Eruvin, Chapter 3, Mishnah 7. This mishnah discusses the status of the two days of Rosh Hashanah with respect to two eruvin. In the previous mishnah we dealt with a Yom Tov that falls next to Shabbos, and with the question of whether the two days are two distinct sanctities or a single sanctity - one day or two days. Here the same question is asked about the two days of Rosh Hashanah.
The View of Rabbi Yehudah:
Rabbi Yehudah says that on Rosh Hashanah, when a person is concerned that the month may be declared full and the festival will therefore extend over two days, he may set up two separate eruvin, one for each day. He may say as follows:
"Eruvi barishon lamizrach uvasheni lama'arav" - my eruv on the first day is to the east, and on the second day to the west.
"Barishon lama'arav uvasheni lamizrach" - and the reverse.
"Eruvi barishon, uvasheni kivnei iri" - the eruv takes effect on the first day only, and on the second day his status is like that of the rest of the townspeople, who have no eruv.
"Eruvi basheni, uvarishon kivnei iri" - the eruv takes effect on the second day only, and on the first day his status is like that of the rest of the townspeople, who have no eruv.
The basis of Rabbi Yehudah's position is that the two days of Rosh Hashanah stem from a doubt: either the first day is the true Rosh Hashanah, or the second day is. Consequently the two days are not a single sanctity, and there is nothing to prevent a person from making an eruv to the east for one day and to the west for the other.
The View of the Sages:
The Sages, however, did not agree with him. In their opinion, the reason for the two days of Rosh Hashanah is not doubt alone, but rather the possibility that the witnesses testifying about the new moon would arrive after the time of Minchah, and once an enactment was instituted that witnesses are not accepted after that time, it emerges that both days become Rosh Hashanah. Since this is a matter of an enactment and a decree, and not a matter of deciding between two doubtful days, it was established that both days together are a single sanctity and one day. Therefore it is impossible to make an eruv in two different directions; rather, one eruv is needed for the entire time.
Rosh Hashanah Compared with the Other Festivals:
This ruling applies to Rosh Hashanah alone. The two days of the other festivals are observed only because of a doubt as to which of the days is the true Yom Tov. True, nowadays we know the calculation of the months, but we conduct ourselves as though the doubt still stands. Therefore, regarding the other festivals even the Sages agree with Rabbi Yehudah that these are two separate sanctities, and one may set up two eruvin in two different directions.
In summary: Rabbi Yehudah and the Sages disagree about the two days of Rosh Hashanah. According to Rabbi Yehudah they stem from a doubt, and therefore one may set up two separate eruvin - in two directions, or an eruv for one day only while on the other day he is like the rest of his townspeople. According to the Sages, the two days stem from an enactment and a decree rather than from a doubt, and therefore they are a single sanctity and one day, and only one eruv may be made. But regarding the two days of the other festivals, which are rooted in doubt, the Sages agree that they are two sanctities and that one may set up two eruvin.