1) INTRODUCTION TO MUKTZAH
One of the central topics of Maseches Beitzah is the topic of Muktzah. The following review of the basic concepts of Muktzah will facilitate a better understanding of the Gemara's discussions.
(a) MUKTZAH. The word "Muktzah" (from the word "Katzah") literally means "set aside at the far edge [of one's intentions for use]." The term is used to describe objects that are set aside from usage on this day, such as wood stacked away in a storage facility (the word for a storage area is "Muktzah"). In a broader sense, the word "Muktzah" includes any object which a person did not intend to use, for any reason, at the time of the onset of Shabbos or Yom Tov.
(b) THE DISPUTE OF THE TANA'IM. Rebbi Yehudah and Rebbi Shimon disagree about the extent of the application of the laws of Muktzah. The Gemara's statement that Rebbi Shimon "does not hold of Muktzah" does not mean that Rebbi Shimon maintains that there is no prohibition of Muktzah whatsoever. Rather, it means that Rebbi Shimon maintains that certain categories of Muktzah are not prohibited. Some categories of Muktzah are prohibited according to everyone, including Rebbi Shimon.
The dispute between Rebbi Yehudah and Rebbi Shimon applies to at least six different categories of Muktzah:
1. HIKTZEHU MI'DA'ATO ("he set it aside from his mind"). This category of Muktzah refers to objects which a person did not have in mind before Shabbos (or Yom Tov) to use during Shabbos (or Yom Tov). According to Rebbi Yehudah, any object one put aside because he did not intend to use it on Shabbos is Muktzah and is prohibited. According to Rebbi Shimon, even an object one put aside because he did not intend to use it may be used and does not become Muktzah, as long as it has a form of use that is permitted on Shabbos (or Yom Tov). Rebbi Shimon prohibits only an object which a person consciously decided not to use by making it unfit for use on Shabbos (such as fruit he put out to dry right before Shabbos, which becomes inedible until it is fully dried). Even if, on Shabbos, the object becomes fit for use (before the time at which he had intended them to become fit), they still may not be used on Shabbos.
2. NOLAD ("born"). An object which did not exist in its present form during Bein ha'Shemashos between Friday and Shabbos, but rather was created (or was significantly changed) on Shabbos, belongs in the category of Muktzah known as Nolad ("born"). Utensils which broke on Shabbos did not exist in their present form before Shabbos, and thus they are considered Nolad. Date pits from dates eaten on Shabbos are Nolad, because they were considered fruit when Shabbos entered and emerged as pits only on Shabbos. Rebbi Yehudah prohibits moving such objects because a person did not have in mind -- before Shabbos, when they did not yet exist -- to use them on Shabbos. Rebbi Shimon disagrees and maintains that advance, positive intention to use an object on Shabbos is not necessary.
3. MUKTZAH MACHMAS ISUR ("set aside because of a prohibition"). According to Rebbi Yehudah, any object that was Muktzah during Bein ha'Shemashos at the onset of Shabbos remains Muktzah for the duration of Shabbos, even if the cause of its Muktzah status is no longer present. The operative principle behind this type of Muktzah is called "Migo d'Iskatza'i l'Vein ha'Shemashos, Iskatza'i l'Chulei Yoma" -- "since it was set aside for Bein ha'Shemashos, it remains set aside for the entire day." According to Rebbi Shimon, there are times when the principle of "Migo d'Iskatza'i" does not apply. For example, when an object was Muktzah during Bein ha'Shemashos and its owner realized that it will probably become usable during Shabbos, he may use or move the object after it becomes usable (see Shabbos 44a, 46b).
4. MUKTZAH MACHMAS MI'US ("set aside because of repulsiveness"). An object which is repulsive is automatically considered set aside from usage (Muktzah) according to Rebbi Yehudah.
5. KLI SHE'MELACHTO EINO ELA L'ISUR ("a utensil used exclusively for a prohibited purpose"). An object which is used almost exclusively for a task which is prohibited on Shabbos or Yom Tov is considered Muktzah according to Rebbi Yehudah. According to Rebbi Shimon, it may be used for a permitted purpose (but it may not be moved for its own protection). This category is not to be confused with "Kli she'Melachto l'Isur," an object which is commonly used for a prohibited purpose but which is sometimes employed for a permitted use. Even Rebbi Yehudah permits one to move a Kli she'Melachto l'Isur in order to use it for a permitted purpose, or to make room for something else ("l'Tzorech Gufo u'Mekomo"). (TOSFOS to Shabbos 36a, DH Ha Rebbi Yehudah, and 44a, DH Mitah)
6. MUCHAN L'ADAM EINO MUCHAN L'KELAVIM ("that which is prepared for use of man is not prepared for dogs"). There are two distinct types of Muktzah included in this category:
a. An object that was designated for human use but cannot be used on Shabbos because of the laws of Shabbos or Yom Tov. For example, a live animal that was designated to be slaughtered and prepared as meat for people is not fit for use on Shabbos since it is forbidden to slaughter an animal on Shabbos. Even though animals that are not properly slaughtered are sometimes fed to dogs, since this animal was designated to be used for people after Shabbos it is Muktzah on Shabbos (according to Rebbi Yehudah) and may not be fed to dogs.
b. An object that was fit for human use when Shabbos arrived, but something happened to the object on Shabbos that renders it unfit for human use. This is a form of Nolad and is comparable to a pit from a date that was eaten on Shabbos. For example, before Yom Tov a live animal was fit for man on Yom Tov since it could be slaughtered, cooked, and eaten on Yom Tov. However, on Yom Tov the animal died and thereby became unfit for man. Rebbi Yehudah prohibits feeding such an animal to dogs, while Rebbi Shimon permits it.
(c) Other categories of Muktzah are prohibited according to both Rebbi Yehudah and Rebbi Shimon:
1. MUKTZAH MACHMAS GUFO ("set aside because of itself"). This refers to any object which intrinsically has no use, such as a rock (which was not designated for any useful purpose).
2. HUKTZAH L'MITZVASO ("set aside for its Mitzvah"). An object which is designated for a Mitzvah may not be used for other purposes which detract from the Mitzvah, even on a weekday. On Shabbos, such an object is Muktzah and may not be moved as long as it is still fit for the Mitzvah (if it becomes unfit for the Mitzvah during Shabbos, its status depends on the Halachah of "Migo d'Iskatza'i," mentioned above in b:3).
3. DAVAR SHE'EINO RA'UY SHE'DECHA'O B'YADAYIM ("an object which is not fit [to be used on Shabbos] because its owner excluded it from use [by rendering it unfit to be used on Shabbos]"). An object which a person consciously decided not to use and also performed an action that rendered it unfit for use throughout Shabbos (such as fruit he put out to dry right before Shabbos, which becomes inedible until it is fully dried). Even if, on Shabbos, the object becomes fit for use (before the time at which he had intended for it to become fit), it still may not be used on Shabbos. (See above, b:1.)
4. DAVAR HE'ASUR BEIN HA'SHEMASHOS SHE'LO CHASHAV SHE'YAVO L'YEDEI HETER B'SHABBOS. An object which was forbidden to be used Bein ha'Shemashos because an Isur Shabbos must be transgressed in order to make the object useable (such as produce which was still attached to the ground) and which one did not think would become permitted on Shabbos remains prohibited even when the Isur that prohibited the object until now is removed. (See Rashi 24b DH Im Yesh, Tosfos 3a DH Gezeirah.)
5. MUKTZAH MACHMAS CHISARON KIS. An object which is set aside from use due to its fragility is Muktzah. (The object will not be used during Shabbos in the way it normally is used, and to use it in any other way may damage it.) For example, a Mohel's scalpel (after the Bris, or when there is no eighth-day Bris to perform that Shabbos) is Muktzah.
(d) According to most Rishonim, the prohibition of Muktzah is only mid'Rabanan. The prohibition was instituted by Nechemyah ben Chachalyah (Shabbos 124b) in order to prevent people from carrying on Shabbos from Reshus ha'Yachid to Reshus ha'Rabim (Beitzah 37b; Shabbos 124b). The Rabanan prohibited moving a Kli she'Melachto l'Isur (to protect it) lest a person use it in a prohibited manner on Shabbos (RAMBAM, Hilchos Shabbos 24:13). Other reasons are proposed by the Rishonim for the prohibition of Muktzah: so that a person will not spend the entire Shabbos moving objects around from place to place and not resting, and so that a person who does not work during the week will have a way to distinguish between Shabbos and a weekday (Rambam, ibid. 13-14).
RASHI (2b, DH v'Hechinu, and 26b, DH v'Iy), however, appears to maintain that Muktzah is a Torah prohibition, at least according to Rabah (the prohibition is known as "Hachanah d'Rabah"). However, the Rishonim quote Rashi as saying that only eating Muktzah is prohibited by the Torah according to Rabah; moving Muktzah is prohibited only mid'Rabanan. (These words do not appear in our texts of Rashi, but they are quoted by the note of the SHITAH MEKUBETZES on Rashi, 2a, DH Man d'Shari; by the PRI MEGADIM in his introduction to Hilchos Yom Tov, section on Muktzah; by the CHASAM SOFER in introduction to Mahadura Tinyana; and by the KOHELES YAKOV OC 509:7).
2) HALACHAH: MUKTZAH ON YOM TOV
OPINIONS: Rav Nachman states that the Mishnah in Shabbos (156b) which discusses Muktzah on Shabbos was compiled by Rebbi in accordance with the view of Rebbi Shimon (who maintains that Muktzah is permitted) without attributing it to Rebbi Shimon's name. The Mishnah here in Beitzah which discusses Muktzah on Yom Tov was compiled by Rebbi in accordance with the view of Rebbi Yehudah (who maintains that Muktzah is prohibited) without attributing it to Rebbi Yehudah's name.
A general principle in the Mishnayos is that when Rebbi compiled a "Stam" Mishnah (with no attribution to any particular Tana), this indicates that Rebbi ruled in accordance with that view. Accordingly, Rebbi seems to contradict himself in the Mishnayos in Shabbos and Beitzah. Rav Nachman answers that Rebbi ruled like Rebbi Shimon with regard to Muktzah on Shabbos, because on Shabbos all Melachos are forbidden and thus the day needs no additional rabbinical safeguards. He ruled like Rebbi Yehudah with regard to Muktzah on Yom Tov, because on Yom Tov some Melachos are permitted, and thus the day needs additional rabbinical safeguards to strengthen the observance of Yom Tov.
What is the Halachah with regard to Muktzah on Shabbos and on Yom Tov? Does the Halachah follow Rav Nachman's explanation of Rebbi's view? (See previous Insight with regard to the different types of Muktzah. Here, we discuss only the type of object which is Muktzah because one did not have in mind to use it at the onset of Shabbos or Yom Tov, or "Hiktzehu mi'Da'ato".)
(a) The RIF, RAMBAM, and other Rishonim rule that the Halachah follows Rebbi as explained by Rav Nachman: Muktzah is prohibited on Yom Tov as an additional safeguard to the sanctity of the day. (The RA'AVAD writes that Rebbi maintains that Muktzah is actually permitted even on Yom Tov. However, Rebbi wrote the opinion of Rebbi Yehudah so that ignorant people who learn only Mishnah will think that the Halachah follows Rebbi Yehudah on Yom Tov and will treat Yom Tov with the proper respect. A Talmid Chacham, however, may be lenient with Muktzah on Yom Tov.)
(b) The BA'AL HA'ME'OR rules like Rebbi as explained by Rav Nachman, but he explains the Gemara differently. He proposes that it is not logical that the law on Yom Tov should be more stringent than the law on Shabbos. Rather, when Rebbi ruled that Muktzah is prohibited on Yom Tov, he referred only to objects which are Muktzah on Shabbos because of a prohibition which applies to Shabbos (such as cooking); those objects are not Muktzah on Yom Tov because the prohibition does not apply on Yom Tov. For example, wood should not be Muktzah on Yom Tov because it may be used as fuel for fire, and making a fire on Yom Tov is permitted. On Shabbos, though, wood is Muktzah because making a fire on Shabbos is forbidden. Rebbi's ruling prohibits objects like wood even on Yom Tov in order to safeguard the sanctity of Yom Tov. Safeguarding the sanctity of Yom Tov ("Lo l'Zilzulei") makes Yom Tov only as stringent as Shabbos, but not more so. According to the Ba'al ha'Me'or, Rebbi is stringent only with regard to objects which are used for burning, Shechitah, or cooking (Melachos which are permitted on Yom Tov and prohibited on Shabbos).
(c) RABEINU CHANANEL (end of Beitzah) rules like Rav Nachman, and the law on Yom Tov indeed is more stringent than on Shabbos in order to safeguard the sanctity Yom Tov. However, this stringency on Yom Tov does not apply to normal Muktzah objects ("Hiktzehu mi'Da'ato"); such objects indeed are permitted on Yom Tov just as they are permitted on Shabbos, like the view of Rebbi Shimon. Rather, the stringency of Yom Tov applies only to objects which are prohibited as Muktzah because of some other reason (such as "Nolad" or "Muktzah Machmas Isur").
(d) The ROSH (5:14) cites RASHI, RI, and RABEINU TAM who are lenient even with regard to Yom Tov. They rule that Muktzah is always permitted. They reason that it was only Rav Nachman who asserted that there is a difference between Yom Tov and Shabbos. He differentiated between Yom Tov and Shabbos only to explain the opinion of Beis Hillel in the Mishnah (who says that an egg laid on Yom Tov is prohibited). According to the other Amora'im who conclude that the egg mentioned in the Mishnah is prohibited not because it is Muktzah but because of other reasons, there is no reason to differentiate between Yom Tov and Shabbos. Since the Gemara at the end of Shabbos says that the Halachah follows Rebbi Shimon, his ruling is accepted with regard to Yom Tov.
There is a slight difference between the view of Rabeinu Tam and that of Rashi and the Ri. Rabeinu Tam rules that although the law is lenient with regard to Muktzah on Yom Tov, the law is stringent with regard to Nolad, both on Yom Tov and on Shabbos. Rashi (33a, DH v'Hilchesa) and the Ri do not differentiate between Muktzah and Nolad, and they permit both types of Muktzah on Yom Tov and on Shabbos.
HALACHAH: The SHULCHAN ARUCH (OC 495:4) rules like the Rif and Rambam who prohibit Muktzah on Yom Tov but not on Shabbos. The REMA, however, rules leniently and permits Muktzah both on Shabbos and on Yom Tov (like (d) above). However, he accepts Rabeinu Tam's stringency and does not permit Nolad on either day.
The MISHNAH BERURAH (OC 495:17) cites Acharonim who are even more lenient and permit Nolad on Shabbos and prohibit it only on Yom Tov (like the opinion of Rabeinu Chananel in (c) above).

2b----------------------------------------2b

3) REBBI'S CONTRADICTION
QUESTION: The Gemara asks why Rebbi followed the view of Rebbi Shimon in the Mishnah in Shabbos (156b) which discusses Muktzah on Shabbos, while he followed the view of Rebbi Yehudah in the Mishnah here (2a) which discusses Muktzah on Yom Tov. The Gemara answers that Rebbi was concerned that people might treat the sanctity of Yom Tov lightly because some forms of Melachah are permitted on Yom Tov, and therefore he was stringent with regard to Muktzah on Yom Tov. Shabbos, however, which is already more stringent than Yom Tov, needs no additional safeguard.
Why does the Gemara not say simply that Rebbi followed the opinion of Beis Hillel? Beis Hillel rules leniently with regard to Shabbos and stringently with regard to Yom Tov, according to Rav Nachman's explanation. The Gemara should have asked why Beis Hillel rules differently with regard to Shabbos than he rules with regard to Yom Tov.
ANSWER: RABEINU CHANANEL explains that neither Rebbi Shimon nor Rebbi Yehudah argue with Beis Hillel. One might have assumed that both Beis Shamai and Rebbi Shimon maintain that Muktzah is permitted, while Beis Hillel and Rebbi Yehudah maintain that it is prohibited. This, however, is not the intention of the Tana'im. Rather, both Rebbi Shimon and Rebbi Yehudah agree with Beis Hillel, but they argue about what exactly Beis Hillel said. Rebbi Yehudah maintains that Beis Hillel ruled stringently and prohibited Muktzah both on Shabbos and on Yom Tov. Rebbi Shimon maintains that Beis Hillel was lenient both on Shabbos and on Yom Tov.
In Maseches Shabbos, Rebbi quoted Beis Hillel according to Rebbi Shimon's version, and in Beitzah he quoted Beis Hillel according to Rebbi Yehudah's version. He wrote the Mishnah in each place "Stam" accordingly. The Gemara therefore asks why Rebbi quoted differing opinions in Beis Hillel in the two places, and it answers that he made that compromise for the sake of preserving the sanctity of Yom Tov. (This is also the explanation of the RAMBAN in Milchamos, who describes it in more detail.)
4) "HACHANAH D'RABAH" -- RABAH'S PRINCIPLE OF "HACHANAH"
QUESTION: Rabah explains that an egg laid on Yom Tov is forbidden because of "Hachanah," according to Beis Hillel in the Mishnah. The formation of an egg is completed one day before it is laid. When Yom Tov immediately follows Shabbos, an egg laid on Yom Tov was completed on Shabbos. Since it is forbidden to use an object that was prepared on Shabbos for Yom Tov, the egg may not be used.
RASHI (DH v'Ein Yom Tov; 26b, DH v'Iy, see PNEI YEHOSHUA) equates the principle of "Hachanah d'Rabah" with Muktzah; the egg that was prepared on Shabbos for Yom Tov is Muktzah. Rashi says that one must prepare the Yom Tov meal in advance, because otherwise the food may not be eaten on Yom Tov, mid'Oraisa (as he learns from Pesachim 47b; see SHITAH MEKUBETZES). The preparation of the food must be done on a weekday and not on Shabbos or Yom Tov.
It is logical that just as an object prepared on Shabbos for Yom Tov may not be used on Yom Tov, an object that comes into existence on Yom Tov should be forbidden because it was not prepared for use on a weekday before Yom Tov. Why, then, does the Gemara say that the case of the Mishnah is when Yom Tov immediately follows Shabbos, and an egg laid today was completed yesterday? If it is forbidden to eat something created on Yom Tov, then the Gemara should say that the Mishnah refers to every Yom Tov, and that an egg is completed on the same day that it is laid. Accordingly, the egg should be forbidden because it was not properly prepared before Yom Tov.
ANSWERS:
(a) The ME'IRI (Chidushei ha'Me'iri, p. 4a) writes that according to Rashi the Gemara does not mean that the egg is forbidden only because it was completed the day before (on Shabbos), and that it would have been permitted had it been completed the same day on which it was laid (on Yom Tov). Even if the egg would have been completed on Yom Tov, it would have been forbidden. It was simply a known fact to the Gemara that an egg does not become completed on the day it is laid, but on the day before it is laid. Therefore, the Gemara has no choice but to explain that the Mishnah's prohibition applies in the case of an egg laid on Yom Tov that follows Shabbos.
(b) The PNEI YEHOSHUA writes that if eggs become completed on the same day they are laid, the opinion of Beis Shamai -- who permits eggs laid on Yom Tov -- would have no basis, because all eggs born on Yom Tov should be forbidden because they were not prepared on the weekday before Yom Tov. (In other words, Rashi preferred the explanation that he gives in order to avoid having to suggest that Beis Shamai argues with the entire notion of Hachanah according to Rabah.)
(c) Tosfos and most other Rishonim (see BA'AL HA'ME'OR) disagree with Rashi. They write that the Isur of Hachanah is not related to Muktzah. The egg is forbidden not because the food was not properly designated for Shabbos or Yom Tov, but because of a special rule in the Torah that one may not use an object on Yom Tov that came into being on the Shabbos that immediately precedes it (nor may one use an object on Shabbos that came into being on the Yom Tov that immediately precedes it). Consequently, if the egg came into being on Yom Tov, there is nothing wrong with using it on Yom Tov because the Torah does not prohibit such an object. The Gemara was forced to conclude that according to Rabah an egg is completed on the day before it is laid.
5) AN EGG LAID ON SHABBOS
QUESTION: Rabah explains that an egg laid on Yom Tov is forbidden because of "Hachanah," according to Beis Hillel in the Mishnah. The formation of an egg is completed one day before it is laid. When Yom Tov immediately follows Shabbos, an egg laid on Yom Tov was completed on Shabbos. Since it is forbidden to use an object that was prepared on Shabbos for Yom Tov, the egg may not be used.
The Gemara questions Rabah's explanation. According to Rabah, why should an egg laid on an ordinary Shabbos be forbidden? It was completed (and thus prepared) the day before, which was a weekday.
Why does the Gemara ask that an egg laid on Shabbos should be permitted according to Rabah? Every hen is Muktzah on Shabbos since it cannot be slaughtered. An egg that comes from the hen has the same status as the hen and should be prohibited because of Muktzah. Indeed, an egg laid on Yom Tov by a hen designated for laying eggs (and not for eating) is forbidden (2a) according to Rebbi Yehudah because of Muktzah and Nolad. Why should the egg that comes from a hen, which is Muktzah on Shabbos, be permitted according to Rabah?
ANSWERS:
(a) The BA'AL HA'ME'OR cites "Yesh Mefarshim" who suggest that the Gemara refers to a case of an egg laid on Shabbos in a home in which there is a very sick person whose life is in danger ("Choleh she'Yesh Bo Sakanah"). The members of the household planned, before Shabbos, to slaughter the hen on Shabbos for the sick person. Therefore, the hen is not Muktzah, and thus the egg that comes from it is not Muktzah.
The Ba'al ha'Me'or rejects this answer, because such a case is very rare (a "Milsa d'Lo Shechicha") and the Rabanan do not apply their Gezeiros in such cases (as the Gemara itself says). The egg in such a case indeed should be permitted.
(b) The RA'AVAD (on the Rif) explains that the Gemara understands that there is no prohibition of Muktzah on Shabbos (like Rebbi Shimon), even Muktzah Machmas Isur (such as a hen, which is excluded from use at the beginning of Shabbos because of the Isur against slaughtering on Shabbos).
(c) The BA'AL HA'ME'OR proposes a new rule for the laws of Muktzah. He explains that whenever a person intends to use a certain object which will come into existence (or become permitted to him) on Shabbos, it is not Muktzah at all, even according to Rebbi Yehudah.
Although the Mishnah in Shabbos says that oil left in a lamp after the flame goes out is Muktzah according to Rebbi Yehudah, that case is different because one knows that there might not be any oil left when the flame goes out. Therefore, before Shabbos he did not expect there to be leftover oil and he did not intend to use any oil that might be left. In this case, though, one expects the item (the egg) to come into the world and he intends to use it when it does.
(d) The RAMBAN (in Shabbos 144b, and Milchamos to Beitzah 21a) explains that Muktzah Machmas Isur makes an object prohibited, according to Rebbi Yehudah, only when the person himself made the object prohibited at the start of Shabbos (for example, by lighting the candle he made the oil prohibited). In this case, the item (hen or egg) became prohibited by itself when Shabbos entered, and therefore when the prohibition is removed the object becomes permitted (i.e., the principle of "Migo d'Iskatza'i" does not apply in such a case). Only when a prohibition actually was performed with an object on Shabbos does the principle of "Migo d'Iskatza'i" apply, even though the object originally became prohibited on Shabbos by itself (for example, when an animal is slaughtered on Shabbos in transgression of the prohibition against slaughtering). (In Milchamos to Pesachim 56b, the Ramban seems to contradict this ruling. He writes that if detached figs are on top of a tree and are not accessible unless one climbs the tree on Shabbos, they become Muktzah Machmas Isur and may not be used even if they fall down from the tree.)
The RAN expresses this answer differently. He explains that there is no general rule that an object which comes from an object of Muktzah is Muktzah. Rather, an egg which comes from a hen designated for laying eggs is Muktzah and prohibited because it is Nolad. Since the hen is not a food and the egg is a food, something new has come into the world. The Gemara here, however, is discussing a hen designated for slaughter (the owner plans to eat it after Shabbos); it is merely the prohibition against slaughtering on Shabbos (which was not imposed by the owner) which prevents one from eating the hen. Such a hen is still considered a food, and therefore its egg is "Uchla d'Ifras," a piece of food that broke off, and it is not Nolad. The fact that the egg came from a hen which is Muktzah does not make the egg Muktzah; anything which is edible is considered prepared for use on Shabbos, as long as it is not Nolad.
6) EGGS FOUND INSIDE OF A HEN THAT WAS SLAUGHTERED ON YOM TOV
QUESTION: The Gemara asks that eggs found inside a hen that was slaughtered on Yom Tov should be prohibited because of a Gezeirah of eggs that were laid on Yom Tov (which, Rashi explains, refers to Yom Tov that immediately follows Shabbos). The eggs found inside a hen, however, should be prohibited for an entirely different reason. Since there is a doubt whether the eggs that were extracted from the slaughtered hen were completed yesterday on Shabbos (in which case they are prohibited because of "Hachanah d'Rabah") or today on Yom Tov (in which case they are permitted according to most Rishonim; see above, Insights to Beitzah 2:4:c), they should be prohibited out of doubt (a Safek Isur). Why does the Gemara not rule conclusively that they are prohibited because of this reason?
ANSWERS:
(a) TOSFOS (DH Milsa) explains that the prohibition of "Hachanah," of having been prepared on Shabbos for Yom Tov, applies only retroactively after the egg is laid. The RAMBAN (in Milchamos) explains that this is because only at the moment the egg is laid does one benefit from the completion of the egg that occurred the day before (on Shabbos), for at that moment it becomes possible to eat the egg without slaughtering the mother. While the egg is still in the mother, nothing is gained from its completion.
The RA'AVAD and other Rishonim cite the Yerushalmi which presents a different reason for why the egg's completion becomes useful only retroactively, after it is laid: Only after it is laid is it fit to develop into a chick.
Another reason for why its completion is beneficial only retroactively when it is laid is because only at that moment does it begin to have a good taste. Before it is laid the fact that it has been completed is of no relevance, and thus it is not called "Hachanah" on Shabbos for Yom Tov.
(b) The RA'AVAD, in his explanation of the opinion of RABEINU EFRAIM, says that an egg that is completed the previous day is laid immediately in the morning. If most of the day has passed when the egg is removed from the slaughtered hen, it is clear that it was not completed the day before, but today, and it is therefore permitted.
(c) RABEINU EFRAIM, cited by the Ba'al ha'Me'or, indeed says that eggs found inside a hen are prohibited because of the doubt that they might have been completed the day before. Although the Ra'avad (in (b) above) understands that Rabeinu Efraim refers only to eggs found in a hen slaughtered at night, it is possible that Rabeinu Efraim refers even to eggs from a hen slaughtered during the day, and he learns the Sugya differently.
Perhaps Rabeinu Efraim understands that the Gemara is not discussing a Yom Tov that immediately follows Shabbos, but rather an ordinary Yom Tov that does not follow Shabbos. When the Gemara says that the eggs should be prohibited because of a Gezeirah of eggs laid on Yom Tov, it does not mean a Gezeirah of other eggs laid on Yom Tov, but it means a Gezeirah because of these eggs themselves: perhaps these eggs themselves were going to be laid today, and thus they should be included in the normal Gezeirah of eggs laid on Yom Tov! The Gemara answers that the Rabanan did not enact such a Gezeirah because it is uncommon to eat eggs found inside a hen. However, if a hen is slaughtered on a Yom Tov which follows Shabbos, since its eggs are prohibited mid'Oraisa the fact that such eggs are not usually eaten makes no difference; the eggs are prohibited. It is to these eggs that Rabeinu Efraim refers when he says that the eggs are prohibited because of the doubt that they might have been completed on the previous day.

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