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Mishna 28b states: כל שבעת הימים אדם עושה סוכתו קבע וביתו עראי. The Rabbis further taught Baraisa 28b that states: ת”ר כל שבעת הימים אדם עושה סוכתו קבע וביתו עראי כיצד היו לו כלים נאים מעלן לסוכה מצעות נאות מעלן לסוכה אוכל ושותה ומטייל בסוכה. Therefore, it can be deduced that according to Rabbis on 3b and Beis Hillel on 3a to make one’s sukkah קבע and to transform his house into עראי, he needs only to אוכל ושותה מטייל בסוכה, because in the end a person may not have elegant dishes or fine linens. And, this requirement corresponds to Beis Hillel’s minimum size sukkah of ראשו ורובו, that a person must be able to literally fit his head and most of his body inside the sukkah in order to be able to fulfill the requirement to אוכל ושותה ומטייל בסוכה.
However, Beis Shammai’s opinion adds to the common denominator of ראשו ורובו, in concluding that a person must literally pull his table out of his house, making his house עראי, and place the table inside his sukkah (ראשו ורובו ושולחנו) in order for him to אוכל ושותה מטייל בסוכה as he normally dwells in his house all year long. And, the proof that Beis Shammai requires the table to be removed from his house is that Mishna 3a states: מי שהיה ראשו ורובו בסוכה ושולחנו בתוך הבית ב”ש פוסלין ובית הלל מכשירין. Why does the Mishna state: ושולחנו בתוך הבית? Let the Mishna simply state that the table is outside the sukkah.
Regarding the requirement to make one’s sukkah קבע, what are the rationales of the Tannaim? In 28b, all hold that the Torah requires us to “תשבו” (dwell) in a permanent manner in a sukkah. Therefore, a sukkah must be a “dwelling” and not like other structures such as a hut to merely sleep in or a watchtower from which to stand guard. Rebbe holds that a sukkah needs to be a permanent dwelling like a house, which if built less than 4×4 amos will lose its ability to be a dwelling, similar to the Baraisa on 3b which explains regarding houses: דאי אית ביה ד’ אמות על ד’ אמות דיירי ביה אינשי ואי לא לא דיירי ביה אינשי. Whereas, Beis Shammai holds that the unique feature of a dwelling is that a person eats meals at a table, otherwise it is not a dwelling but more like a hut, or some other type of structure. However, Beis Hillel holds that if a person simply sat in the sukkah and ate from their hand it was enough to make it a valid dwelling, even without a physical aspect of קבע that would make it a דירת קבע structurally in a physical sense, as is found in the opinions of the Tannaim on 7b.
Therefore, the argument between Rebbe, Rebbi Yehuda, Beis Shammai and Beis Hillel is regarding the nature of קבע that constitutes a dwelling within which one can fulfill the commandment to “תשבו”. Beis Hillel uniquely makes his sukkah קבע through simply eating in the sukkah as opposed to his house, while at the same time maintaining that the physical structure of a sukkah requires a דירת עראי based on the words שבעת ימים, like Rava on 2a.
לעולם בתרתי פליגי פליגי בסוכה קטנה ופליגי בסוכה גדולה וחסורי מיחסרא והכי קתני מי שהיה ראשו ורובו בסוכה ושולחנו בתוך הבית ב”ש אומרים לא יצא וב”ה אומרים יצא ושאינה מחזקת אלא כדי ראשו ורובו בלבד ב”ש פוסלין ובית הלל מכשירין
The main issue of dispute in both a small and large sukkah is concerning whether a literal table is required inside the sukkah to qualify as a valid dwelling. Consequently, regarding a small sukkah of ראשו ורובו the issue is not that the sukkah is approximately 6×6 tefachim, but that a sukkah of 6×6 tefachim necessarily does not permit Beis Shammai’s required table inside the sukkah from which a person must be able to eat. Therefore, a sukkah that is too small is structurally invalid on a דאורייתא level according Beis Shammai, therefore ב”ש פוסלין. Whereas, regarding the dispute in a large sukkah the issue is not that the table cannot physically fit inside the sukkah. In this case, the sukkah itself is structurally valid according to the Torah, but since the table is not inside the sukkah from which one must eat their meals, the person does not discharge his דאורייתא obligation to dwell (תשבו) in a permanent manner, therefore ב”ש אומרים לא יצא to dwell in a sukkah. This is because according to Beis Shammai the table is what makes it a dwelling.
Therefore, the Gemara is always referring to Beis Shammai’s requirement as an actual table which is required to be inside of the sukkah to be qualified as a dwelling, which tangentially reveals a minimum size for a sukkah as ראשו ורובו ושולחנו on a דאורייתא level. The difference being not just semantics, but critical to the essence of the argument. For, if a person always dwelt in a small sukkah without placing a table inside, Beis Shammai would say to them as they did to R’ Yochanan ben HaChoranis on 28a: “In all your days you have never fulfilled the mitzvah of sukkah”. They did not state that he was dwelling in an invalid sukkah that was too small, but that they found him dwelling without a table.
And this is the answer to confusion recorded in Mishna 28a between the students of Beis Hillel and the students of Beis Shammai. The students of Beis Hillel viewed the dispute only in terms of the size of the sukkah and found a proof in the fact that the Elders of Beis Shammai did not say a word to R’ Yochanan ben HaChoranis about the small size of the sukkah which was ראשו ורובו. And Beis Shammai said, a proof from that! But, the elders of Beis Shammai said to him that if you have always eaten without your table inside the sukkah you have never fulfilled the mitzvah of sukkah.
Since Beis Hillel holds that a sukkah is a דירת עראי, which limits the height of a sukkah in accordance with שבעת ימים to 20 amos, it allows a sukkah as small as ראשו ורובו in regards to length. Therefore, the students of Beis Hillel viewed the dispute between ראשו ורובו and ראשו ורובו ושולחנו in terms of a measurement of length. And therefore, they found a proof that a sukkah is a דירת עראי from the fact that Elders of Beis Shammai did not say anything to R’ Yochanan ben HaChoranis regarding the smallness of his sukkah. Beis Shammai then discounted their proof and supported their own opinion that a sukkah is a דירת קבע in pointing out that while the Elders of Beis Shammai did not speak about the small size of R’ Yochanan ben HaChoranis’ sukkah they strongly objected to his eating without a table. Therefore, the Elders did object to the small size of R’ Yochanan ben HaChoranis’ sukkah when rebuking him for not eating from his table.