OPINIONS: Rebbi Yitzchak says that mid'Oraisa, if the "majority of a person" is covered by an intervening substance, and that person is bothered by the presence of that substance on him, it serves as a Chatzitzah and invalidates his Tevilah. If the substance covers only a small part, or if it covers a majority but he does not care about it, mid'Oraisa the Tevilah is valid. The Rabanan, though, decreed the Tevilah invalid in all of these cases.
What type of Chatzitzah is the Gemara discussing?
(a) RASHI (DH Rubo) explains that the Torah law applies only to one's hair. If most of one's hair is covered by an intervening substance which disturbs him, mid'Oraisa the Tevilah is invalid. If his hair is covered by a substance which does not disturb him, then it is not a Chatzitzah unless it covers most of his hair. If, however, the intervening substance is on his body, the Tevilah is invalid mid'Oraisa even if it covers only a small part of his body. (Tosfos raises several questions on this opinion. The SEFAS EMES, in order to answer those questions, adds that, according to Rashi, the intervening substance is a Chatzitzah mid'Oraisa when it covers only a small part of the body only if the person prefers that the substance not be on him (that is, he is "Makpid").)
(b) TOSFOS (DH Davar Torah) and other Rishonim explain that the Torah law refers to most of one's body. Only when a majority of one's body is covered by an intervening substance is the Tevilah invalid mid'Oraisa. Even if it covers all of one's hair, the Tevilah is valid mid'Oraisa.
The RITVA explains that perhaps Rashi agrees with Tosfos that "Rubo" applies to the body as well. Rashi, however, rules in accordance with the GE'ONIM (cited by the RAMBAM, Hilchos Mikva'os 2:15, who disagrees with the ruling of the Ge'onim). The Ge'onim maintain that we measure the proportion of hair that is covered and the proportion of the body that is covered individually. If most of the hair is covered, then even though the rest of the body is not covered, the substance is still considered a Chatzitzah mid'Oraisa.
(The SEFAS EMES asserts that, according to the Ge'onim, all of the hair on the body is taken into account when one measures whether "most of the hair" is covered by the substance, and not just the hair on the head and facial hair.)
The SEFAS EMES points out that Rashi's conclusion may be based on the wording of Rav. If Rav means that only the size of the Chatzitzah is a Halachah l'Moshe mi'Sinai, then why does he say that "Chatzitzin" themselves are learned from a Halachah l'Moshe mi'Sinai? According to the Ge'onim, Rav indeed means that the Chatzitzin themselves are learned from a Halachah l'Moshe mi'Sinai, in the case of hair. The Halachah l'Moshe mi'Sinai teaches that a Chatzitzah that affects the hair alone is also considered to be a Chatzitzah. (See also Insights to Nidah 67:3 and Eruvin 4:2.)
QUESTION: The Gemara quotes a Beraisa in which Rebbi Shimon and the Rabanan argue about the minimum number of walls required for a valid Sukah. Rebbi Shimon maintains that a Sukah must have three full walls and a fourth wall at least the width of a Tefach. The Rabanan maintain that a Sukah must have two full walls and a third wall at least the width of a Tefach.
The Gemara explains the reasoning of each opinion. Both Rebbi Shimon and the Rabanan interpret the word "Sukos" written in the Torah as plural, since that is the way that it is read ("Yesh Em la'Mikra"). Consequently, each word "Sukos" indicates two walls. Since the word "Sukos" is written three times, this implies that a Sukah must have six walls. However, Rebbi Shimon maintains that one word "Sukos" is necessary to teach the simple meaning of the verse, that it refers to a Sukah (RAN, MAHARAM to Sukah 6b), which leaves two words "Sukos," or four walls. A Halachah l'Moshe mi'Sinai teaches that one wall may be a Tefach wide, and thus the number of walls needed for a Sukah is three full walls and one wall with the width of a Tefach.
According to the Rabanan, the first word "Sukos" is used for the plain meaning of the verse, as Rebbi Shimon says. The second word "Sukos" is used to teach the law of Sechach (Rebbi Shimon, on the other hand, maintains that the law of Sechach is included in the definition of a Sukah).
This is difficult to understand. If the second word "Sukos" is used for the Sechach, then only one word "Sukos" is left. With the Halachah l'Moshe mi'Sinai, this should teach that only one full wall and one partial wall (with the width of a Tefach) is necessary.
The MAHARAM explains that the Rabanan learn that the Sechach is equivalent to a wall. This means that when the two words "Sukos" teach the necessity for four walls, one of those "walls" refers to the Sechach, so that the two words "Sukos" teach that a Sukah is comprised of three walls and a roof of Sechach.
However, even according to the Maharam's explanation, it is not clear why the Rabanan deem it necessary to have one word "Sukos" for the simple meaning of the verse and another word "Sukos" for Sechach. Why is the need for Sechach not included in the simple meaning of the first word "Sukos" (since without Sechach, a Sukah is not a Sukah)?
(a) The RAN in Sanhedrin (4a) is bothered by this question. He answers that the Rabanan agree that even without the extra word, we would have known that a Sukah needs Sechach. However, the extra word teaches that the Sechach has Halachic requirements that must be fulfilled; for example, it must be "Ta'aseh v'Lo Min ha'Asuy," and it may not be made with objects that are able to become Tamei.
(b) The ARUCH LA'NER has difficulty with the Ran's explanation. The Halachos relevant to Sechach are derived from different verses in the Torah (see Sukah 11a). Why is another verse necessary to teach those laws? The ARUCH LA'NER, therefore, suggests a different answer. He suggests that the Rabanan, who say that an extra word is needed to teach the requirement of Sechach, maintain that no word "Sukos" is necessary to teach the simple meaning of the verse (that it refers to a Sukah). When they say that an extra word is necessary to teach the requirement of "Sechach," they are referring to the law that all three walls must touch the Sechach (or at least be within three Tefachim of the Sechach). They learn that the six "walls" implied by the words "Sukos" are actually three walls that each touch Sechach (three "Sechachs"). Without the third word "Sukos," we would not have known this law about Sechach (we would have derived only one full wall and one wall with the width of a Tefach, which is not a logical description of a Sukah).
The explanation of the Aruch la'Ner has significant ramifications. There is a well-known argument among the Rishonim with regard to a Sukah that has walls that meet the required height, but which do not touch the Sechach. The ME'IRI (Sukah 2a) and RITVA maintain that such a Sukah is valid only because of the principle of "Gud Asik" (walls that are at least ten Tefachim tall are considered as though they extend upward beyond their actual height). This makes them "touch" the Sechach from the Halachic point of view.
The Ran (4b) argues that the principle of "Gud Asik" never applies to a Sukah, because a Sukah has a special requirement of "Mechitzos Nikaros" -- the walls must be physically present and visible. According to the Ran's opinion, such a Sukah is valid even without the mechanism of "Gud Asik." Accordingly, we understand why the Ran in Sanhedrin does not explain the Gemara like the Aruch la'Ner; he maintains that there is no requirement for the walls to actually touch the Sechach (see PNEI YEHOSHUA to Sanhedrin 4b, who argues with the Ran and gives another source for the requirement that the walls touch the Sechach).
RAV ELYASHIV shlit'a (quoted in HE'OROS B'MASECHES SUKAH, Sukah 6b) suggests a similar answer. The REMA (OC 635) states that if one places Sechach on his Sukah before he erects the walls, his Sukah is unfit because it does not fulfill the requirement of "Ta'aseh v'Lo Min ha'Asuy." He says that the law that Sechach is invalid unless it has walls underneath it is derived from the extra word "Sukos" here, which refers to Sechach according to the Rabanan.
(c) Perhaps it is not necessary to repeat the word "Sukah" to teach that Sechach is necessary. However, when the Tana'im derive the number of walls needed for a Sukah from the number of times the word "Sukah" is repeated, the Tana Kama maintains that it is natural for the count to include the total number of walls and Sechach, since the Sechach and the walls together constitute the Sukah. Accordingly, since the Torah counts the total of Sechach plus walls (four), only three walls are implied by the verses; the fourth word "Sukah" refers not to any additional walls, but to the requirement of Sechach, which is known already from the word "Sukah" that was written "l'Gufei." In contrast, Rebbi Shimon maintains that the four walls are a complete unit unto themselves. The Sechach need not be included in the count since it serves a different purpose. (M. Kornfeld, Y. Montrose; see also Insights to Sanhedrin 4:3.)