The sugya examined here is that of Eruvin 3a-b. There is no parallel sugya anywhere else in the Talmud yet a close study demonstrates that the treatment is typical of the contrived arrangement of the material by the final editors of the Babylonian Talmud.
The rules as stated in the Mishnah (Eruvin 1: 1 and Sukkah 1: 1) are that the beam to be placed at the entrance of an alley in order to permit people to carry objects there, and the covering of a sukkah both are required to be within twenty cubits. And there is a minimum size for both the beam and the covering of the sukkah. The size of the beam must be such that it can hold a half-brick. The size of the covering must be such that there is more covering than empty space—in the language of the Talmud, its ‘shade must be greater than its sun’. The question discussed in our passage is whether it is valid when the beam and the covering are so placed that some part is within the required twenty cubits and some part above the twenty cubits. Does this count as being within or without the twenty cubits? It is assumed that we are dealing with a beam or covering that is of the minimum size; otherwise the part that is above the twenty cubits should not invalidate the rest and can safely be disregarded. A number of opinions are now given.
Rabbah said: In the case of the beam it is valid but in the case of the sukkah covering it is invalid. The Talmud asks: Why do you say that it is valid in the case of the beam? The reason can only be because we say that we thin it out i.e. disregard the part that is above twenty cubits so that there is still a line of beam, albeit a very thin one, within the twenty cubits. But, if that is case, why not say that the covering, too, is valid because of the thinning out principle? To this the reply is given, if the covering is thinned out what remains will no longer qualify as a valid covering since there will be more sun than shade. But, then, in the case of the beam, too, what remains after the thinning out will be unable to stand in a normal wind i.e. it should be invalid because it is too thin just as the sukkah covering is held to be too thin. You must perforce say that, thin though it is, it is treated as if it were a strip of metal which, though very thin, can hold a half-brick and is not dislodged by the wind. In that case why not say the same with regard to the covering, namely, that it is treated as if its shade were greater than its sun. The meaning of this is that although that part of the beam and the covering is technically not there it is still physically there so that; unlike a physically very thin line, it can hold the half-brick in the one case and provides sufficient shade in the other. Consequently, it is difficult to see why Rabbah declares the beam to be valid and the covering invalid. If the principle of thinning out is accepted in the one case it should be accepted in the other and if rejected, for the reason given, there is no logic in refusing to reject it in the other. Two replies are given to explain why Rabbah does invalidate it in the case of the covering but validates it in the case of the beam. Rava of Parazika replies that a sukkah is usually intended for an individual and if the covering within the twenty cubits became lost through dropping away and the like so that only the part above the twenty cubits remained, he would not notice it. Hence Rabbah declares the covering to be invalid. In the case of the beam, on the other hand, it is intended for public use and since they are many they will notice when anything goes wrong and will put it right. Ravina gives a simpler reply. Rabbah is stricter in the case of the sukkah because the command to dwell in the sukkah is Biblical and as such has to be treated very strictly whereas the requirement of the beam in the alley is only Rabbinic and hence can be treated with less severity.
At this stage R. Adda b. Mattenah enters the scene and the whole argument is presented in an exactly opposite form. According to R. Adda b. Mattenah, Rabbah said the opposite: In the case of the beam it is invalid but in the case of the covering it is valid. And now the whole argument proceeds in a reverse picture image of the previous arrangement. The Talmud asks: Why do you say that the covering is valid it must be because you apply the principle of thinning out. Well, then, apply it to the beam. But if you apply it to the beam the beam would be too thin? In that case the covering would be too thin. Perforce we must say that the covering is still treated as having more shade than light so why not say with regard to the beam that it is treated like a metal strip and is valid? The two replies of Rava of Parazika and Ravina are given but now to explain why the covering is valid and the beam invalid. Rava of Parazika now argues that since the sukkah is intended for an individual he will notice if anything goes wrong, hence it is valid in the case of the covering. But the beam is for public use and they will rely one another to notice if anything goes wrong so that none of them will notice it. The Talmud adds ‘As people say: “A dish in charge of two cooks is neither hot nor cold”’ i.e. since each relies on the other the dish does not get properly cooked. Ravina replies that the greater leniency in the case of the covering is that since the law of sukkah is Biblical people will take care to observe it properly without any precautionary measures being required. Hence the covering is valid. But in the case of the beam Rabbah is strict since the whole law is Rabbinic and hence liable to abuse unless it is treated severely.
The Talmud now asks: What is the final decision with regard to these two cases i.e. since we have now had two opinions, according to one of which the beam is valid and the covering invalid and according to the other the beam invalid and the covering valid. Rabbah b. R. Ulla said that indeed both are invalid. But Rava said in both cases it is valid since when the Mishnah speaks of twenty cubits it does not mean that the bar or the covering must not be above twenty cubits but that the space within must not be more than twenty cubits. Hence even if the beam or the covering is considered to be above the twenty cubits it is still valid if the space beneath is less than twenty cubits.
R. Pappa said to Rava that a proof for the correctness of this view can be gathered from a Baraita, in which it is stated that the beam must not be placed higher than twenty cubits which was the height of the entrance to the Hekhal, the Temple Hall. Now with regard to the Hekhal it was the space beneath that was twenty cubits and since the Baraita uses the entrance of the Hekhal as its measurement this demonstrates that the beam must not be higher than twenty cubits above the space beneath it i.e. and if it is placed within this space it is valid even if part of it is above the twenty cubits from the ground. Although the Baraita speaks of the beam presumably the same would be true of the covering.
R. Shimi bar Ashi raised an objection to R. Pappa from another Baraita which states that the beam must be placed beneath the space of twenty cubits. This seems to show that the beam itself must be under twenty cubits. To this the reply is given: Read: ‘Above the twenty cubits’. But how can you say that, the Talmud objects, since it says explicitly ‘beneath’? To this the reply is given that the reference of ‘beneath’ is to a different matter. The rule is that both the beam and the covering must not be higher than twenty cubits and not lower than ten handbreadths. When the Baraita speaks of ‘beneath’ it is to state that just as the higher altitude refers to the space within so, too, the lower altitude i.e. that the beam must clear the ten handbreadths.
The symmetrical nature of the arrangement becomes perfectly clear. The two versions—the first and that of R. Adda—and the discussions around them are perfectly balanced. In the first version it is the covering that is invalid and the beam that is valid. In the version of R Adda b. Mattenah this is reversed. But in each version the arguments are basically the same or rather the same approached from two different angles. After having established that there is no reason to make any distinction between the beam and the covering the two opinions are quoted whether this means that both are invalid or both valid. There follows R. Pappa’s proof that both are valid and then R. Shimi’s objection and the reply. In other words, the whole of the material has been reworked by the final editors in a dramatic way so that each stage in the argument comes in at just the right time.
 On contrivance in the Babylonian Talmud see my: Studies in Talmudic Logic and Methodology. London, 1961, pp. 53ff.
 This not stated explicitly but is implied in the whole passage since there is no objection to having further beams upon the original valid beam even if these extend to above twenty cubits.
 The word used here is kalush, past participle of the root kalash, ‘to weaken’. Obviously the meaning is that by a legal fiction the part above twenty cubits is treated as if it were no longer there.
 It is highly speculative but is it just possible that R. Addah b. Mattenah (in some text Mattena, with an alef) means: R. Adda who taught it differently; see Kossovsky’s Otzar ha-Shemot under this name for further example of him giving different versions or teaching differently. This requires further investigation as does the whole question of symmetrical arrangement in the Bavli.