The Mishna (2a) discussed whether an egg that is laid on Yom Tov can be used on that day, taking for granted that it can certainly be used once the holiday has ended. How about the situation, common in the Diaspora, where we celebrate two days of Yom Tov, one after another? Can an egg laid on the first day of Yom Tov be used on the second day?
The Gemara teaches that this is the subject of a disagreement between Rav, who permits its use on the second day, and Rav Asi, who forbids it.
Given the reality that, today, we operate with a set calendar, the basis for the continued tradition of keeping two days of Yom Tov in the Diaspora demands explanation. While Rav Saadia Ga’on writes that keeping a second day of Yom Tov in the Diaspora is based on biblical law, Rav Hai Ga’on argues that he only said that as a response to heretics, but it should not be accepted as a true halakhic statement. His explanation is that although the second day was established for reasons of doubt (i.e. Diaspora communities oftentimes did not receive the information about the establishment of the new month until after the Yom Tov began), it was a rule already established by the prophets, which carries with it significant halakhic weight. The prophets needed to establish the second day because of the distance of Jewish communities from Israel, where the Sanhedrin sat and established the months based on testimony from witnesses.
According to the Rambam in his Sefer Mitzvot, the calendar that we currently use is, itself, the establishment of the Sanhedrin, who, during the time of Hillel ha-Sheni, determined the beginning of every month. Indeed, the Ra’avan quotes the Sages of Magence as teaching that the two days of Yom Tov are not kept because of the question regarding the actual date of the holiday, but rather as a takkana – a Rabbinic ordinance that the holiness of the Yom Tov extends for an extra day. This helps us understand why Diaspora Jews continue to recite the blessings for the holiday even on the second day, which we ordinarily would not do if the mitzva were only being done mi-safek – for reasons of doubt.
The Hatam Sofer writes that when we recite the blessing asher kidshanu be-mitzvotav ve-tzivanu – that we are fulfilling a commandment with this activity – the reference is not to the activities of the second day, but rather to the concept of the holiday, which is what we are truly commanded.