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The Rabbanan of Rav’s Beis Medrash hold that empty space of 3 tefachim invalidates a sukkah, and possul schach of 4 tefachim invalidates a Sukkah
Rabbah holds that while 3 tefachim of empty space invalidates a sukkah only 4 amos of possul schach will invalidate a sukkah.
According to Rabbah, the measurement of 4 amos is an absolute handed down from Moshe at Sinai. Such a measurement cannot be connected to the empty space which has a different shiur.
But according to the Rabbanan a strip just a bit less than 4 tefachim of schach possul running down the middle of the sukkah, adjacent to an empty space of just under 3 tefachim should be possul. Since there is no tradition regarding the shiur of schach possul, it is only that 4 tefachim is considered a breach, just as 3 tefachim of empty space is a breach. In that case, two almost-breaches should add up to make one breach!
Summary
Abayye to Rabbah: You’re correct regarding a large sukkah but in the instance of a small sukkah [of precisely 7 tefachim], 3 tefachim of anything other than kosher schach [both airspace and schach possul] would be possul. Since airspace and possul schach can sometimes combine, they should combine in the case of less than 3 tefachim airspace adjacent to less than 4 amos possul schach as well?!
Rabbah: The law you’re quoting regarding a small sukkah is a mere circumstance. But in ordinary cases we say that the shiur of airspace is different from the shiur of possul schach, and they do not add up.
Challenge: Is it true that when two shiurim are different, they do not add up?
Mishna: A cloth textile is mekabel tumah when it is the size of 3x3 fingers.
A textile woven from goat’s hair needs to be the size of 4x4 fingers.
Leather needs to be the size of 5x5 fingers.
A woven straw mat needs to be the size of 6x6 fingers.
A beraisa adds: Cloth and goat’s hair; Goat’s hair and leather; Leather and woven straw, add up together.
Resolution: Ordinarily different shiurim cannot add up, but there a reason is given:
Rabbi Shimon: Why do they add up? Because in one instance they can become tamei as “a seat”, as we learned in a mishna: If one combined shreds of these materials to make a square tefach, it is mekabel tumah.
What can be done with such a small square? Rabbi Shimon ben Lakish from Rabbi Yannai: It can be used to patch up a donkey’s saddle.
[Here the gemara ends and it seems that Rabbah is victorious but actually the halacha doesn’t follow his opinion. 4 tefachim of possul schach make a sukkah possul].
The gemara up to here was presented as memorized in Sura. In Neharda’a they memorized it as follows:
Rav Yehuda quoting Shmuel: Possul schach running down the middle of a sukkah is possul when it’s 4 tefachim. Near the wall, it is only possul if it’s 4 amos.
Rav says that it’s always 4 amos.
(We note that in Sura, Rav’s city, this sugya was presented as if Rav’s shittah is the one we follow in practice. In Naharda’a, city of Shmuel, they presented his shittah as the correct one. This sugya was a very difficult sugya, because of Rabbah’s style; Rabbah was very great in pilpul, as was his talmid Abayye. Here and in many other cases the halacha doesn’t follow their opinions). This podcast has been graciously sponsored by JewishPodcasts.fm. There is much overhead to maintain this service so please help us continue our goal of helping Jewish lecturers become podcasters and support us with a donation: https://thechesedfund.com/jewishpodcasts/donate