GEMARA

Mishnah - R. Yehudah: One may use boards for Sechach;

R. Meir forbids.

If one used a board four Tefachim wide it (the Sukah) is Kosher, just one may not sit underneath it.

Rav: They argue about boards that are four Tefachim wide. R. Meir decrees Gezeiras Tikrah (not to use boards, lest one think that he is Yotzei Sukah by sitting under his roof); R. Yehudah does not. All permit boards less than four.

Shmuel: They argue about boards less than four, but all disqualify boards that are four wide.

Question: Does Shmuel disqualify even if they are less than three? They are like mere reeds!

Answer (Rav Papa): Shmuel means that all allow if they are less than three, and all disqualify boards that are four wide. They argue about boards between three and four:

R. Yehudah does not decree because each board is less than the Shi'ur for a Reshus;

R. Meir decrees because each is bigger than the Shi'ur for Lavud.

Question (Seifa): If one used a board four Tefachim wide it is Kosher, just one may not sit underneath it.

This is like Shmuel, who says that all disqualify a board four wide. According to Rav, R. Yehudah allows such boards!

Answer: Indeed, Rav holds that the Seifa is R. Meir.

14b: A Beraisa supports Rav, and a different Beraisa supports Shmuel.

Beraisa (supporting Shmuel): If one use for Sechach cedar boards four Tefachim wide, all agree that it is Pasul. If they are less than four, R. Meir disqualifies and R. Yehudah is Machshir.

R. Meir agrees that if the space between boards is as thick as the boards, one puts Kosher Sechach there and it is Kosher;

R. Yehudah holds that if there is a board four wide it is Kosher, but he agrees that one may not sleep under it and one who sat underneath was not Yotzei.

15a - Question: Do R. Yehudah and R. Meir argue about Gezeiras Tikrah in two Mishnayos (14a and 15a)?

Answer #1 (R. Yochanan): The Mishnah of 14a discusses smooth boards. They argue about whether or not we decree lest one use Kelim (which are Mekabel Tum'ah and are Pasul) for Sechach.

Question: Rav Yehudah said that Rav allows 'male' arrow shafts (they are Klei Etz without a receptacle and are not Mekabel Tum'ah) for Sechach. He does not decree lest one use 'female' arrow shafts (they have a hole to hold the arrow head, they are Mekabel Tum'ah). Similarly, he would not forbid smooth boards lest one use Kelim!

Answer #2: Indeed, they argue about Gezeiras Tikrah in both Mishnayos.

RISHONIM

Rif: The Halachah follows Shmuel, for Rav Papa and the Sugya are like him.

Rebuttal (Rosh 1:28): We cannot learn from Rav Papa, for Amora'im often explain earlier Amora'im even if they disagree with them.

Rambam (Hilchos Sukah 5:7): One may use boards less than four Tefachim wide for Sechach, even if they are smooth. One may not use boards four wide even if they are not smooth. This is a decree lest one sit under his roof and think that it is like a Sukah. If one used a board four Tefachim wide it is Kosher, but one may not sit underneath it. One who sat underneath was not Yotzei.

Rosh (1:28): Usually, the Halachah follows Rav against Shmuel in Isurim. However, Amora'im argue about turning a thick board on its edge. According to Rav this applies only according to R. Meir; according to Shmuel it applies to everyone. Since the Halachah follows R. Yehudah, the Halachah follows Shmuel. The Ra'avad says that the Halachah follows decrees of R. Meir, and the Halachah follows Rav. This is the same as R. Yehudah according to Shmuel.

Rashi (DH Machlokes and DH keshe'Ein): R. Yehudah does not decree about boards less than four because it is uncommon to make roofs from them. R. Meir is concerned for the minority who use them for roofing.

Question: In some places they do not use wide boards for roofing. Even reeds are used (Bava Metzi'a 117a)!

Answer (Ran DH Gemara): The reeds are tied in bundles four wide.

Question: The Gemara says that the Pesul depends on Reshus or Lavud, not on whether or not it is commonly used for roofing!

Answer (Ran ibid.): Sukah is Diras Arai, therefore one normally uses for Sechach things too narrow to be a Reshus (or narrow enough to apply Lavud), so we do not decree against these.

Question: R. Yehudah holds that if there is a board four wide on the side it is Kosher through Dofen Akumah, but one who sat underneath was not Yotzei. Why was this taught here? The Mishnah (17a) discusses Dofen Akumah!

Answer (Ran DH u'Modeh): One might have thought that Gezeiras Tikrah applies only to disqualify an entire Sukah, but not to disqualify part when the Sukah is Kosher in any case. Our Mishnah teaches that this is not so.

POSKIM

Shulchan Aruch (OC 629:18): It is forbidden to use boards four wide for Sechach. If they are less than four they are Kesherim, even if they are smooth and resemble Kelim.

Levush (brought in Taz 20): Why are boards Kosher? They are Mekabel Tum'as Medras! We must say that they are not meant to be trodden on, rather, for building. They are not Mekabel Tum'ah until they are prepared or intended to be trodden on.

Question (Taz 20): Smooth boards are prepared and fitting for use! Also, the Gemara discusses whether or not we decree lest one use Kelim. We should decree lest one use boards meant to be trodden on!

Answer (Taz 20): A Keli is not Mekabel Tum'as Medras until it is fixed in a place where it will be stepped on. Until then it is Mechusar Ma'aseh. Tosfos (5a Sof DH Misgarto) says that because a baker's board is wide and useful for putting things on it, it is Mekabel Tum'ah mid'Rabanan. We must say that it is wider and more useful than regular boards.

Magen Avraham (21): We must say that the boards were not designated to sit on, for then they would be Mekabel Tum'as Medras.

Shulchan Aruch (ibid.): Our custom is not to use boards at all for Sechach.

Source (Beis Yosef DH v'Chosav bi'SMaK, citing SMaK): Even though it is permitted to use boards less than four, our custom is not to. This is because the Sechach must be Arai, so that rain would come through (Tosfos 2a DH Ki). If boards are used one might make the ceiling impervious to rain.

Mishnah Berurah (49): Some say that nowadays Gezeiras Tikrah applies even to boards less than three wide, because they are used for house roofs. Also, one should not use anything which could make a ceiling impervious to rain (e.g. tiles), even if it is not used for houses.

Mishnah Berurah (50): In pressed circumstances, one may use anything that is Pasul only because of a decree. Poskim argue about whether or not one may bless in such a case. The Rashba permits.