we have arrived at the opinion of Rabban Shimon ben Gamliel, who said: Concerning any gap less than four handbreadths wide, the principle of lavud is applied. As had it been taught in accordance with the opinion of the Rabbis, why does the baraita list from three to four handbreadths as a separate category? In the case of both three and four handbreadths, the halakha is one and the same: The principle of lavud does not apply from three handbreadths upward.

Abaye said: From the fact that the first clause is in accordance with the opinion of the Rabbis, the latter clause must also be in accordance with the opinion of the Rabbis. And the Rabbis concede that with regard to any case where the halakha permits sowing other species in the area opposite the standing portion, if there is an area of four handbreadths, it is considered a significant partition, which permits sowing; and if not, it is not considered a significant partition and does not permit sowing. Accordingly, there is a difference between a fence of three handbreadths and one of four handbreadths, as even the Rabbis concede that a fence of four handbreadths is more significant.

Rava said: From the fact that the latter clause is in accordance with the opinion of Rabban Shimon ben Gamliel, the first clause must also be in accordance with the opinion of Rabban Shimon ben Gamliel. And when Rabban Shimon ben Gamliel said that we say the principle of lavud in the case of a gap up to four handbreadths wide, this applies above, off the ground, e.g., in the case of a cross beam suspended at a distance from the wall. However, below, near the ground, it is like a partition through which goats can pass, and therefore he too agrees that we do not say the principle of lavud in that case.

The Gemara returns to the dispute with regard to a breach equal to the standing segments of a partition and cites another proof. Come and hear that which was taught in the following baraita: With regard to an area enclosed by these walls, in a case where most of them consist of entrance and windows, it is permitted to carry on Shabbat within the area, provided that the standing segments are greater than the breached segments.

The Gemara analyzes the formulation of the baraita: Can it enter your mind that the baraita is referring to a case where most of the walls are entrances and windows? If so, the standing segments are certainly not greater than the breached segments. Rather, emend the baraita as follows: Carrying in the area enclosed by these walls, to which one added many entrances and windows, is permitted, provided that the standing segments are greater than the breached segments.

The Gemara draws an inference: If the standing segments equal the breached segments, carrying is prohibited in that enclosure. This is a conclusive refutation of the opinion of Rav Pappa. The Gemara concludes: Indeed, it is a conclusive refutation. Nevertheless, the halakha is in accordance with the opinion of Rav Pappa.

The Gemara wonders: A conclusive refutation and the halakha? The Gemara answers: Yes, that is the case, because the precise reading of the mishna is in accordance with the opinion of Rav Pappa. As we learned in the mishna the following phrase: Provided…there will not be breaches in the partition greater than the built segment. This is clearly indicating that if the breached segments are equal to the built segments, carrying is permitted, as maintained by Rav Pappa.

MISHNA: If a caravan is camped in a field, and the travelers seek to construct partitions to render the area fit for one to carry within it on Shabbat, one surrounds the area with three ropes, one above another, and a third one above the other two. One is permitted to carry within the circumscribed area provided that there will not be a gap of three handbreadths between one rope and the next.

The measure of the ropes and their combined thickness must be greater than a handbreadth, so that the entire partition, consisting of three ropes and the empty spaces between them, will be ten handbreadths high.

Alternatively, one may surround the area with boards that stand upright, provided that there will not be a gap of three handbreadths between one board and the next.

When the Sages issued this ruling, they spoke exclusively of a caravan; this is the statement of Rabbi Yehuda, who maintains that a partition of this kind, which consists of only horizontal or vertical elements, is permitted exclusively in exigent circumstances. Otherwise, full-fledged partitions are required. However, the Rabbis say: They spoke of a caravan in the mishna only because they spoke in the present, citing the most typical case. Those traveling in caravans were typically unable to erect full-fledged partitions, so they would surround their camps with ropes or boards. However, the halakha in the mishna applies in all cases.

The mishna cites an additional dispute: Any partition that is not constructed of both warp and woof, i.e., vertical and horizontal elements, is not a partition; this is the statement of Rabbi Yosei, son of Rabbi Yehuda. He holds that the vertical boards and the horizontal ropes are not considered a partition, even in the exigent circumstances of a caravan. However, the Rabbis say: One of the two elements, either vertical or horizontal, is sufficient.

GEMARA: Rav Hamnuna said that Rav said: It was concluded in the previous mishna that the Rabbis said that in the case of a partition that consists only of warp, i.e., vertical, elements, if the standing segment of the partition is greater than the breached segment, the fence is considered standing. Rav Hamnuna raised a dilemma: What is the halakha in the case of a partition that consists only of woof, i.e., horizontal, elements? Is it also considered standing if the standing segment is greater than the breached segment, or not?

Abaye said: Come and hear a resolution to this dilemma from the mishna: The measure of the ropes and their combined thickness must be greater than a handbreadth, so that the entire partition will be ten handbreadths high. And if it is so that, in a case where the standing segment is greater than the breached segment, the partition is considered standing even in the case of a fence that consists of horizontal elements, why do I need ropes with a combined thickness of greater than a handbreadth?

Instead, let one leave a space slightly less than three handbreadths, and place a rope of any size, leave another space slightly less than three handbreadths, and place another rope of any size, leave a third space slightly less than four handbreadths, and place a third rope of any size. The ropes between which there is a space less than three handbreadths should be considered joined, based on the principle of lavud. The entire partition should be considered standing because the standing segment, measuring six handbreadths, is greater than the breached segment, which measures four handbreadths.

The Gemara presents a difficulty: And how can you understand that this would be effective? Where does he position the space of slightly less than four handbreadths? If he positions it at the bottom, its legal status is like that of a partition through which goats pass, which is not a valid partition.

If he positions it at the top, then the air on this side, above the uppermost rope, and on that side, below that rope, come and negate it. As there are more than three handbreadths between them the upper and lower ropes, they are not joined together based on the principle of lavud. The four handbreadths below the uppermost rope and the airspace above it combine to negate the connection.

If he positions it in the middle, then the standing segment of the partition is greater than the breached segment, provided that the standing portions on the two sides of the breach are combined. However, if each side is considered separately, the breach is greater than the standing portion. If it is nevertheless deemed a partition, conclude from it that even if the standing segment is greater than the breached segment only when the standing segments on the two sides of the breach are combined, the partition is considered standing. However, that circumstance was raised as a dilemma and remained unresolved.

Rather, Rav Hamnuna raised the following dilemma: What is the halakha in a case where one brought a mat that is seven handbreadths and any additional amount, and carved in it a hole three handbreadths wide, and left four handbreadths above the hole and any additional amount below it, and positioned the mat less than three handbreadths off the ground?

Rav Ashi said: The dilemma he raised is with regard to the legal status of a ten-handbreadth partition suspended off the ground. That dilemma is similar to that which Rabbi Tavla raised as a dilemma before Rav: Does a suspended partition act as if it were a partition that reaches the ground and render it permitted for one to carry in a ruin? Rav said to him: A suspended partition renders it permitted for one to carry only when it is suspended over water, as there is a leniency introduced by the Sages with regard to water.

We learned in the mishna: One may surround the area with boards that stand upright, provided there will not be a gap of three handbreadths between one board and the next. Rabbi Yehuda said that this leniency, which allows the establishment of a partition consisting exclusively of horizontal or vertical elements, was stated only with regard to a caravan. The Gemara infers: With regard to a caravan, yes, it is permitted; with regard to an individual, no, it is not permitted. Wasn’t it taught in a baraita: Rabbi Yehuda says: With regard to all unsteady partitions of Shabbat, e.g., those consisting exclusively of horizontal or vertical elements, the Sages did not permit their use for an individual if the space that they enclose is greater than two beit se’a? This indicates that, for an area of up to two beit se’a, Rabbi Yehuda permits these partitions even for an individual.

The Gemara answers: Rabbi Yehuda’s statement in the mishna can be understood in accordance with that which Rav Naḥman, and some say it was Rav Beivai bar Abaye, said with regard to a different statement: This halakha was necessary only in order to provide those traveling in the caravan with space to satisfy all their needs. Here, too, in the mishna, Rabbi Yehuda’s statement can be understood as coming to provide those traveling in the caravan with space to satisfy all their needs. In other words, Rabbi Yehuda does not dispute the fundamental effectiveness of a partition of this kind, even for an individual. When he says that the halakha applies solely to a caravan, he means that it applies only in the case of a caravan, regardless of the size of the area in question. However, in the case of an individual, a partition of that kind is effective only if it encloses an area up to two beit se’a.

The Gemara asks: Where was this statement of Rav Naḥman, and some say of Rav Beivai bar Abaye, stated? It was stated with regard to this ruling at the end of the mishna: Any partition that is not made of both vertical and horizontal elements is not a partition; this is the statement of Rabbi Yosei, son of Rabbi Yehuda.

The Gemara asks: Did Rabbi Yosei, son of Rabbi Yehuda, actually say this? Wasn’t it taught in a baraita: For both an individual and a caravan, partitions made of ropes are effective? And what, then, is the difference between an individual and a caravan? With regard to an individual, the halakha provides him with an area of two beit se’a, in which he may carry by virtue of partitions of this kind. With regard to two individuals as well, the halakha provides them with an area of two beit se’a. Three individuals assume the legal status of a caravan, and the halakha provides each of them with an area of two beit se’a, for a total of six beit se’a. This is the statement of Rabbi Yosei, son of Rabbi Yehuda.

And the Rabbis say: With regard to both an individual and those traveling in a caravan, one provides them with space to satisfy all their needs, provided that there will not be an unoccupied space of two beit se’a. They may not enclose an area that is two beit se’a larger than the space that they require. Apparently, Rabbi Yosei, son of Rabbi Yehuda, relies on the ruling that ropes render an area fit for one to carry within it, even for an individual.

Rav Naḥman, and some say it was Rav Beivai bar Abaye, said: The opinion of Rabbi Yosei, son of Rabbi Yehuda, in the mishna was necessary only to provide them with the space to satisfy all their needs in the case of a properly constructed partition consisting of both horizontal and vertical elements. A partition consisting of exclusively horizontal or vertical elements renders an area of six beit se’a fit for one to carry within it, only in the case of a caravan.

Rav Naḥman taught in the name of Rabbeinu Shmuel: With regard to an individual, the halakha provides him with an area of two beit se’a. With regard to two individuals, the halakha provides them with an area of two beit se’a as well. Three individuals assume the legal status of a caravan, and the halakha provides each of them with an area of two beit se’a, for a total of six beit se’a.

Rav Naḥman was asked: Did you abandon the majority opinion of the Rabbis and act in accordance with the individual opinion of Rabbi Yosei, son of Rabbi Yehuda?

Rav Naḥman then placed a speaker standing over him, and taught: The matters that I stated before you are an error on my part. Indeed, this is what the Rabbis said: With regard to an individual, the halakha provides him with an area of two beit se’a. With regard to two individuals, the halakha provides them with an area of two beit se’a as well. Three individuals assume the legal status of a caravan, and the halakha provides them with space to satisfy all their needs.