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Masechet Eiruvin begins by discussing the shituf mavoi. The mavoi discussed in the Mishnah is a dead-end alleyway onto which a number of shared courtyards open. We learn that for one to be able to carry within the mavoi, a shituf mavoi must be performed. This involves the residents of each chatzer contributing food that will be placed together in one chatzer. The Mishnah however first discusses the tikkun (modification) to the mavoi that is also required. That involved either the placement of a korah (crossbeam) or lechi (side post) at the entrance of the mavoi. We shall focus our attention on the korah.
The fourth Mishnah records the debate regarding the substance of the korah. The Chachamim argue that it not only has to be wide enough to support a brick, but strong enough also. R' Yehuda however maintains that as long as it is wide enough, that would be sufficient.
R\' Yehonatan explains the debated as follows. According to the Chachamim the korah simply functions as a heker (reminder). In other words, the dead-end alleyway is distinct from the public domain and one can is allowed to carry in the alleyway but not into or to the public domain. Consequently, the korah must be substantial, so that it is clear that it was placed there intentionally for a long period of time. R' Yehuda however understands that he korah functions as a mechitzah (partition). Even though the korah is only a beam, we apply pi tikra yerod ve sotem. In other words, since it is wide enough, halachically we view the edge of that beam as if it stretches to the ground thereby completely the wall. That being the case as long as it satisfies the halachic requirements for pi tikra, it does not need to be any more substantial.
Returning to the position of the Chachamim, Rashi (13b) explains that the requirement for it be strong enough to build upon, is that it is perceived as permanent fixture. The Biur Halacha (363:17) explains that the Rashi understands the Mishnah like R' Yehonatan above. The Biur Halacha however notes that Rashi earlier (3a) explains that the requirement was so the beam would not get blown off. If it could then it would not be considered substantial enough to permit the mavoi. How do we understand these two explanations?
The Biur Halacha continues that the Shulchan Aruch rules that if the korah was four tephachim wide, it would be a valid korah, even if it was too thin to support bricks. A difference between the two understandings above is if this wide korah was so thin that it could blow away in the wind. The Biur Halacha understands that according to the earlier Rashi, who understands that the requirement of "strong enough" was so that it would not blow away in the wind, since once it is four tephachim wide it no longer needs to be strong enough, then even it is very thin it would be valid. According to the R' Yehonatan and Rashi on our Mishnah, who understand that this requirement of strength was so that it appeared permanent, then perhaps even if in this case they would still require that it could not blow away in the wind.
The Eshed HaNechalim (97, cited by Biurei Rashi, 3a) however explains the two comments of Rashi do not contradict one another, but rather express different concerns. The earlier Rashi explains why the beam must be strong enough to support bricks. The Rashi on our Mishnah however is explaining why it needs to be wide enough to support bricks.
Returning then to the beginning of the article, we explained that the Chachamim understood that the korah functions as a heiker. For the korah to function as this heker there are two requirements. The first is that it must be the correct dimensions so that it can be perceived as being placed there deliberately and permanently. That, it would seem, is a function of size -- it must be wide enough. The second requirement however is that it must also be chashuv -- substantial. Consequently, if it could not support bricks which would mean it would blow away in the wind, then even if one might notice it there, it is not halachically substantial enough to be defined as a korah.
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