SHINUY BA'ALIM IS UNLIKE LO LISHMAH
Rejection (Rava): Lo Lishmah is a Pesul [of intent] in the Korban itself, it applies to all four Avodos, it applies after death of the owner (if his son brings the Korban), and it applies to the congregation as well as an individual - you cannot learn to Shinuy Ba'alim, which is not a Pesul in the Korban itself, does not apply to all four Avodos (except for Pesach, it applies only to Zerikah), does not apply after death, and does not apply to the congregation, only to individuals!
Even though two of these are not proper objectios, two of them are proper;
Shinuy Ba'alim is not a Pesul in the Korban itself, it is a Pseul of intent - the same applies to Lo Lishmah!
Rava said that Shinuy Ba'alim does not apply after death - but Rav Pinchas brei d'Rav Ami holds that it applies after death!
However, the other two are proper objections.
Answer #2 (Rava): Rather, if Pesach was slaughtered any other day b'Shinuy Ba'alim, it is as if it was slaughtered without owners in its time - it is Pasul.
SLAUGHTER FOR PEOPLE WHO CANNOT EAT PESACH
(Mishnah): If a Pesach was slaughtered for the following, it is Pasul - Lo l'Ochlav (people who cannot eat), Lo li'Mnuyav (they do not own a share), Arelim or Temei'im.
If it was slaughtered l'Ochlav and Lo l'Ochlav, li'Mnuyav and Lo li'Mnuyav, for Mulim (circumcised men) and Arelim, or for Temei'im and Tehorim it is Kosher.
If it was slaughtered before midday it is Pasul, for it says "Bein ha'Arbayim";
If it was slaughtered before the Tamid it is Kosher, but someone must mix the blood [so it will not congeal] until [it is thrown] after Zerikah of the Tamid;
If Zerikah [of a Pesach] was done [before that of the Tamid], it is Kosher.
(Gemara - Beraisa) Question: What is the case of Lo l'Ochlav?
Answer: It was for a sick or elderly person [who cannot eat a k'Zayis].
Lo li'Mnuyav is when one Chaburah (a group that will eat Pesach) was Manuy on it, and it was slaughtered for another Chaburah.
Question: What is the source of this?
Answer (Beraisa): "B'Michsas" (this connotes counting; "...Tachosu" connotes slaughter, like Rebbi will explain) - this teaches that we slaughter Pesach only for those Menuyim on it;
Suggestion: Perhaps one who slaughtered it Lo li'Mnuyav transgressed, but it is Kosher!
Rejection: "B'Michsas [Nefashos] Tachoso" (this also connotes counting) - the repetition teaches that it is Me'akev.
Rebbi says, Tachoso is a word of Sursi (Aramis, the language of Surya) - the root is Kos (slaughter).
Question: This teaches about Lo li'Mnuyav - what is the source for Lo l'Ochlav?
Answer: "Ish l'Fi Ochlo Tachoso" - this equates those who can eat it to those who are Menuyim on it.
(Rav Chisda): If Pesach was slaughtered for Mulim to eat it, and in order that Arelim will fulfil their obligation through Zerikah, it is Pasul, because of the intent for Arelim in Zerikah;
(Rabah): It is Kosher - the intent for Arelim in Zerikah has no effect (this will be explained).
Support (Rabah, for himself - Beraisa) Suggestion: Perhaps an Arel is Posel the Pesach for the entire Chaburah [if it was slaughtered for everyone]!
This is unreasonable! Arelus is Posel, just like Tum'ah - partial Tum'ah (this will be explained) does not Posel like full Tum'ah, the same should apply to Arelus!
Or, we could say otherwise - Arelus is Posel, just like [intent to eat at the wrong] time - just like intent for [eating] part of the [meat at the wrong] time is [Posel] like intent for [eating] the entire [Korban at the wrong] time, also partial Arelus is Posel slaughter like full Arelus!
Decision: It is more reasonable to learn Arelus from Tum'ah, for these do not Posel other Zevachim, and not from [intent to eat at the wrong] time, which is Posel all Zevachim.
Question: Perhaps we should rather learn Arelus from time, for neither of these is ever totally permitted, and not from Tum'ah, which is totally permitted (Korbanos Tzibur may be brought b'Tum'ah)!
Answer: "Zos [Chukas ha'Pesach" teaches that an Arel does not Posel the entire Chaburah].
Question: What do we learn from the verse?
It cannot teach that a Chaburah of all Arelim is Posel, but not a Chaburah that is partially Arelim - we learn this from "V'Chol Arel [Lo Yochal Bo]"!
Answer: Rather, the Beraisa [is abbreviated, it] means as follows - "V'Chol Arel" teaches that partial Arelus [of a Chaburah] is not Posel, only full Arelus;
Suggestion: Perhaps full Arelus is also Posel regarding [intent for] Zerikah!
Rejection: "Zos" - it is Posel only [in one Avodah, i.e.] slaughter.
Question: Why is Zerikah more lenient?
Answer: Intent Lo l'Ochlav does not Posel Zerikah.
Rav Chisda explains just the contrary:
"V'Chol Arel" teaches [regarding slaughter] that partial Arelus is not Posel, only full Arelus - but regarding Zerikah, even partial Arelus is Posel.
Suggestion: Perhaps full Arelus is needed to Posel also regarding Zerikah!
Rejection: "Zos" - full Arelus is needed to Posel only regarding slaughter.
Question: Why is Zerikah more stringent?
Answer: Pigul is finalized only through Zerikah (because it is the last Avodah - if there is another Pesul in addition to Pigul in one of the four Avodos, it is not proper Pigul for which is one is Chayav Kares).
Objection (Rav Ashi): What is the source to say that "V'Chol Arel" connotes that the entire Chaburah is uncircumcised? Perhaps it connotes that any amount of Arelus is Posel, and "Zos" teaches that only full Arelus is Posel, both regarding slaughter and Zerikah!