The third perek of Eiruvin deals with the laws of eiruv techumin. One is may not travel beyond the edge of the city further than two-thousand amot. We learnt, that for the sake of a mitzvah, one can move their shevita (dwelling place) in one direction (less than two thousand amot from their home). Doing so, would move the centre from where we calculate the two thousand amot limit to that location, thereby allowing the person to walk further in that direction. One way of doing this is to place an eiruv techum (some food) at that location during bein hashmashot prior to Shabbat.
The Mishnah (3:3) taught that if one placed their eiruv in a tree ten tephachim above the ground, the eiruv is not valid. The Bartenura explains that the tree is located in reshut harabim (public domain) - where he intends his makom shevita to be. The space of the tree is at last four-by-four tephachim, meaning that the eiruv is in a reshut hayachid (private domain). Since it would be prohibited from him to take his eiruv to the makom shevita during bein hashmashot the eiruv is not effective.
The Mishnah continues that it would be valid if the eiruv was placed in the tree below ten tephachim. Even though that location is defined as a karmelit and it would normally be prohibited on a rabbinic level to take the eiruv, the Chachamim did not apply such decrees (shevutim) during bein hashmashot. The Tosfot Yom Tov explains that this is true only for the sake of a mitzvah. Since however one can only make an eiruv techum for a mitzvah the logic stands.
The Mishnah then continues that if the eiruv was placed in a pit, at least ten tephachim deep and four wide, then the eiruv is likewise valid. In this case, the Bartunera explains that the pit is in a karmelit, e.g. an open field. That way, since the prohibition to transfer from a karmelit to a reshut hayachid is a shevut and shevutim are permitted during bein hashmashot, it explains why the eiruv is effective.
The Tosfot Yom Tov asks that the according to this understanding, the two cases are not similar. In the first case the tree is in reshut harabim while in the second case the pit is in a karmalit. The Tosfot Chadashim argues that the case involving the tree is also located in a karmelit. The reason why the eiruv techum is ineffective if it is above ten tephachim is because it involves two shevutim: transferring from a reshut hayachid to a karmelit and using a tree.
The Tosfot R’ Akiva Eiger however finds this explanation difficult. When the Gemara discussed this case, one understanding is that tree was in reshut harabim. According to that understanding, transferring from a location below ten tephachim would also involve two shevutim: transferring from a karmelit to reshut harabim and using a tree. Nevertheless, the Gemara did not reject this understanding based on those grounds.
The Chidushei Mahariach asks a further question. Why was the case of the pit necessary? If it was to teach that one can transfer from a reshut hayachid to a karmelit during bein hashmashot, we learn that that is true from the case where the eruv was placed in the tree below ten tephachim from the ground. In that case, one would be transferring from a karmelit to the reshut harabim and the Mishnah already taught that it is valid.
The Chidushei Maharaich explains that all the cases are indeed necessary. The end of the Mishnah records the debate where the eiruv was locked in cupboard. According to the Tana Kama (first opinion) only one shevut would need to be violated (cutting the rope) so the eiruv is valid. According to R’ Eliezer carrying the knife for this purpose would be an additional shevut so the eiruv is not valid.
The Chidushei Mahariach explains that the case involving the pit (located in a karmelit) is required to teach that if accessing the eiruv involves one shevut then everyone agrees that the eiruv is valid. The case of the tree however involves an additional shevut of using a tree on Shabbat. That case is required since from the case where the eiruv was locked in the cupboard, it would be possible to understand that in principle the Tana Kama agrees that if it involved two shevutim then the eiruv would be invalid; the Tana Kama simple argues that the case only involves one. Therefore the case of the tree located in reshut harabim, where if it is below ten tephachim the eiruv is valid, is necessary. It teaches that the Tana Kama maintains that the eiruv is valid even when accessing the eiruv during bein hashmashot would involve two shevutim.
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