In the third perek we learn that one is limited regarding how far they can travel outside their city on Shabbat. The limit, the techum, is two-thousand amot. When there is a need for the purpose of a mitzvah, one can move their makom shevitah (dwelling place) such that they can travel two thousand amot from that location in any direction. One can do so by placing an eruv techum to one side of the city. Doing so will enable them to walk further in that direction but less in the other. Importantly however, one must be within two-thousand amot of the eruv techum at onset of Shabbat.
The Mishnah (3:4) teaches that if the eruv techum rolled away prior to Shabbat, such that it is now further than two thousand amot away, the eruv techum does not work.
It is important to understand that an eruv techum takes effect at bein ha'shmashot (between sunset and nightfall). Furthermore, we learnt in the previous Mishnah that if the eruv techum is placed in a location, such that it cannot be accessed from the makom shevita during bein hashmashot then the eruv techum does not work. During bein hashashot however, the Chachamim did not apply shevutim (rabbinic prohibitions). Consequently, it is only a biblical prohibition that would present a problem.
Based on the above, one might ask as follows. Walking beyond two-thousand amot (but less then twelve mil) is a rabbinic prohibition. That being the case, since shevutim do not apply at the critical time, then the eruv techum in our Mishnah should work.
The Tosfot Yom Tov cites the answer of the Tosfot, who explain that if the eruv techum worked, then it would mean the person would be standing outside his techum. The law in that case is that he would only be allowed to walk four amot -- an undesirable result. Consequently, the Chachamim built into the law of eruv techumim that one must be within two thousand amot of it. In other words, it is not the prohibition of reaching the techum that prevents the eruv techum in this case, but rather a law in eruv techum itself.1
The Ritva (Eiruvin 351) however writes that if one would not be able to reach their techum "beheter gemur" -- in a completely permissible way -- then the eruv techum would not work. What does "heter gemur" mean, considering that shevutim are permitted during bein hashmashot.
The Beit Meir (368:8, s.v omnam) explains that whether a shevut prevents the eiruv techum from working depends on the shevut. If we are dealing with a rabbinic prohibition that is not related to the issur techum, then we can say that shevutim do not apply during bein hashmashot and the eruv techum works. The previous Mishnah is one such example. The case is where one placed the eruv techum in a tree, less than ten tephachim from the ground with the intention that the makom shevitah will be at the base of the tree. The location in the tree is a carmelit and the makom shevitah is in the reshut ha'rabim. Transferring between those location is rabbinically prohibited. Since however that prohibition does not relate to eruvim techumim, it would not ruin the eruv techum. If however the rabbinic prohibition relates directly to the prohibition of techumim, for which the eruv techum is trying to permit, then it would clearly present a problem. In other words, for the eruv techum to work, the Ritva requires that it is completed permitted with respect to all the law of techumim, to access the eruv techum.
1 The Beit Meir, cited later in this article, finds the Tosfot difficult. Since during bein hashmashot one would be able to access the eiruv, then why could one not move the eruv techum back to the location of the originally intended makom shevittah. This would be comparable to the previous Mishnah where one could move the eruv techum that was in tree (less than ten tephachim from the ground) to the makov shevitah at the base of the tree.
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