The Mishnah (6:6) taught that if a man fell into a deep pit and called out that anyone who can hear his voice should write a get and deliver it to his wife, those that hear should do so. In other words, even though the husband did not nominate these individuals directly and they did not know who this person is (other than the names he called out) it is nonetheless considered as if they are the husband's agents to write, sign and deliver the get. The Gemara explains that this is a special leniency afforded in times of danger. Rashi explains that if we wait, it might end up being too late.
The Tosfot (66a, s.v. kol) raising a question based on a Mishnah we learnt back in Nedarim. Recall that if, e.g. Reuven made a neder against deriving any benefit from Shimon, that there is still a way that Shimon can still separate terumah for Reuven. The Gemara (Nedarim 36b) explains that Shimon can only separate terumah if is acts as Reuven's shaliach to do so. However if Reuven directly nominates Shimon, he will be deriving benefit from Shimon in violation of the neder. The Gemara explains that the permissible avenue would be if Reuven declared that anyone who wishes to separate terumah for him can do so.
If regarding terumah, the open ended declaration is not equivalent to nominating a shaliach directly, how then in our case, can those that hear the husband, write and deliver the get?
The Tosfot provide two answers. The first is that the open declaration is indeed considered as nominating a shaliach in both cases. Regarding the case in terumah however, despite Shimon effectively being designated as the shaliach, since Reuven did not nominate Shimon directly, it is not considered a violation of the neder.
The Tosfot provide a different answer and suggest that our case is different. In our case the husband did not call out, "anyone who wants to write the get" which would parallel the case in Nedarim, but rather "anyone who hears me should write the get". In other words, despite not knowing who can hear him, the husband is instructing them to write the get – he is nominating them directly.
Note that according to the second answer, it appears that shelichut is not required for the separation of terumah. The Chazon Ish (Even HaEzer 147) however notes that it is clear, that to separate terumah for another, one must act as the other’s shaliach. This is because one is not allowed to sanctify something that does not belong belong to them.
The Chazon Ish however explains that indeed separating terumah would require shelichut. We have however explained in the past that based on the principle of zachin one can act on another’s behalf if it is in their favour, even without their knowledge. Having one’s terumah separated is considered a benefit. The reason why we can’t rely on zachin to separate another’s terumah is because the act of separating terumah is a mitzvah and we have a principle that it is a greater mitzvah to perform the mitzvah one’s self than via an agent. Consequently, it is not necessarily a benefit to the owner if someone else separates terumah for them. In the case in Nedarim, when the owner declares that one who wishes to separate terumah can do so, Reuven is not nominating Shimon as his shaliach. Nevertheless, he has demonstrated that he is happy for someone to separate the terumah. That being the case, Shimon can then rely on the principle of zachin.
For Gittin however one cannot rely on zachin even if the husband indicates that he wants to divorce his wife. This is because divorce is not a zechut (unlike separating terumah). Even if the husband indicates that he wants to, it does not define the case as being a zechut. Instead it is comparable to the husband wanting to do something to his detriment. Since we cannot rely on zachin, according to the second answer of the Tosfot, for Gittin the open-ended declaration "anyone who wants to write and deliver the get" would be insufficient. This explains why the more directly language in our Mishnah, "anyone who hears me should write a get" is used since it is that language, according to the second answer of the Tosfot, that designate the listeners as the husband's shaliach.
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