1) A THIRD WALL FORMED BY A "LECHI"
QUESTION: The Gemara relates that Rav Kahana constructed a Sukah by placing Sechach over two perpendicular walls, with an Achsadrah on the third side. There was no wall on the third (or fourth) side. Rather, there was a pillar that was wider than a Tefach just outside of the wall perpendicular to the opening of the Achsadrah. From inside the Achsadrah, one could see the pillar just outside the wall of the Sukah. The pillar appeared to be the beginning of a third wall, but it did not extend across the face of the Sukah and thus was not visible from within the Sukah. Rav Kahana said that since such a pillar serves as a Lechi in the case of a Mavoy (and permits one to carry inside of the Mavoy on Shabbos), so, too, it serves as a third wall for the Sukah, and the Sukah is valid.
Rav Kahana seems to invoke the principle of "Migu" -- "since" it serves as a partition for the laws of a Mavoy on Shabbos, it also serves as a partition for a Sukah (7a).
However, the use of this method to consider the Sukah as though it has a third wall is problematic for several reasons.
First, TOSFOS (7b, DH Sikech) maintains that the principle of "Migu" works only to fulfill a requirement that is mid'Rabanan. The requirement that a Sukah have a third wall is mid'Oraisa, and thus "Migu" should not work. (TOSFOS DH Achvi)
Second, when the Rabanan enacted the requirement that a Mavoy have a Lechi at its entrance, they enacted that the Lechi serve as a "Heker," or reminder, but not that it serve as a partition. (Even according to the opinion that maintains that a Lechi is a full-fledged Mechitzah (Eruvin 12b), it is a Mechitzah only when it is in place of a fourth wall. Here, the Lechi is in place of a third wall.) How, then, can Rav Kahana derive that a Lechi serves as a partition for a Sukah from the fact that a Lechi serves as a reminder for a Mavoy?
Third, even if the principle of "Migu" could teach that as long as a Lechi is in some way effective for a Mavoy it is also effective for a Sukah, the "Migu" would work in this way only if a Lechi was effective for a Mavoy with regard to a Halachah d'Oraisa. In this case, though, the Lechi merely fulfills a rabbinical requirement for the Mavoy. How, then, can it fulfill the d'Oraisa requirement for a Sukah? (ROSH 1:34)
ANSWER: The ROSH answers that in addition to the two walls and the pillar (Lechi) on the outside of one wall, Rav Kahana's Sukah also had a Tzuras ha'Pesach along the side with the Lechi. Indeed, it is Rav Kahana himself (7a) who rules that the only situation in which a one-Tefach-wide board may serve as the Sukah's third wall is when that side also has a Tzuras ha'Pesach. In this case, the Tzuras ha'Pesach makes the Sukah valid mid'Oraisa (because a Tzuras ha'Pesach is considered a partition), and the one-Tefach-wide board is necessary only mid'Rabanan. Therefore, the rule of "Migu" applies and teaches that since the pillar is effective to fulfill the d'Rabanan requirement of Lechi for a Mavoy, it is also effective to fulfill the d'Rabanan requirement to have a one-Tefach-wide board on the third side of the Sukah.
Alternatively, the Rosh answers that even if there was no Tzuras ha'Pesach on Rav Kahana's Sukah, the need for the one-Tefach-wide board still was only mid'Rabanan, because the third wall was formed, mid'Oraisa, by the beam of the Achsadrah (through "Pi Tikrah Yored v'Sosem"). Mid'Rabanan, though, that does not suffice, because the beam of the Achsadrah was not made to serve the outside of the Achsadrah (where the Sukah is located) but to serve the inside, and thus mid'Rabanan a third wall of at least one Tefach is required. The "Migu" suffices to fulfill that requirement.
However, TOSFOS (DH Achvi) asks a fourth question. The Gemara earlier (7a) teaches that any entity that is considered a partition for the laws of Shabbos is also considered a wall for a Sukah. The Rishonim (see Rashi 7a, DH v'Chen l'Shabbos) explain that this rule applies only on Shabbos itself; that is, on Shabbos the Sukah is valid, but not on any other day. Why, then, was Rav Kahana's Sukah valid during the rest of the days of Sukos (besides Shabbos)?
The ARUCH LA'NER answers that the Rosh relies on the opinion of the RIF, who argues with the other Rishonim and maintains that since the "Migu" works to make the Sukah valid on Shabbos, it also works to make the Sukah valid during the rest of the week.
2) MUST THE WALLS OF A SUKAH BE MADE FOR THE PURPOSE OF THE SUKAH
QUESTION: The Gemara cites the Tosefta which states that when the Sechach of a Sukah extends beyond the Sukah ("Pesel ha'Yotzei Min ha'Sukah"), the area beneath that extension is considered part of the Sukah. Ula explains that this refers to Sechach which extends over the middle wall of a Sukah, when the two side walls also extend past the middle wall, so that the extension of Sechach actually covers an area surrounded by three walls. The Gemara asks that since, in this extension, there are three walls, valid Sechach, and more shade than sunlight, it obviously is a valid Sukah. What new teaching does the Tosefta intend to convey?
The Gemara answers that one might have thought that since "it was constructed for the inside of the Sukah, and it was not made to serve the outside of the Sukah," it is not a valid Sukah. RASHI (DH l'Vra'i) explains that this refers to the middle wall. Since the middle wall was made to be a wall only for the inside of the Sukah, it does not serve as a wall for a Sukah constructed on the outer side of the wall (from the extension of the Sechach).
Rashi's words imply that he maintains that the walls of a Sukah must be constructed for the purpose of the Sukah (according to the Havah Amina). This is difficult to understand, though, because nowhere does the Gemara make any mention that the walls of a Sukah must be made for the sake of a Sukah. (Only with regard to the principle of "Pi Tikrah" does Rava maintain that in order to apply "Pi Tikrah" the walls of the Sukah must have been constructed for the sake of the Sukah.) On the contrary, the Mishnah (17a) states that the walls of the houses around an Achsadrah may be used as the walls of a Sukah (through "Dofen Akumah"), even though those walls were not made to serve the Sukah.
This question prompts TOSFOS (DH l'Vra'i) to explain that the Gemara's statement that "it was constructed for the inside of the Sukah..." refers to the Sechach that extends beyond the Sukah, and not to the middle wall. Since the Sechach was placed on the Sukah for the purpose of the inside of the Sukah and not to serve the outside of the Sukah, one might have thought that the extension is not valid. Therefore, the Tosefta teaches that it is valid.
How does Rashi answer this question on his explanation?
(a) The RITVA answers that the walls of a house may be used for a Sukah because they were built with intention that they would be permanent, and that they would be used for any purpose for which they might be needed. In contrast, walls built for a Sukah are temporary, and thus one might have thought that such walls are valid only for the purpose for which they were made (the inside of the Sukah).
(b) The PNEI YEHOSHUA answers that in the case of the Mishnah (17a), the walls of the houses are considered to have been built for the use of the surrounding porch as well, since the porch is subordinate to the house (and therefore the Sukah built in that porch may utilize those walls). In the case of the extension of the Sukah, however, the middle wall was constructed specifically for the purpose of the inside of the Sukah, and thus one might have thought that the area outside of the wall cannot be a valid Sukah.
(c) The ARUCH LA'NER says that, indeed, the Mishnah itself teaches that the walls of the outside of a house may be used for a Sukah, and in this regard the Tosefta teaches nothing new. However, it is the manner of the Tosefta and Beraisa to teach laws that are already expressed in the Mishnah.
(d) The MAYIM AMUKIM suggests that perhaps Rashi understands that the Gemara's case involves a Sukah whose middle wall is not an actual wall but only a Halachic wall. That is, in the place of the middle wall, there is a row of vertical boards within three Tefachim of each other, and thus the principle of "Lavud" creates a Halachic wall. Alternatively, the middle wall does not reach the Sechach, and it serves as a wall only because of the principle of "Gud Achis." One might have thought that "Lavud" and "Gud Achis" work only for the side for which the partition was constructed (just as the principle of "Pi Tikrah Yored v'Sosem" works only with Mechitzos that were made to serve the Sukah, according to Rava; see Rashi DH d'Mechitzos, and Rashi in Eruvin 95a, DH Lav l'Sukah). Therefore, the Tosefta teaches that such a partition is considered valid even for the area of the extension outside of the Sukah.