Masechet Shabbat opens by discussing the melacha of hotzaah -- transferring an object from a private domain to the public domain or back. We learn in the Mishnah that the melacha is made up of two parts. Akira -- raising the object out of one of the domains, and hanacha -- placing the object down in the other. For one to be liable on a biblical level, they must perform both these actions. The Mishnah includes a case where the akira was performed by one person and hanacha by another. For example, one person picked the object up and stretched his hands into the other domain, and the other took the object and placed it on the ground. The Mishnah teaches that they are both exempt. This implies that while not liable on a biblical level, the action is nonetheless rabbinically prohibited. We shall try to understand this ruling.
The Bartenura explains that the reason is that each of them only performed half the melacha. It is rabbinically prohibited out of concern that one person might (easily) performed the entire melacha on their own.
As we learn masechet Shabbat, each of the melachot have a shiur -- a minimum measure -- that if performed, one desecrates Shabbat. It would seem that for the melacha of hotzaah, the shiur would be both akira and hanacha. The Tifferet Yisrael (Boaz 1:4) therefore asks that even though one would not be liable for punishment if they performed a chatzi shiur -- half the minimum amount -- it is nonetheless biblically prohibited to do so. The reason is that the amount one has already performed can combine with more, to breach that shiur. That being the case, it would seem that each of the individuals in our Mishnah would have violated biblical prohibitions and not rabbinic ones. Each seemingly performed a chatzi shiur.
The Tifferet Yisrael cites his father, who explains that the issue of performing a chatzi shiur is only if we are discussing one action. For example, writing one letter, when the full shiur is writing two letters. This case however is different since it consists of two different actions and the full melacha is a combination of those two actions. Consequently, performing one is not considered like perform a chatzi shiur. He continues citing other similar prohibitions, e.g. the prohibition of wearing wool and linen clothing. Wearing wool alone is not considered a chatzi shiur and obviously permitted. The same then is true in our case. Akira on its own would be permitted on a biblically. Nevertheless, we learn in our Mishnah that the Chachamim prohibited our case since it is not exactly the same as kilayim since both akira and hanacha are performed on the same object.1
The Tifferet Yisrael also cites an answer provided by his son. He explains that the melachot on Shabbat are different from other prohibitions. The activities that are defined as melachot and prohibited, are derived from the activities involved in the construction of the mishkan. Akira or hanacha on their own are not melachot and therefore permitted (on a biblical level).
1 The Tifferet Yisrael continues to address why carrying less than four amot in the public domain is also only rabbinically prohibited. In that case, it should be considered a chatzi shiur and prohibited on a biblical level. He answers that, as we explained above, the reason a chatzi shiur is prohibited biblically is because one could add to that shiur and perform the full melacha. If one carried only two amot and placed the item down, since hanacha has already been performed, it is no longer possible to add to that action to turn it into a melacha.
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