ABAYE AND RAVA ON PI TIKRAH (as learned in Sura)
Question: Our Mishnah indicates that we do not say Pi Tikrah (since, if we did, the courtyard Sukah would be Kosher)!?
Answer (Rava explaining for Abaye): Our Mishnah invalidates the courtyard Sukah when he placed the Sechach level with the overhangs, not lying on top of them (this leaves nothing visible on which to say Pi Tikrah Yored ve'Sosem).
ABAYE AND RAVA ON PI TIKRAH (as learned in Pumbedisa)
All agree that Sechach placed on an Achsadra without uprights is Pasul.
(Abaye): If it has uprights it is Kosher (Lavud).
(Rava): It is still Pasul (Lavud does not apply here since the uprights were not made for the Sukah).
The Halachah is like Rava in the first Lashon.
R. Ashi was surprised to find R. Kahana making a Sukah in the way that Rava just invalidated (with two adjacent walls, but no third wall of one Tefach, thus relying on Pi Tikrah for the third wall).
R. Kahana pointed out a third wall consisting of one Tefach which jutted out into the adjoining porch, and which could be seen by people standing outside the Sukah but not by those who were standing inside (we learned in Eruvin that a Lechi, like the uprights, is Kosher, and permits carrying in a Mavoy).
PESEL HA'YOTZEI MIN HA'SUKAH
Question: What constitutes a Pesel ha'Yotzei which is considered part of the Sukah?
Answer (Ula): It refers to Sechach which protrudes to an area behind the middle wall of the Sukah.
Question: But that area would need three walls!?
Answer: It has them.
Question: But that area must be seven by seven Tefachim!?
Answer: It is.
Question: But the area must have more shade than sunshine!?
Answer: It has.
Question: Then what is the news of Pesel ha'Yotzei!?
Answer: Even though the middle wall was not made for this Sukah (it was made for the Sechach on the other side) it is still Kosher.
Answer (Rabah and R. Yosef): It refers to Sechach which extends from inside the Sukah but when only one of the walls fully extends to the length of the Sechach (i.e. that section of Sukah only has one wall and we might have invalidated it on that basis).
Answer (Rabah bar bar Chanah citing R. Yochanan): It refers to a case where the majority of the Sechach casts more shade than sunshine and a minority does not (the minority [called Pesel] is Kosher even though it is not in the [Hechsher] Sukah).
Answer (R. Oshiya): It refers to Sechach Pasul of less than three Tefachim in a minimum small Sukah (even though it has left the [laws of] Sukah, it is still Kosher).
Question (R. Hoshaya): It should not differ from the same amount of open space in the Sechach of a minimum Sukah (which we already know does not invalidate)!?
Answer: One may not sleep under a space of even less than three Tefachim in a small Sukah, whereas under Sechach Pasul of less than three Tefachim sleeping is permitted.
Question: Where do we find anything which contributes to the Shiur of something Kosher but is, itself, not Kosher!?
Answer: Soft mud is itself not Kosher, yet it complements the deficient Shiur of water in a Mikvah.
MISHNAH: SECHACH AT AN ANGLE
(R. Eliezer): A Sukah which is shaped like a tent or which is angled against a wall is Pasul (its roof cannot be differentiated from its walls).
(Chachamim): It is Kosher.
METHODS FOR CORRECTING THE PROBLEM
R. Eliezer concedes that one could raise the Sukos of the Mishnah one Tefach from the ground
The leaning Sukah may be corrected by moving the top of the Sechach one Tefach away from the wall.
Question: What is the rationale of the Chachamim?
Answer: They hold that a sloping Ohel is considered an Ohel.
In the reported incident, R. Yosef justified the fact that he was sleeping under a Kilas Chasanim in a Sukah because he saw in a Beraisa, that R. Eliezer and the Chachamim switched their opinions, in which case, he was following the opinion of the Chachamim (and not of R. Eliezer).
Question: But why did R. Yosef give credence to the Beraisa over the Mishnah?
Answer: Because from another Beraisa, he learned that the author of our Mishnah is a lone opinion (R. Nasan quoting R. Eliezer) and that the Chachamim disagree.
MISHNAH: REED MATS
(Tana Kama): A large reed mat that is made to sleep on, is subject to Tum'ah, and is Pasul for Sechach.
If it was made to be Sechach it may be used, and is not susceptible to Tum'ah.
(R. Eliezer): Regardless of size, it depends only on the intent with which it was made (as bedding or Sechach).
UNSPECIFIED REED MATS
Question: The Mishnah seems to create a contradictory implication!?
From the Reisha we infer that a mat made without any particular intention it is not subject to Tum'ah.
From the Seifa we infer that if it is made without specific intent it is Pasul.
Answer: The Reisha speaks of a large mat (larger than needed for sleeping), and the Seifa of a small one.
Question: But the words of R. Eliezer create the same contradictory inference!?
We cannot say that the first part of his statement speaks of large mats and the second of small, since he says explicitly that regardless of size, only intent matters!?
Answer (Rava): All agree that a large mat is normally meant for Sechach (and is not therefore subject to Tum'ah).
The Tana Kama holds that a small mat (which he does not mention in the Mishnah) which is made S'tam, is subject to Tum'ah and is Sechach Pasul.
R. Eliezer maintains that a small mat has the same Din as a large one in this regard.