THE TODAH MAY BE BROUGHT AS SIMCHAH BUT NOT AS CHAGIGAH
Question: Is it not obvious that an obligation, such as Chagigah, must come from Chulin!?
Answer: We might have permitted the use of the Todah as a Chagigah in the case where he stipulated such when he designated the Korban.
We learn that such stipulations are not effective from the exchange between Resh Lakish and R. Yochanan.
Resh Lakish asked about a conditional Todah and a conditional Nezirus and, in both cases, R. Yochanan responded that his vow is binding and his condition is not acceptable.
We find a similar concept where a statement being binding and an apparent condition is void.
A person, on his deathbed, instructed that money be given to Reuven and that Reuven should marry the dying man's daughter.
(R. Papa): The money is to be given and he need not marry the daughter.
It appears that the second part of the statement losses its binding nature because it was stated as additional to the first statement; had it been stated as a formal condition (let him marry my daughter and give him the money) then the condition is binding.
Mereimar reported R. Yochanan's Din (that the condition to use Ma'aser Sheni for the Korbanos of his Nezirus is not valid) in his own name.
Ravina pointed out to him, that he had learned it in the name of R. Yochanan as an answer to Resh Lakish's question.
SEMICHAH BY OLAS CHOVAH
The Beraisa expert, quoting a Beraisa, learns from the Pasuk that an Olas Chovah (where Semichah is not mentioned explicitly) requires Semichah just like an Olas Nedavah (where it is explicit).
(R. Yitzchak b. Aba): The author of this Beraisa must be Beis Shamai who needs a special Pasuk for Olas Chovah, because he does not learn it automatically with a Binyan Av (unlike Beis Hillel who learn Shalmei Chovah from Shalmei Nedavah).
Question: How are you so certain that Beis Hillel learns the Semichah of Shalmei Chovah from Shalmei Nedavah; perhaps (we do not learn Chovah from Nedavah and) they learn it from Olas Chovah (and thus Olas Chovah itself needs a Pasuk, and the Beraisa is all opinions)!?
Answer (R. Yitzchak): It is not more reasonable to learn Shalmei Chovah from Olos Chovah, than from Shalmei Nedavah because Olos Chovah are completely burned, whereas Shalmei Chovah are not.
Beis Hillel might learn Shalmei Chovah from both Shalmei Nedavah and Olas Chovah together.
If so, Beis Hillel too, must learn Olas Chovah from "ka'Mishpat".
Consequently, Beis Hillel could well be the author of the Beraisa, and R. Yitzchak's question on the Beraisa expert is not valid.
Question: But we have a Beraisa which teaches that Beis Shamai does require Semichah (and their dispute is whether the Semichah must come immediately prior to the Shechitah [Beis Hillel], or whether it can be performed the day before [Beis Shamai])!?
Answer: R. Yitzchak based himself on R. Yosi b'Rebbi Yehudah who learns that Beis Shamai and Beis Hillel dispute whether Shalmei Chovah require Semichah or not.
THE INCIDENT OF HILLEL HA'ZAKEN AND SEMICHAH
Hillel ha'Zaken was approached by a large group of disciples of Shamai, who demanded to know what sort of animal he was bringing (they suspected that it was an Olah, and wanted to stop him from making Semichah on Yom Tov).
He replied that the animal was a female (and must therefore be a Shelamim, and not an Olah); to prove his point (and put them off), he swished its tail.
They would have fixed the Halachah like Beis Shamai, were it not for the intervention of Bava b. Buta, thus assuring that the Halachah was fixed like Beis Hillel.
When a disciple of Beis Shamai tried to stop a disciple of Beis Hillel him from making Semichah on an Olah on Yom Tov, he countered his query 'Mah Zu Semichah' with 'Mah Zu Shesikah.'
From his three word retort we can learn how to counter an argument.
One should counter using language as curt as that of the first disputant.
BRINGING OLAS RE'IYAH ON YOM TOV
Question (Beis Hillel): We should learn from Shabbos where Melachos are forbidden for a Hedyot (to cook for oneself), but permitted for Hash-m (as a Korban Tamid) then on Yom Tov, when Melachos are permitted for a Hedyot, they should certainly be permitted for Hash-m (as an Olas Re'iyah)!?
Answer (Beis Shamai): This may be refuted from Nedarim and Nedavos, which are forbidden on Yom Tov, even though Melachos are permitted for ones personal needs.
Question (Beis Hillel): But Olos Re'iyah have a fixed time and ought to be permitted (like the Korban Tamid on Shabbos), while Nedarim and Nedavos ought be forbidden because they don't!?
Answer (Beis Shamai): The time of Olos Re'iyah is also not fixed for (the first day of) Yom Tov (one who failed to bring an Olas Re'iyah on Yom Tov, has the remainder of Yom Tov on which to bring it).
Question (Beis Hillel): Olas Re'iyah does have a fixed time since, as the Mishnah there continues, once Yom Tov has passed, he no longer remains obligated to bring it.
(Beis Shamai): Lachem teaches that only your needs, not those of Hash-m, may be performed on Yom Tov.
(Beis Hillel): la'Shem teaches that one does bring an Olas Re'iyah on Yom-Tov.
Question: How will Beis Hillel understand Lachem?
Answer: Your needs and not those of other nations or species.
ALTERNATE RENDITION OF BEIS HILLEL'S KAL VA'CHOMER
(Aba Shaul): If when your oven is closed (on Shabbos), Hash-m's is open, then when your oven is open (on Yom Tov), Hash-m's should certainly be open (and anyway, it is not right that your table should be full and your master's, empty).
Question: What is the dispute between the Tana Kama and Aba Shaul (leading to a difference in the claims)?
Answer: Beis Shamai do not refute Beis Hillel's argument with Nedarim and Nedavos (according to Aba Shaul) because, in his opinion, Beis Hillel hold Nedarim and Nedavos are brought on Yom Tov.
THE RESTRICTION OF NEDARIM AND NEDAVOS- D'ORAISA OR D'RABANAN
(R. Huna): Bringing Nedarim and Nedavos on Yom Tov is not only an Isur d'Rabanan;
If it were, the Rabanan's reason for prohibiting it would be out of the fear that one may postpone one's Korbanos for Yom Tov.
He would then be unable to bring them.
It is even an Isur d'Oraisa.
As learned from the Sh'tei ha'Lechem on Shavuos, which cannot be brought before Yom Tov (because it is premature).
The decree that he might postpone it does not therefore apply; yet their preparation over-rides neither Shabbos nor Yom Tov.
Question: If someone slaughtered Nedarim or Nedavos on Yom Tov (against the prohibition of those who hold it to be Asur), may the Zerikah be still done (to permit it)?
Answer (Rava): The Kohen sprinkles the blood only if it was in order to permit the flesh of the Korban to be eaten.
Answer (Rabah bar R. Huna): The Kohen would even sprinkle the blood if he only had the fat-pieces to be burned after nightfall.
Question: What difference would their answers make?
Answer: Whether he would be permitted (Rabah bar R. Huna) or prohibited (Rava) to sprinkle it even if the flesh became Tamei or lost (sprinkling the blood is only an Isur d'Rabanan there where there is no Chiyuv to sprinkle it).
Question: The Beraisa (speaking of improperly slaughtered lambs of the Shalmei Tzibur of Shavuos) implies that ideally one would not do the Zerikah on Shabbos!?
Answer: This is indeed a good question on Rabah bar R. Huna.
Alternate Answer: Given that the Beraisa is speaking on Shabbos, and not on Yom Tov, perhaps Chazal were more stringent by Shabbos than they were by Yom Tov.