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Sukah 18


QUESTION: The Beraisa states that according to both Rebbi Yehudah and Rebbi Meir, if a Sukah was covered with wooden boards which are each four Tefachim wide, the Sukah is Pasul. Rebbi Meir says that even if the boards are three Tefachim wide, the Sukah is also Pasul. Rebbi Meir agrees, though, that if one placed an equal width of valid Sechach between each board, the Sukah is valid.

The Gemara challenges the view of Shmuel from this Beraisa. According to Shmuel, the amount of invalid Sechach that will invalidate a Sukah when placed in the middle of the roof (as opposed to at the sides) is four Tefachim. If so, why should the Sukah be valid in the case of boards which are four Tefachim wide but are separated by strips of valid Sechach? The very presence of the four-Tefach-wide boards should invalidate the Sukah!

The Gemara answers that the Beraisa is referring to a case of a Sukah which is exactly eight Amos long, and one placed Sechach Pasul alternating with valid Sechach atop the Sukah. One starts from each side of the Sukah by placing a four-Tefach wide Sechach Pasul, followed by valid Sechach, and then another strip of Sechach Pasul, until the center, where one ends up with two pieces of valid Sechach in the middle of the roof of the Sukah. The Sukah is valid because the invalid Sechach on each side is disregarded because of the principle of "Dofen Akumah," leaving eight Tefachim of valid Sechach in the middle. The Gemara concludes that this will only work with a Sukah which is *exactly* eight Amos, i.e. 48 Tefachim, wide. Each half of the Sukah (i.e. 24 Tefachim of its width) is covered by three pairs of invalid/valid strips of Sechach, each strip of which is four Tefachim wide.

If the goal of the Gemara is to arrive at a Sukah which has alternating strips of invalid and valid Sechach such that the final two valid strips end up next to each other in the middle, why does the Gemara say there must be *three* sets of invalid/valid strips? It is obvious that having four sets will not work (because then the valid strips of Sechach in the center will be too far away from the walls of the Sukah for "Dofen Akumah" to work.) Likewise, the Beraisa is certainly not discussing one set of invalid/valid Sechach on each side of the Sukah, because then there would be no two boards that have between them "a single board's width of valid Sechach," the Beraisa's description of how to validate the Sukah. Why, though, did the Gemara not give a case where there are *two* sets of invalid/valid Sechach? (Each set is eight Tefachim wide, so if it takes two sets to cover each half of the Sukah's width, its total width would be 32 Tefachim.) In such a case, "Dofen Akumah" would still apply, and the eight Tefachim of valid Sechach in the middle should be considered a full-fledged Sukah. Why did the Gemara insist that the Beraisa can *only* be talking about a 48 Tefach (eight Amah) Sukah! (MAHARSHA -- the ARUCH LA'NER'S answer that 32 Tefachim is not an even number of Amos seems rather forced.)

ANSWER: We first must ask another question. Why did the Gemara say that the Sukah which the Beraisa is discussing is exactly eight Amos (48 Tefachim), "not more and not less" (Rashi)? The Sukah could also be a Tefach *less* than eight Amos (7 5/6 Amos, or 47 Tefachim)! Since one starts to cover the roof with a four-Tefach board (= invalid Sechach) at the walls on each side, the missing Tefach will be lost from the valid Sechach at the center, leaving only seven Tefachim of valid Sechach. But we know that seven Tefachim of Sechach is a valid Sukah! (It cannot be that the Gemara did not mention it because then the width of the valid Sechach in middle would not equal the width of the boards on either side, as the Beraisa stipulates -- this cannot be, because as it is there is not an equal amount. Each board of invalid Sechach is four Tefachim, while the valid Sechach in the middle is eight Tefachim). What is the Gemara gaining by saying that the Sukah is exactly eight Amos wide?

The answer is as follows. Rashi (top of the page) explains that when the Beraisa says, "Rebbi Meir agrees that the Sukah is valid if between each board there is an equal width of valid Sechach," it is referring to *even* when the boards are four Tefachim wide. This is, Rebbi Meir in the Beraisa was talking about *both* boards of four Tefachim and boards of three Tefachim. Thus, the same case that he permits with boards of four Tefachim must also work with boards of three Tefachim.

If the Sukah is one Tefach less than eight Amos (47 Tefachim instead of 48 Tefachim), it will work out to be a valid Sukah when the boards are four Tefachim wide, but when the boards are three Tefachim wide it will not work out, as follows: How many sets of invalid/valid Sechach will there be on each side of a 47 Tefach Sukah, if each board is three Tefachim wide? Starting from the walls on each side, there will be three pairs of invalid and valid boards of three Tefachim (for a total of 18 Tefachim), plus another invalid board of three Tefachim, plus valid Sechach of 2 1/2 Tefachim (for a total of 23 1/2 on each side, or a 47 Tefachim in the entire width of the Sukah). As such, he loses some of the valid Sechach, but not any of the invalid Sechach, leaving a majority of invalid Sechach, which disqualifies the Sukah! "Dofen Akumah" will not be able to cut off the invalid Sechach (as is the case with the 4 Tefach boards), because there are only five, and not seven Tefachim of valid Sechach in the middle. Therefore, the Sukah must have exactly 48 Tefachim, so that each side has 24 Tefachim (four full sets of invalid/valid Sechach), balancing the invalid and valid Sechach, which validates the Sukah (as the Mishnah and Gemara explains on 15a). That is why the Sukah cannot be one Tefach less than eight Amos.

For the same reason, the Beraisa cannot be talking about a 32 Tefach-wide Sukah. Although such a Sukah would be valid if the boards were four Tefachim wide, it would not if the boards were three Tefachim wide. There would be 16 Tefachim in each half, comprising two sets of invalid/valid Sechach (3+3, 3+3), plus one invalid board (3 Tefachim), plus 1 Tefach of valid Sechach. The Sukah would have a total of 2 Tefachim of valid Sechach in the middle, leaving it with a majority of invalid Sechach and without the minimum Shi'ur of a valid Sukah in middle. (M. Kornfeld)


QUESTION: Rava and Abaye argue concerning the use of the principle of "Pi Tikrah Yored v'Sosem" to make a Sukah. Rava says that a Sukah that has walls only because of "Pi Tikrah" is invalid, and Abaye says that such a Sukah is valid. Rava attempts to refute Abaye's opinion by pointing out that in a case of a Sukah which has only two walls parallel to each other, Abaye should also say that the Sukah is valid, because the edge of the beam ("Pi Tikrah") above the open side joining the two walls should be "Yored v'Sosem" and form the third wall. Rashi explains that Rava's question is that the edge of the Sechach that juts out above the third side of the Sukah should be considered a "Pi Tikrah." (When it is resting on an Achsadrah the Sechach cannot form a Pi Tikrah since it cannot be seen from within the Sukah, but when it is stand-alone it should form a Pi Tikrah.)

Abaye answers that in the case of two parallel walls we cannot say "Pi Tikrah Yored v'Sosem" because people are constantly walking through it, like a Mavoy Mefulash.

What is Rava's question on Abaye? Rava himself says a few lines later (19a) that he holds like Rav, who says that "Pi Tikrah" normally *does* work to enclose the area inside of an Achsadrah (for example, to permit carrying in there on Shabbos). He does not apply "Pi Tikrah" in the case of a Sukah adjacent to an Achsadrah because the beams of the Achsadrah were made only to serve what is *inside* (the porch that they cover), but not to serve what is *outside* of them (such as the Sukah adjacent to the Achsadrah). The Pi Tikrah of the Sechach itself, though, was certainly made to serve the Sukah that is *inside* of them, and therefore even Rava should agree that "Pi Tikrah" works in such a case! If so, why does Rava ask this question on Abaye? It is also a question on his own opinion! (PNEI YEHOSHUA)


(a) The PNEI YEHOSHUA answers that Rava knew the answer that Abaye would give him (that such a Sukah is similar to a Mavoy Mefulash and thus "Pi Tikrah" does not apply). Since Rava knew the answer, the question did not bother him according to his own opinion. If so, why did he ask the question on Abaye's opinion? Rava reasoned that Abaye -- who is so lenient and says that "Pi Tikrah" works even to make a partition to enclose what is outside of the beam -- would also rule leniently in the case of a Mavoy Mefulash and say that "Pi Tikrah" works there as well. After all, Abaye's logic is that Pi Tikrah is like a solid wall (and does not begin with a Halachah l'Moshe mi'Sinai, which has certain prerequisites, see Rashi 19a DH d'Mechitzos).

The Gemara answers that Abaye differentiates between partitions that are made to enclose what is inside of them (in which case "Pi Tikrah" works even to enclose what is outside of the partition), and partitions through which people walk (in which case "Pi Tikrah" does not work). (See TOSFOS, Zevachim 77b, DH Odu Li, who applies a similar form of reasoning.)

(b) TOSFOS (DH Sikech), the RAN and the RITVA learn that the question of the Rava is not that the side of the Sechach should be "Yored v'Sosem" to make a third wall; Sechach cannot be "Yored v'Sosem," because it is only Arai, temporary. Rather, Rava is asking that the side of the beam of an Achsadrah which is adjacent to the open space between the parallel walls should be "Yored v'Sosem" to make the additional wall according to Abaye. According to Rava, though, the Achsadrah cannot be Yored v'Sosem to enclose the Sukah which lies outside of the Achsadrah.

If this is Rava's question, why indeed should "Pi Tikrah" *not* work in such a case according to Abaye? Abaye certainly should say that it works in such a case -- after all, Abaye just stated that "Pi Tikrah" works to make the beam of an Achsadrah into a wall, even when there were *no* other walls to the Sukah!

The answer is that these Rishonim explain the Gemara that "Pi Tikrah" of an Achsadrah only can form one wall of the Sukah but not to form two walls (see TOSFOS DH Achsadrah). The case in which Rava and Abaye are arguing is that of an Achsadrah that has two adjacent walls, and in order to make a Sukah one needs to make only the third wall. Rava asks that according to Abaye, even if the two walls are opposite each other (parallel) and not adjacent, the beam of the Achsadrah should work through "Pi Tikrah" to make the third wall (as TOSFOS DH Sikech explains).

The RITVA adds that according to this interpretation, Rava's question on Abaye is understandable even according to the second version of their Machlokes (on 19a). According to that version, Abaye and Rava are arguing in a case of an Achsadrah that *has* Petzimin (pillars beneath the beams); in such a case Abaye says that "Pi Tikrah" works to enclose the third wall and Rava says that it does not. When there are no Petzimin, they agree that "Pi Tikrah" does not work to enclose it.

According to Rashi's explanation of "Petzimin" this argument has nothing to do with "Pi Tikrah"; the Petzimin are pillars that are within three Tefachim of each other, and Rava and Abaye are arguing about the application of "Lavud." In such a case, Petzimin would certainly be able to enclose the third wall of a Sukah which has only two parallel walls. If so, the question that Rava asked Abaye (on 18b) never took place according to this version of their Machlokes.

However, says the Ritva, according to Tosfos, even according to the second version of the Machlokes, Rava could have asked this question on Abaye. According to Tosfos and the others, explains the Ritva, Petzimin do not mean pillars that are within three Tefachim of each other, but rather two posts at the end of eac of the parallel walls of a Sukah. If these parallel walls are set next to an Achsadrah (with its beam crossing from one wall to the other, and with Petzimin below the beam), then Abaye says that since there are Petzimin, "Pi Tikrah" *in the presence of Petzimin* works to close the additional, third wall. Rava asks Abaye that if "Pi Tikrah" works when there are Petzimin, then it should also work when there are no Petzimin, just two parallel walls adjacent to an Achsadrah. Abaye answers that the normal "Pi Tikrah" cannot apply here because it is Mefulash, open on both ends with people crossing through. Only in the presence of Petzimin is "Pi Tikrah" able to form the third wall.

(In fact, this is also why Rava -- in the first version of the argument -- agrees that "Pi Tikrah" works only when there are Petzimin; in the presence of Petzimin the Achsadrah can certainly form a Pi Tikrah even though it is made to serve the inside of the Achsadrah. Petzimin are not working through "Lavud" at all. Although the Gemara uses the word "Lavud" with regard to the Petzimin on Daf 19a it is using the word figuratively to mean that the wall becomes "solid" -- but by way of "Pi Tikrah" and not the normal "Lavud," since the Petzimin are at a distance of more than three Tefachim from each other.)

(c) Rabeinu Chananel (and SHITAS RIVAV, on the Rif), appear to have an entirely different approach the Sugya. They learn that even in the case of an Achsadrah adjacent to a Sukah, it is the Pi Tikrah of the *Sechach* that is Yored v'Sosem. The walls of the houses around the Achsadrah, and the Pi Tikrah of the Achsadrah, cannot enclose the Sukah (even according to Abaye), because they are made to serve what is inside of them, and not the Sukah that is outside them. Only when combined with Pi Tikrah of the Sukah will such walls suffice, according to Abaye. Rava, on the other hand holds that even with Pi Tikrah such walls cannot be used. (In the presence of Petzimin, though -- that is, poles at the four corners of the Sukah that are not part of adjacent houses, and therefore may be considered part of the Sukah -- even Rava will allow Pi Tikrah to enclose the Sukah.)

Rava, then, is asking on Abaye that if Pi Tikrah of the Sechach works it should enclose the Sukah even when it is not adjacent to an Achsadrah, such as a normal Sukah, the third wall of which has collapsed. Abaye answers that "Pi Tikrah" alone will not suffice to be considered walls of a Sukah when it is not near an Achsadrah (i.e. when it is not surrounded by walls of other houses), since it is similar to a Mavoy Mefulash. (This appears to be the intention of Rabeinu Chananel -- M. Kornfeld.)

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