Daf Yomi - Sukkah 17 - Lavud

Rav Chisda rules that if one suspends a mat which is a bit larger than four tefachim, it can be utilyzed as one of the walls of a sukkah. This is based on the principle of lavud, which connects a wall to the ground or to the roof above it, providing that the wall is within three tefachim of the ground or roof. In this instance, this concept will required twice - once to connect the four tefach wall to the floor below and once to connect it with the s'chach above it thereby creating a wall of ten tefachim high.

The Ritva explains that it is evident from our Gemora that lavud accomplishes that the gap which is less than three tefachim is deemed to be closed and filled up, not only serving as a connection between the two portions. The proof is because if this four - plus tefach wall is just connected to the s'chach and to the ground, it would not constitute a ten tefach wall and would disqualify the sukkah.

The Shulchan Aruch 632, citing Tosofs on our daf, is in doubt as to what the ruling should be in the following case: One placed two tefachim of ineligible s'chach and another two tefachim of ineligible s'chach separated by less than three tefachim of airspace. Does the principle of lavud apply in this case to combine the two sections of invalid s'chach creating in total four tefachim of ineligible s'chach, thereby disqualifying this sukkah or perhaps we do not apply the concept of lavud to be stringent?

Tosofs writes that the above shaila is only when the two sections of ineligible s'chach add up to four tefachim, however if it would be less than four tefachim it would certainly be a valid sukkah. We do not say that the principle of lavud should close the gap between the two s'chach's thereby creating an area of more than four tefachim of ineligible s'chach because we don't apply the concept of lavud when it would cause a stringency in halacha.

What is the distinction between the two cases? Why in the former case is there a question if we apply lavud even to cause a stringency and in the latter case, there is no doubt at all?

The Magen Avrohom and the Pri Megadim explain that lavud can function in two ways. Lavud can accomplish that the gap between the two areas is viewed as being closed and filled up with the same material as is surrounding it. This method is not applied when it would cause a stringency. This is the reasoning to explain why the gap between the two areas of ineligible s'chach which in total are less than four tefachim is not deemed to be filled up with the ineligible s'chach. There is another manner in which lavud can function and that is to connect the two section together when there is less than three tefachim in between them. The rishonim question if this method can apply when it would cause a stringency. This is why there is a doubt as to what is the ruling when there are two tefachim of ineligible s'chach on both sides of the gap. Can we apply the principle of connecting the two sides to create four tefachim of ineligible s'chach, thus invalidating the sukkah.