1) A SUKAH LESS THAN TEN TEFACHIM TALL
QUESTION: The Mishnah (2a) states that a Sukah that is less than ten Tefachim tall is invalid. The Gemara asks what the source is for this Halachah. Perhaps a Sukah lower than ten Tefachim is also valid, as the Gemara itself suggests later (5b) in the case of a Sukah that is nine Tefachim tall. The Gemara commences a lengthy discussion about the source for the height of ten Tefachim as derived from the height of the Aron ha'Kodesh.
Why does the Gemara ask for the source that a Sukah less than ten Tefachim tall is invalid? The Gemara (4a) already taught the reason why it is invalid -- it is a "Dirah Seruchah" (an uninhabitable dwelling). The Gemara there said in the name of Rava that if the branches ("Hutzin") of the palm leaves of the Sechach dangle below ten Tefachim, the Sukah is invalid because it is a "Dirah Seruchah." The same principle ("Dirah Seruchah") should invalidate any Sukah less than ten Tefachim tall! (Indeed, the BARTENURA on the Mishnah writes that the reason why such a Sukah is invalid is because it is a "Dirah Seruchah.") Why does the Gemara here not give this logic as the source for the Pesul of a Sukah less than ten Tefachim tall?
(a) The ME'IRI infers from the words of the RAMBAM (Hilchos Sukah 5:5) that when branches dangle below ten Tefachim, the Sukah is invalid only l'Chatchilah; b'Di'eved it is a valid Sukah. Apparently, the Pesul of "Dirah Seruchah" invalidates a Sukah only l'Chatchilah. Accordingly, perhaps the Gemara here seeks a source to invalidate a Sukah less than ten Tefachim tall even b'Di'eved (i.e. mid'Oraisa). (ARUCH LA'NER 4a; BEIS YISRAEL, cited by SEFAS EMES)
(b) The other Rishonim, however, seem to learn that the Pesul of "Dirah Seruchah" is mid'Oraisa and invalidates a Sukah even b'Di'eved. The Halachah is that if the decorations of a Sukah dangle below ten Tefachim, the Sukah remains valid. TOSFOS (10b, DH Noyei) explains that the fact that the decorations hang down so low does not make the Sukah into a "Dirah Seruchah," because "they are made for decorating" the Sukah. Tosfos apparently means that only objects that interfere with the use of the Sukah make it a "Dirah Seruchah." The branches that hang down are sharp and pointed and make it difficult to use the Sukah (as the Me'iri and Rabeinu Yehonasan mi'Lunil explain). In contrast, the decorations of a Sukah do not interfere with the use of the Sukah.
According to this explanation, when the entire ceiling of the Sukah reaches only nine Tefachim, one might have thought that the Sukah is valid because the low ceiling does not interfere with the normal use of the Sukah. Therefore, the Gemara seeks another reason (other than "Dirah Seruchah") for why such a Sukah is invalid.
(c) The PNEI YEHOSHUA points out that TOSFOS here (DH Asarah) explains that the source which the Gemara finds to invalidate a Sukah that is less than ten Tefachim tall is not only a source for Sukah, but it also teaches that any wall or partition that is ten Tefachim tall suffices to separate the area enclosed within it from the area outside of it and give it the status of a separate domain. This Halachah is particularly relevant to the laws of the different domains on Shabbos.
The Pnei Yehoshua explains, therefore, that it is true that the Gemara does not need another source to teach that a Sukah less than ten Tefachim tall is invalid, because the reasoning of "Dirah Seruchah" teaches that. However, the Gemara wants to find a source that teaches that any wall ten Tefachim tall effectively separates one domain from another. Since that question happens to apply to Sukah as well, the Gemara phrases its question as a search for a source that a Sukah less than ten Tefachim tall is invalid.