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1. The flesh of fish and grasshoppers are not included in the Isurim of Bishul Basar b'Chalav, Ha'alas Basar b'Chalav, and Neder on Basar.
2. The Reisha of the Mishnah, which forbids "Of" Min ha'Torah, is not in accordance with the view of Rebbi Akiva, who maintains that Chayah and Of are Basar b'Chalav only mid'Rabanan.
3. The Seifa, which categorizes "Of" as meat for the purpose of Nedarim, is in accordance with the view of Rebbi Akiva, who maintains that anything associated with the object of the Neder is included in the Neder, even if it needs additional confirmation.
4. Rav Ashi says that both the Reisha and Seifa are in accordance with the view of Rebbi Akiva, and the Isur of "Of" in the Reisha is mid'Rabanan.
5. Rav Yosef says that the Mishnah must maintain that the Isur of "Of" is Min ha'Torah, for otherwise the Isur of Ha'alas Of would be a Gezeirah l'Gezeirah. Abaye argues that Ha'alas Of is only one Gezeirah.
6. According to Rav Yosef, who maintains that the Isur of "Of" is Min ha'Torah, the Gezeirah of Ha'alas Of must be that one might bring the meat in a Kli Rishon to the table.
7. In the Mishnah, Beis Hillel and Beis Shamai disagree about whether the Isur of Ha'alas Of applies to a table for eating or also to a buffet table.
8. The fact that the Mishnah says in an awkward way that the Tana is Rebbi Yosi teaches the importance of saying a teaching b'Shem Omro, as doing so brings Geulah to the world.
9. Igra, the father-in-law of Rebbi Aba, ate "Of" after cheese without washing his mouth and hands in between. Rav Yitzchak brei d'Rav Mesharshiya even are Basar after cheese without washing, but only during the day when he could do a visible inspection.
A BIT MORE
1. The reason why fish and grasshopper flesh is not deemed "Basar" is that people simply do not refer to it as meat. If it would be referred to as meat, it certainly would be included in the prohibition of Nedarim.
2. While it is also not according to the opinion of Rebbi Yosi ha'Glili, who holds that chicken and milk is not a forbidden mixture (see Shabbos 130a), the Gemara is focusing on Rebbi Akiva's opinion, as it is a very prevalent (and ultimately the consensus) opinion.
3. Rebbi Akiva explains that if a messenger is told to purchase item A and finds that it is unavailable, and therefore asks the sender if he should purchase item B instead, this indicates that B is essentially in the same category as A.
4. The Mishnah meant that all meat is forbidden to be cooked with milk -- some types according to Torah law, while some only according to Rabbinic law -- with the exception of the flesh of fish and grasshoppers, which is permitted to be cooked with milk.
5. Rav Yosef sees Ha'alas Of as a Gezeirah of Achilas Of, while Abaye sees it as a Gezeirah of Ha'alas Basar, which is likely to lead to eating.
6. If it is Tzonen or in a Kli Sheni, even meat is forbidden only mid'Rabanan and is still a Gezeirah l'Gezeirah.
7. This is one of the rare rulings in which Beis Shamai is lenient and Beis Hillel is stringent.
8. The Mishnah mentions Rebbi Yosi's name late, as the Tana remembered only then that Rebbi Yosi was the author of this teaching (Rashi).
9. These opinions clearly maintain that while fowl and milk may not be eaten together according to Rabbinic law, one is not required to ensure that no residue remains on one's hands when eating the second type of food.
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