrace it, therefore Rebbi was stringent like R. Yehudah.

Objection: If they argue about Muktzah, why do they argue about the egg (which is Nolad)?

Answer: This is to teach the extremity of Beis Shamai, who permit even Nolad.

Objection: They should also argue about the hen itself, to teach that Beis Hillel forbid even Muktzah (that is not Nolad)!

6a: Rav forbids a chick born on Yom Tov, but permits a calf born on Yom Tov. This is because a calf is Muchan prepared along with its mother through Shechitah (i.e. even had it not been born, it could have been permitted through Shechitah of the mother).

Question (Rav Kahana and Rav Asi): Why is a chick different than a calf born to a Tereifah? (It is permitted even though Shechitah of the mother would not have permitted it!)

Rav did not answer.

Question (Rabah or Rav Yosef): Why didn't Rav answer that a calf was already Muchan along with its mother for dogs to eat? (Tereifos are normally fed to dogs.)

Answer (Abaye): (The opinion that forbids Muktzah, i.e. R. Yehudah, holds that) something Muchan for people is not considered Muchan for animals (in the following Mishnah). All the more so, something Muchan for animals is not considered Muchan for people!

Mishnah: We may cut gourds in front of animals, and a Neveilah in front of dogs (on Shabbos);

R. Yehudah says, if it was not a Neveilah when Shabbos began we may not cut it, since it was not Muchan.

Rejection (Rabah or Rav Yosef): Indeed, something Muchan for people is not considered Muchan for animals, for a person does not give to dogs something that he can use himself;

Something Muchan for animals is Muchan for people, for a person plans to use anything he will need.

Shabbos 144b - Shmuel: One may squeeze a cluster of grapes into a pot (for the sake of the food inside, not for drinking), but not into an (empty) bowl.

Rav Chisda: This teaches that one may milk a goat into a pot, but not into a bowl.

Rishonim

Rif (1a): We establish the Mishnah like Rabah (not like Rav Nachman).

Rif (2a): If wood fell off a tree on Yom Tov one may not burn it, for it is Nolad. Chachamim forbade this lest one climb a tree and detach wood.

Rif (Shabbos 60b): Even though Shmuel discusses squeezing on Shabbos (and permits into a pot but not into a bowl), Rav Chisda learns that the same applies to milking on Yom Tov.

Rebuttal (Ba'al ha'Ma'or Beitzah 1a): Rav Chisda's law applies even on Shabbos. Even though the goat is Muktzah, since one intends for the milk from before Shabbos it is permitted. According to Rabah, the egg is not Muktzah at all; Hachanah is a Gezeras ha'Kasuv. Rabah needed to say that an egg is finished one day before it is laid, for otherwise it would be permitted. Hachanah on Shabbos or Yom Tov for the day itself is permitted, unlike Muktzah.

(Milchamos Hash-m Shabbos 60b): The Ge'onim explain that the issue of milking is not Muktzah, rather, Melachah. The goat is not considered a food, therefore milking is Dash (extracting the food). It is permitted on Yom Tov because it cannot be done from before Yom Tov. However, the Gemara connotes that Rav Chisda discusses the same case as Shmuel, i.e. Shabbos. Nevertheless, the goat itself is considered a food. The opinion that forbids Muktzah would forbid; Rav Chisda learns from Shmuel that Muktzah is permitted.

Hagahos Ashri (1:1 DH v'Chalav): Milk milked on Yom Tov is Nolad, even if it came out by itself, whether it was milked into a pot or bowl. If the following day is Yom Tov it is forbidden because of Hachanah. The Gemara permits milking a goat ready to be eaten. The goat is considered a food, so the milk is not Nolad. But if it is milked into a bowl is Nolad, for it was a food and is now a drink. On Shabbos it is forbidden in every case.

Question: The Gemara suggested that an egg laid on Shabbos not after Yom Tov should be permitted. A hen is Muktzah on Shabbos, so also an egg that comes from it should be Muktzah! Also, why does the Gemara (Shabbos 144b) permit milking a goat into a pot?

Answer #1: The case is, there was a dangerously sick person in the house (we expected to slaughter the hen or goat on Shabbos).

Rejection (Ba'al ha'Ma'or ibid.): This is uncommon. We would not decree about Shabbos after Yom Tov in an uncommon case.

Answer #2 (Ba'al ha'Ma'or ibid.): Even though the mother is Muktzah, there is no Isur on the egg or milk.

Ran (Beitzah 1a DH v'Ika): The Gemara assumed that all agree that Nolad is forbidden. A hen kept for eggs is not a food, so even if one intended before Shabbos to eat the egg that would be laid, it is Nolad. However, a hen ready to be eaten is a food, even though one may not slaughter it on Shabbos. Therefore, the hen is Muktzah because of the Isur, but the egg is permitted. Similarly, if a goat is ready to be eaten one may milk it into a pot.

Rambam (Hilchos Yom Tov 1:18): Just like Muktzah is Asur on Yom Tov, also Nolad.

Question (Lechem Mishneh): He should say that all the more so Nolad is Asur, for some permit Muktzah and forbid Nolad!

Rambam (ibid. 2:11): If wood fell off a tree on Yom Tov one may not burn it, for it is Nolad. If it fell into an oven one may mix it with a larger amount of Muchan wood and burn them.

Rosh (5:14): BaHaG rules like R. Shimon regarding Muktzah, but like R. Yehudah regarding Nolad. He learns from Rava (33a), who forbids to burn Kelim that broke on Yom Tov.

Rebuttal (Rosh ibid.): Rava forbids all Muktzah, like the Gemara says (there and Shabbos 142b). We permit Muktzah, so perhaps we also perhaps Nolad!

Rosh (ibid.): R. Tam learns from Shmuel. Shmuel rules like R. Shimon regarding Muktzah (Shabbos 156b), but he would move date pits only through bread (143a), because of Nolad.

Rebuttal (Rosh ibid.): Shmuel was stringent on himself, but he permits Nolad regarding Shemen of Badadim (Shabbos 19b), i.e. oil that exudes on Shabbos from olives. Also R. Yochanan permits bones and peels (157a), which are Nolad.

Rosh (ibid.): R. Tam proves from the Stam Gemara which forbids date pits (143a) even though animals can eat them, because they are Nolad. Rav Nachman does not distinguish Nolad from Muktzah, but the Halachah does not follow him. Everyone else equates them. We hold like R. Yehudah regarding Yom Tov, but this is only regarding Muktzah due to Isur and Nolad.

Poskim

Shulchan Aruch (OC 322:3): If fruits fell from a tree on Shabbos they are forbidden on Shabbos and permitted immediately after Shabbos.

Shulchan Aruch (495:4): Even though Muktzah is permitted on Shabbos, Chachamim were stringent and forbade it on Yom Tov.

Mishnah Berurah (15): Several kinds of Muktzah that are permitted on Shabbos, such as things designated for sale, or in a storehouse, and Muktzah due to Mi'us (disgust), are forbidden on Yom Tov.

Rema: Some permit Muktzah even on Yom Tov, but they forbid Nolad even on Shabbos.

Mishnah Berurah (17): The Rema means that even one who is lenient should be stringent about Nolad on Yom Tov. Therefore, bones that became detached from meat on Yom Tov should not be moved. Even though they are fit for animals, at the start of Yom Tov they were fit for people.

Chazon Ish (43:10): An animal that died on Shabbos or Yom Tov is not Nolad. This is because we kill animals to use (eat) them.

Kaf ha'Chayim (37): When Yom Tov is on Shabbos, it is like Shabbos regarding Muktzah.

Kaf ha'Chayim (38): Anything that was fitting for something Bein ha'Shemashos but now it not fitting for that is Nolad. If a Keli broke on Yom Tov and it cannot be used similar to its original use, it is Nolad.