The Relationship Between the Sekhakh and the Walls of a Sukka
The first mishna in Masekhet sukka presents three criteria pertaining the sekhakh (roof covering) of the sukka. It cannot be placed higher than twenty amot nor lower than ten tefachim. In addition, it must produce more shade than the sunlight it admits (tzilatah merubah me-chamatah). Ostensibly, these requirements apply to the sekhakh, which, as Rashi already notes (2a s.v. veshechamta), constitutes the essence of the sukka and lends the sukka its name (sekhakh = sukka). The gemara debates whether the final clause - the sunlight/shade quotient - might apply to the walls as well. Though ultimately rejected, this provocative position might disclose certain basic functions of the sukka and reveal something of its identity.
The gemara (7b) cites Rav Yoshia's dissenting opinion: he believes that the walls of the sukka must also produce shade. If a person were to construct a sukka with glass walls, the sukka would be invalid, even if the sekhakh were completely kosher. How are we to understand this position?
Conventionally, we define the mitzva of sukka as sitting underneath sekhakh. Admittedly, sekhakh can be considered a halakhic roof only if it produces more shade than the sunlight it admits. However, the mitzva doesn't demand sitting in actual shade. Rather, the existence of shade enables the sekhakh to be halakhically valid. If the walls admit sunlight but the sekhakh performs its function, the mitzva can still be fulfilled.
Presumably, Rav Yoshia redefines the mitzva of sukka. A person must actually sit in shade (and not just under shade-producing sekhakh) to execute the mitzva. If the shade is eliminated, even by sunlight streaming through the walls, the mitzva can no longer be performed. Thus, the dispute between R. Yoshia and the Tana Kama would seem to revolve around the definition of the mitzva act - must one sit under sekhakh or actually sit in shade?
However, when discussing the source for R. Yoshia's position, the gemara cites a verse and derasha that indicate a very different rationale. When describing the parokhet (curtain) that separated the Holy of Holies from the rest of the Temple, the Torah employs the word, "ve-sakota" (literally, you should cover or "roof"). Even though the parokhet actually served the function of a vertical wall, it is referred to as a roof. From this syntax, R. Yoshia determined that a vertical wall is also defined as a roof in Halakha, and the walls of a sukka must adhere to the same laws as a roof – namely, tzilatah meruba me-chamata.
This perspective, that the walls of the sukka are part of the roof or possess roof-like qualities, is reminiscent of a famous position of the Rambam. The gemara claims that one may not derive benefit from the wood of a sukka (it is "assur be-hana'a"), and most Rishonim (see, e.g., Rosh) assume that the prohibition only applies to the sekhakh. This is in line with Rashi's claim that the sekhakh constitutes the essential part of the sukka. The walls – whose only function is to enclose the area and support the sekhakh - do not possess any sanctity. By contrast, the Rambam (Hilkhot Sukka 6:15) claims that even the walls possess sanctity and no pleasure may be derived from them. In effect, the Rambam defines the entire structure of a sukka, walls included, as part of the "cheftza shel mitzva" (the object of the mitzva or the essential sukka).
It should be noted that R. Yoshia takes the Rambam's concept to a much further extreme. The Rambam merely extends the halakhic sukka to include the walls. R. Yoshia (based upon the verse) actually imparts to them a quality normally associated with the roof of a sukka: the capacity to produce shade). The Rambam did not necessarily view the wall as a quasi-roof. Even as a wall, it participates in the essence of the sukka. R. Yoshia, however, deems the wall a roof and requires it to produce shade.
Tosafot (8b s.v. mechitza) allude to another potential source for R. Yoshia's halakha. Earlier (6b), the gemara had derived the number of walls necessary to enclose a sukka from the iteration of the term "sukkot" in the Torah. (The term "ba-sukkot" appears only once – Vayikra 23 – but, depending upon the spelling, it might refer to numerous sukkot). Tosafot claim that by referring to walls as "sukkot" (a term generally associated with roof), the gemara itself conveys this function. Ultimately, Tosafot reject this source, but the similarity between the walls and sekhakh seems to be latent in the Torah itself.
Having established a basis for R. Yoshia's position, we might question this based upon the ensuing gemara. The dominant opinion voiced throughout Masekhet Sukka claims that a sukka must be a "dirat arai" - a temporary residence. For example, one reason the sekhakh cannot be situated higher than twenty amot is because such a tall structure can no longer be considered temporary. Several tannaim, however, make statements about the sukka which suggest that they require a sukka to be a "dirat keva" – a permanent structure. The gemara (7b) lists these various tannaim and includes R. Yoshia! Somehow, his requirement that the walls not admit light indicates that he regards a sukka as a dirat keva.
Is this inference merely technical or incidental? Are we to assume that if R. Yoshia demands walls which produce shade, the resultant sukka is likely to be constructed from solid materials that will probably entail a dirat keva? Could it not be possible to construct a durable sukka with materials that admit sunlight?
By drawing this alignment, the gemara might have been suggesting an alternative understanding for R. Yoshia. R. Yoshia demands that a sukka serve in a manner similar to a house (the quintessential permanent structure), and therefore the walls cannot admit light. Had a sukka been merely a temporary residence, we would view the walls only as necessary to bear the sekhakh. Similar to the walls of a hut or a gazebo, the walls of the sukka would be uni-dimensional – pillars to support a roof. Once, however, we define a sukka as a permanent residence, the walls become multi-functional, serving to enclose and protect the area and not only to facilitate the sekhakh. See especially Rabbenu Yonatan (Sukka 7b), who draws this analogy between sukka as dirat keva and R. Yoshia's definition of walls. Based upon this approach, we do not define the walls as part of the sekhakh, but still can justify R. Yoshia's demand that the walls produce shade. If the walls admit sunlight, we can no longer consider this house a dirat keva.
Conceivably, there might be an interesting difference between the two understandings of R. Yoshia. The Ra'avya claims that, according to R. Yoshia, the walls must be constructed from material which is not mekabel tuma (it does not become impure, i.e., non-foods as well as items that have no designated utility), just as the sekhakh must be comprised of these materials. The Ra'avya's extension of R. Yoshia's concept highlights his designation of walls not only as integral to the sukka, but as a semi-roof. If we do not impart the status of sekhakh to the walls (and still require shade-producing potential based upon dirat keva), we should not accept this extra sekhakh-like demand, limiting the materials that can be used to construct the sukka.