Quoting%20commentary for Eruvin 3:7

רַבִּי יְהוּדָה אוֹמֵר, רֹאשׁ הַשָּׁנָה, שֶׁהָיָה יָרֵא שֶׁמָּא תִּתְעַבֵּר, מְעָרֵב אָדָם שְׁנֵי עֵרוּבִין וְאוֹמֵר, עֵרוּבִי בָרִאשׁוֹן לַמִּזְרָח וּבַשֵּׁנִי לַמַּעֲרָב, בָּרִאשׁוֹן לַמַּעֲרָב וּבַשֵּׁנִי לַמִּזְרָח. עֵרוּבִי בָּרִאשׁוֹן, וּבַשֵּׁנִי כִּבְנֵי עִירִי. עֵרוּבִי בַּשֵּׁנִי, וּבָרִאשׁוֹן כִּבְנֵי עִירִי. וְלֹא הוֹדוּ לוֹ חֲכָמִים:

R. Yehudah says: If one apprehended that beth-din might intercalate Rosh Hashanah, he puts down two eruvin and says: "My eruv for the first day is to the east, and for the second day to the west" (or) "for the first day to the west, and for the second day to the east." "My eruv is for the first day, and on the second day, as the people of my city" (or) "My eruv is for the second day, and on the first day, as the people of my city." [If he were afraid that the great beth-din might intercalate Elul, so that there would be two holy days (the thirtieth and the thirty-first of Elul), and he had to go in one direction on the first day and in another direction on the second, he puts down two eruvin on the eve of yom tov, one in either direction, and says, etc.] And the sages did not concur with him. [For they hold that they are one sanctity. And the halachah is in accordance with the sages vis-à-vis the two days of Rosh Hashanah. For it is not because of doubt alone that two days were instituted, (doubt as to) whether beth-din had sanctified the thirtieth day or the thirty-first day and one of them is chol (i.e., not yom tov), but also because of the possibility that witnesses (had come) from minchah on, in which instance that day is observed as holy, and the next day as holy, both (together) being reckoned as one sanctity. But with the other festivals of the exile, where they instituted two days only because of doubt, our not knowing when the great beth-din had sanctified the new moon, the sages concur with R. Yehudah that they are two distinct sanctities. (The "sages" here are R. Yossi.)]

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