The Mishnah (4:6) explains that the korban must be nizbach (slaughtered) with six intentions -- for the purpose that korban must be brought (lishmah); for the person it must be offered for; for Hashem; so that the sacrificial parts are offered on the mizbeach; so that it produces a pleasing fragrance when it is burnt; and so that it gives nachat to Hashem as we fulfil His will. How does this Mishnah fit with our discussion in the beginning of Zevachim that already discussed the requirement of lishma?
The Griz (Zevachim 2a) first explains that there are two types of lishma in Zevachim. The lishma discussed at the beginning of the masechet relates to the requirement of lishma for a korban for it to be considered a korban. This requirement of intent only relates to the type of korban and for whom the korban is brought. The other four types of lishma discussed in our Mishnah resembles the broader question of whether mitzvot require kavana (intent) -- that requirement is lechatchila and without it, the performance is still valid.
The Griz uses this to answer several questions. It explains why the Gemara cites two separate pesukim - one for the requirement of lishma mentioned in the beginning of the masechet and one for our six. Furthermore, it explains why the Rambam records the two laws in two distinct halachot (Maaseh Korbanot 4:10-11).
The Griz however ultimately rejects this approach. The reason is that the Rambam links the two halachot together ruling that in both cases if the korban is slaughtered with no intent (stam) then it is valid. The connection means that in both cases, slaughtering stam provides lishmah. This implies that all six are also necessary for the din of the korban.
The Griz therefore brings a different explanation. He introduces his answer with the following question: what is issue with a korban that is not brought lishmah? There are two ways to understand the problem. The first is that the invalid thought uproots the original stam li'shmah. In other words, there is a requirement for the korban to be lishmah which is normally satisfied by default. When not offered lishmah, that requirement is no longer met. The other way to understand the issue is that shelo lishmah introduces a foreign intent that constitutes a new pesul in the korban.
The Griz explains that a practical difference between the two understandings would be if one collected the blood shelo lishmah; could he rectify the situation by collecting the remaining blood lishmah? If it was just a lack of lishmah then the situation could be repaired. If however the machshava constituted a pesul -- like pigul -- then the korban would be irredeemable.
The Griz argues that since the Rambam groups shelo lishmo with pigul when teaching the types of intent that invalidate a korban, he contends that the Rambam understands that shelo lishmo is a machsehvet pesul -- an intent that expressly invalidates the korban.
The Griz therefore explains that our Mishnah is discussing the intent that is essential for a korban. The novelty is that these are satisfied even stam by virtue of the animal being a korban. Were it not the case, without having these six things in mind the korban would be invalid. The difference with the two discussed in the beginning of the masechet -- intent for the korban type and that it be brought for the owner -- is that they introduce a new pesul in the korban itself. To be clear, both are laws relating specifically to requirements or laws in the korban itself.
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