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The Mishnah (7:2) lists the thirty-nine melachot -- the activities that one is forbidden from engaging in on Shabbat. One of those listed is tzad -- trapping a deer. We shall try to understand the definition of this melacha.
In the first perek we saw the debate regarding whether one can set a trap prior to Shabbat if the animal will be caught on Shabbat itself. Beit Hillel maintained that it was permitted. Consequently, the trap must be set on Shabbat itself to constitute the melacha. Nevertheless, one is not liable for setting the trap alone.
The Tosfot (Shabbat 17b) explains that the reason is that when setting the trap, one is not sure whether the animal will get trapped inside it. That said, one cannot set a trap in case an animal is immediately caught inside the trap. The Chazon Ish (36:1) explains that the Tosfot does not differentiate between whether the animal triggers the trap immediately or moments later. There is no difference between the two since in both cases the animal is the one that activates the trap. Instead, the distinction is whether, when setting the trap, if he knows the animal will get caught inside it.
The Minchat Chinnuch however finds the Tosfot difficult. He asks, even if the person knows that the animal will enter the trap he is setting, the trapping of the animal occurred on its own. The person did not directly trap the animal. Since his actions indirectly caused the animal to be trapped, he should not be liable.
The Chazon Ish however explains that one is liable in this case and also in the case of cooking, since it is the nature of those melachot that they are set in motion and complete on their own. In other words, it is true that for other melachot one would be exempt on a biblical level if executed via gerama (indirect action). Nevertheless since the nature of these melachot is that they are completed on their, one would be liable.
The Birkat Shmuel explains similarly that for Shabbat, some melachot do not require active input to be defined as a melacha. For example, in the melacha of winnowing, it is the wind that assists in separating the wheat from the chaff. Consequently, for some melachot one is liable even in the case of gerama.
One might still ask, if one is liable when that animal is trapped, how can one set a trap on erev Shabbat if he knows the animal will get trapped on Shabbat? We have just learnt that one does not need to actively trap the animal for it to be defined as a melacha. Even if the animal walks into the trap on its own, one has performed the melcha. Consequently, one would think that even if the trap was set prior to Shababt, if the animal was trapped on Shabbat they should be liable.
The Birkat Shmuel explains that the melacha of trapping is not simply the outcome that the animal is trapped. Instead, the definition of the melacha is that one actively did something on Shabbat that will bring about the trapping of the animal -- even if the animal walks into the trap on its own. If the trap was set on erev Shabbat, it is true that the main part of the melacha occurred on Shabbat. However, since no action occurred on Shabbat -- the trap was not set on Shabbat -- no activity was performed on a Shabbat to define this as a melacha performed on a Shabbat.
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