A SMALL SUKAH
(R. Shmuel b. Yitzchak): A Sukah must be able to accommodate most of a person (his head and most of his body) and his table (7x7 Tefachim - 6 for his body and 1 for his table).
Question (R. Aba): Is this in accordance with Beis Shamai?
Answer (R. Shmuel b. Yitzchak): Who else?!
Question (R. Aba): Who taught you this?
Answer (R. Shmuel b. Yitzchak): Beis Shamai and it is the Halachah!
Question: Maybe there is no Machlokes Beis Hillel and Beis Shamai over a small Sukah!?
Perhaps Beis Hillel and Beis Shamai argue only where a Sukah is large enough for him and his table.
When he, in that case, sits at the door and places his table inside the house, they may argue over whether we worry about him "following his table" into the house [Beis Shamai] or not [Beis Hillel].
If, however, the Sukah were so small that only his body (and not his table) could fit in, then even Beis Hillel might agree that this is not considered a dwelling?
This suggestion gains support from the Mishnah which speaks of one who has his table in the house, but does not discuss the (more basic) issue of one whose Sukah is too small for his table altogether (presumably because that would not be a Machlokes).
Answer: We can demonstrate from the resolution of two Beraisos that they argue by such a small Sukah as well.
The first Beraisa:
(Tana Kama): A Sukah needs only to be large enough to contain the majority of his body and his table.
(Rebbi): It must be 4x4 Amos.
The second Beraisa:
(Rebbi): It must be 4x4 Amos.
(Chachamim): Even if it only can contain his head and the majority of his body.
We see that the (second) Beraisa does not mention his table!
Question: But the Beraisos are contradictory!
Answer: We must conclude that the first Beraisa is Beis Shamai (body plus table) and the second is Beis Hillel (even body alone is sufficient), and they indeed argue even by a small Sukah.
(Mar Zutra): The Mishnah (28b) also indicates this extension of the Machlokes since it uses the language of Kosher and Pasul which indicates that it is speaking about the Sukah itself being Kosher or Pasul (meaning its size), but not about his ability to fulfil the Mitzvah with it (for fear of being drawn into the house).
Question: But the wording of the Mishnah is, "He who was in a Sukah [and his table was in the house]..." which implies that we are speaking of a sufficiently large Sukah!?
Answer: They argue both by a large Sukah (if he is Yotzei if his table is in the house) and by a small Sukah (is it a Shiur)
To fit this into the Mishnah we need to emend the text.
It should read, 'If one were in and his table was out... it is a Machlokes; and if it were so small... it is also a Machlokes.'
A HOUSE OF LESS THAN FOUR AMOS
Question: Are we to understand that this Beraisa (which lists 10 Halachos for which a house of less than 4x4 Amos is not qualified) is Rebbi and not the Rabanan?
Answer: No, the Rabanan could agree that regarding permanent homes, four Amos is the minimum Shiur, without disqualifying a Sukah (Diras Ar'ai) which is smaller.
Five of the above disqualifications are clear since the word Bayis is used in reference to these Halachos.
Bayis is written by Mezuzah, Ma'akeh, Tumas Nega'im, Chalatah of a house in a walled city, and by returning from the battlefront for a new house.
We understand that a house of less than four Amos would not qualify as a Bayis.
Three of the above are clear since they require a place fit for dwelling.
Participating in an Eiruv Chatzeiros, restricting the other B'nei ha'Chatzer, and storing the collected Eiruv Chatzeiros in the home.
These require actual dwellings, not such a small house.
We can infer that the Shituf Mevuos could be stored in that home.
This is inferred from the restriction stated regarding storing the Eiruv Chatzeiros.
This is so since it is not worse than storing it in the Chatzer itself.
The Mishnah permits this by teaching that the Eiruv Chatzeiros is stored in the Chatzer while the Shituf Mevuos is stored in the Mavoy.
Question: How can we say that we may store the Eiruv Chatzeiros in the Chatzer (presumably, anywhere in the Chatzer) given the Mishnah which says that it is invalid if left in any of the small structures in the Chatzer!?
Answer: Rather, the Beraisa means by 'in the Chatzer' that it is stored in one of the homes of the Chatzer (as opposed to another Chatzer), while Shituf Mevuos may, as stated, be left in any protected place in the Mavoy.
The ninth disqualification (that it will not extend the boundary of one city towards the other) is clear.
This is so because a house of less than 4x4 Amos is not even considered as legitimate a dwelling as a Burgenin.
A Burgenin is, at least, fit for its defined function, unlike this small 'house.'
The tenth disqualification is that brothers and partners cannot divide it.
We assume that this means that one cannot force the other to divide a house of less than 4x4 Amos.
The inference is that anything larger would be subject to a forced division.
Question: The Mishnah has taught that a division may only be forced if each partner would end up with at least four Amos!?
Answer: We mean that a house of less than 4x4 Amos does not have the "Din Chalukah in a Chatzer."
This "Din Chalukah in a Chatzer" is the method for dividing the Chatzer adjoining its houses after the partners have decided who will take each house.
R. Huna holds that it is divided and allocated according to the number of doorways which open into it.
R. Chisda holds that each door must be given four Amos (depth, by the width of the door) with the balance divided equally between the partners.
Both would agree, however, that a house of less than 4x4 Amos does not exact space allocation in the Chatzer (since this structure is likely to be taken down given its lack of utility).