Question #1: Why do we need the post of four Tefachim? Why can one not make a post of two Tefachim and place it close to the wall; then leaving a gap of a fraction less that three Tefachim, place another post of two Tefachim? ...

Precedent: Since the Gemara asks a similar Kashya in the first Perek of Eruvin (Daf 10b), when Rav Yehudah rules, regarding a Mavoy which is fifteen Amos wide, that one leaves a two-Amah space and places a post of three Amos ...

Precedent (cont.): On which the Gemara asks 'Why? Let them placce a post of one and a half Amos, leave a space of two Amos and place a second post of one and a half Amos?'

Refuted Answer #1: And one cannot answer here, like it does there 'that the air on either side negates it' ...

Refutation: Because in this case, whatever is less than three Tefachim, we apply 'L'vud', in which case it (the gap) is closed, seeing as even if the entire Sukah consists of canes that are less than three Tefachim, it is Kasher ...

Source: As we learned in a Beraisa earlier (on Daf 7a), which compares the wall of a Sukah to a wall of Shabbos, provided there is no gap of three Tefachnim between one cane and the next.

Refuted Answer #2: Nor can one in any way differentiate between a Sukah of three walls and one of four walls.

Question #2: It will even suffice to place two posts, each measuring half a Tefach plus, one of which one places within three Tefachim of the wall, the other, within three Tefachim of the first one?

Answer: Because the Gemara says at the end of the first Perek of Eruvin (Daf 16b) that 'Any Mechitzah that is not made Shesi va'Areiv (criss-cross) is not a Mechitzah', and two posts, neither of which measures four Tefachim, constitute a Mechitzah of Shesi (only).

Clarification: ... the entire Sukah with a Shi'ur of three Tefachim.

Pasul S'chach: Renders the Sukah Pasul with four Tefachim, if it is in the middle - four Amos from the wall, since it cannot become Bateil based on the principle of 'Dofen Akumah' (a bent wall)

Reason: In which case it interrupts between two lots of Kasher S'chach.

Pasul S'chach (cont.): This speaks specifically where it (the Pasul S'chach) begins from the middle wall and stretches across the entire length of the Sukah up to the opening, because that is when the air or the Pasul S'chach interrupt between the two lots of Kasher S'chach, leaving neither side with three walls.

Pasul S'chach (cont.): But if it begins from one of the side walls and stretches across to the other, then, assuming that from the Kasher S'chach to the middle wall comprises a Shi'ur Sukah (seven Tefachim), then it is Kasher, seeing as it has three walls; But the section towards the opening is Pasul.

When the Sukah is Kasher: And there where the air or the Pasul S'chach does not stretch across the entire Sukah - such as where, three by three Tefachim of air, or four by four of Pasul S'chach are situated in the middle of the Sukah ...

When the Sukah is Kasher (cont.): Then if, from it to the middle wall there is a Shi'ur Sukah, the entire Sukah is Kasher, both the sides and the section towards the entrance ...

Outside the Sukah: And even what protrudes to the outside completely ...

Reason: Because, seeing as it is all joined to the Shi'ur Hechsher Sukah, it it like 'Pesel' (foliage) the sticks out from the Sukah which is permitted even without walls ...

Source: As the Gemara will say later (on Daf 19a) - that ity has the Din of a Sukah.

Outside the Sukah (cont.): It may be that, even if from the P'sul to the middle wall there is not a Hechsher Sukah, they (that section and the Pesel) will combine to make up a Hechsher Sukah, and th air and the Pasul S'chach are not Chotzeitz ...

Reason: Since the Hechsher is joined via the sides.

Clarification: Because, seeing as neither the air nor the Pasul S'chach have the Shi'ur to render the Sukah, they do not combine to render the Sukah Pasul ...

Reason: Since they both have different Shi'urim, as the Gemara explains.

She'eilah: However, there where there are two lots of Pasul S'chach, each comprising two Tefachim, with a space of less than three Tefachim in between, it is not certain whether the two lots combine, to make up four Tefachim to render the Sukah Pasul ...

Reason: Since on the one hand, perhaps, since there is air in between them, they do not combine, whilst on the other, since the air comprises less than three Tefachim, they do.

Conclusion: There however, where the two lots of Pasul S'chac h combined measure less than four Tefachim, the air in between will not complete the Shi'ur of four Tefachim, due to the fact that it is considered closed on account of 'L'vud ...

Reason: Because we not apply 'L'vud' Lehachmir.

Source: It is a Mishnah in Keilim (Perek 27 Mishnah 2) which states that 'Cloth of three by three Tefachim is subject to Tum'as Medras, and one of three by three Etzba'os (finger-breadths) to Tum'as Meis; sack-cloth of four by four Tefachim, leather of five by five and a reed mat of six by six are equally subject to Medras and Tum'as Meis.

Source: And the reason that cloth of three Etzba'os is Mitamei Meis is because the Gemara in Perek Bameh Madlikin (Shabbos, Daf 26b) learns from the word "ve'ha'Beged" - to include what is fit for a poor man (to wear)

Source (cont.): Whereas the criterion for Medras is that it is fit to sit on.

Source (concl.): And if it is less than three Tefachim by three Tefachim it is not.

Conclusion: Whereas the Shi'ur for sackcloth, leather and a reed mat is the same for Medras as for Tum'as Meis.

Source: It is Mishnah in Perek Kodshei Mizbe'ach, in Maseches Me'ilah (Daf 18a), where the Seifa, citing Rebbi Shimon, states 'Why is that? Because they are fit to become Tamei Tum'as Moshav'.

Source (cont.): The Mishnah there reads: 'Cloth and sackcloth, sackcloth and leather, leather and a reed mat, combine - specifically in that order (of pairs), because their Shi'urim are close to one another ...

Source (concl.): But cloth and leather, or sackcloth and a reed mat, whose Shi'urim are far from each other, do not combine.

Clarification: And it is only the more stringent that combines with the more lenient, but not vice-versa ...

Source: As the Mishnah states there in Maseches Keilim (Perek 27 Mishnah 3) 'If one made two Tefachim from cloth and one from sackcloth, three from sackcloth and one from leather or four Tefachim from leather and one from a reed mat, it remains Tahor ...

Source (cont.): But five from a reed mat and one from leather, four from leather and one from sackcloth or three from sackcloth and one from cloth, it is Tamei.

Source (concl.): This is the K'lal (the rule) - "Wherever one joins something to it that is more stringent than it, it is Tamei; something that is more lenient than it, it is Tahor" '.

Conclusion: The K'lal, which comes to include, implies that when the Mishnah states that it specifically in that order that they combine, it is La'av Davka.

Clarification: It is a Mishnah there in Maseches Keilim (Ibid. Mishnah 4), that from whichever one he cuts off a Tefach and makes it into a patch for the pack-saddle of a donkey, it is Tamei.

Alternative: It could equally-well have said - 'Since they are all equal with regard to the Beraisa in Me'ilah, at the end of Perek Kodshei Mizbe'ach (Daf 18a) - 'If one cut off from all of them and made from them a garment to lie on, the Shi'ur is three Tefachim; to sit on, it is one Tefach; to hold, a Kol she'Hu (a minimal Shi'ur)' ...

Clarification: This means 'to make a patch to lie on' - such as a cushion or a cover or for other things that are meant specifically for lying on, the Shi'ur of the patch is three Tefachim ...

Clarification (cont.): Similar to 'for sitting, a Tefach', which refers to making a patch for sitting on - such as for the pack-saddle of a donkey, as is evident in our Sugya.

Precedent: And similarly, the case cited in the Tosefta (See Mesores ha'Shas) 'Someone who cuts off a piece for lying on, the Shi'ur is not less than three Tefachim; for sitting on, a Tefach, and for 'Ma'amad', Kol she'Hu' ...

Clarification: And Ma'amad is equivalent to 'Ahcizah' in Me'ilah.

Definition #1: Where, in answer to the question 'What is Achizah', Resh Lakish explains 'that stands to be used for weaving ...

Definition #2: Whereas a Beraisa explains that it is fit to be used by people who cut figs.

Explanation of Definition #1: The Aruch explains that Mashehu is fit to be used by weavers - 'When they smoothen the material with oats or some other commodity, in order to strengthen it, they tie a bit of cloth on their finger and proceed to smoothen the material ...

Explanation (cont.): And the bit of cloth around his finger protects it against being cut by the thread

Explanation (concl.): And the piece of cloth on his finger is called 'Navlah' and is also fit to be used by fig-cutters - The people who split the figs open and salt them, tie the bit of cloth around their finger to prevent the juice of the figs from sticking to it.