In the eighth perek of masechet Arachin, we begin learning about a cherem vow. The cherem is (unfortunately) more popularly known in the context of excommunication or a ban. In our context the term used is with respect to one's property that one has "banned" for their own use, since it has been dedicated to be in the possession of another. We learn that there are two types of cherem. One is where on dedicates the property for the bedek ha'bayit -- temple treasury. The other, is where the property is given to the kohanim as a gift; not to be redeemed. We shall focus on the latter of these two -- charmei kohanim.
The Mishnah (8:5) records the debate regarding kohanim and leviim making charmei kohanim. While everyone agrees kohanim cannot, the debate is focused on whether leviim are excluded also. Why does everyone agree that kohanim cannot make a cherem-vow?
R' Yehuda, the first opinion in the Mishnah, explains that kohanim cannot make a cherem since cherem property are given to them. The Bartenura explains that the declaration would serve no purpose since it would immediately become the kohen's possession and therefore not required to be given to another kohen.
The Tosfot notes that that logic is true regarding movable objects, since cherem objects can be given to any kohen. However, when it comes to land that has been designated as cherem property, that land is given to the mishmar -- group of kohanim -- that are serving in the Beit HaMikdash that week. In other words, it is not a given that the kohen that dedicates land as cherem property would be the recipient of that land.
The Tosfot explains that the rationale provided by R' Yehuda is indeed only really for metaltelin -- movable property -- for which the logic does apply. For land however, the reason is that land belonging to kohanim simply can not become cherem property since the Torah refers to that property as an achuzat olam (eternal heritage) (Vayikra 25:34) -- logic provided by Rebbi at the end of the Mishnah.
The Tifferet Yisrael however argues that even though ordinarily charamim need to be given to the kohanim that are serving that week, in this case it can be retained by the kohen. He equates this case with a kohen that needs to offer a korban in the Beit HaMikdash. Ordinarily the offering of the korbanot is the responsibility of the serving mishmar and parts of those korbanot that are gifted to the kohanim are retained by them. if a kohen from a different mishmar needs to bring a korban he can offer it himself and retain the gifted parts.
The difference between the Tosfot and Tifferet Yisrael's explanation can be found in a question raised by the Rosh (cited by the Shitah Mekubetzet). Recall that the reason that kohanim cannot make movable objects cherem is that since it is given to them, they immediately acquire it. The Rosh asks that until kohen physically (re)acquires the object, it should be considered cherem property and a prohibition of meilah would apply. Even if one would argue that the kohen automatically acquires the object since it is located in his property, then considering a case where the object is not located in his property it should be considered a cherem. The Rosh leaves this question unresolved.
The Achronim provide novel ways of resolving the Rosh's difficulty. Nevertheless, if we accept the basis of the Rosh's questions, then we find a difference between the explanation of the Tosfot and Tifferet Yisrael. According to the Tifferet Yisrael's understanding of R' Yehuda, who reasons that the same logic applies to land as it does to movable objects, if the kohen would designate land as cherem it would briefly have the status of cherem property until the kohen reacquired it. (Note that the prohibition of meilah would nevertheless not apply since it does not apply to land.) According to the Tosfot however, the land would never become cherem property since the exclusion from the pasuk prevents it from being so.
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