There are opinions in the Rishonim that it is permitted or even a mitzva to fast on Rosh Hashana. After learning the following gemara [Rosh Hashana 18b-19a], those opinions will be under threat of extinction.
ומשיבים: הכא במאי עסקינן, בזמן שבית המקדש קיים [ואז נשמרו כל הימים המנויים במגילת תענית. ואף הוסיפו מפעם לפעם ימי זכרון נוספים. ומה שאמרנו שבטלה — זה לאחר החורבן].
[ומקשים: אם היה זה בזמן שבית המקדש היה קיים] ותיפוק ליה [ויצא לו דין זה שהוא יום שמחה מטעם אחר כי] דהוה ליה [הרי הוא] יום שנהרג בו גדליה בן אחיקם, [והרי אמרנו שבזמן בית המקדש עשו את ימי הצום לימי שמחה!] אמר רב: לא נצרכה [תקנה זו של שמחה בשלישי בתשרי] אלא לאסור את יום שלפניו. [כי ימי השמחה הקבועים לחגים במגילת תענית לא רק הם עצמם אסורים בתענית אלא גם היום שלפניהם ושלאחריהם, ודין זה לא היה קיים קודם, גם כאשר בטל צום גדליה.]
Rav Aḥa bar Huna raised an objection: It is stated in Megillat Ta’anit: On the third of Tishrei the ordinance requiring the mention of God’s name in legal documents was abolished, and on that day fasting is forbidden. For the kingdom of Greece had issued a decree against the Jews forbidding them to mention the name of Heaven on their lips. When the Hasmonean kingdom became strong and defeated the Greeks, they instituted that people should mention the name of Heaven even in their legal documents. And therefore they would write: In year such and such of Yoḥanan the High Priest of the God Most High.
And when the Sages heard about this they said: Tomorrow this one, the borrower, will repay his debt, the lender will no longer need to save the loan document, the document will be cast on a dunghill, and the name of Heaven written there will come to disgrace. And so they annulled the ordinance to mention God’s name in documents, and they made that day into a Festival. And if it enters your mind to say that Megillat Ta’anit has been nullified, can you say that the first prohibitions against fasting they annulled, and then later ones were added?
The Gemara answers: With what are we dealing here? This is referring to a time when the Temple was standing and all the days listed in Megillat Ta’anit were in force. From time to time new days of commemoration were added. When the amora’im stated that Megillat Ta’anit was nullified they were referring to the time after the destruction of the Temple.
The Gemara raises a difficulty: But if this was at the time that the Temple was standing, derive the prohibition against fasting on the third of Tishrei from the fact that it is the day that Gedaliah, son of Ahikam, was killed. During the time of the Temple the biblical fast days were celebrated as days of joy.
Rav said: It was only necessary to include the third of Tishrei in Megillat Ta’anit in order to prohibit fasting on the preceding day as well. Fasting was forbidden not only on the actual days listed in Megillat Ta’anit, but also on the preceding day and the following day.
The Gemara raises another difficulty: With regard to the prohibition against fasting on the preceding day, the second of Tishrei, also derive it because it is the day after the New Moon, and fasting is forbidden not only on festive days, but also on the preceding day and the following day. The Gemara rejects this argument: The New Moon is by Torah law, and festive days that are by Torah law do not require reinforcement. Therefore no decree was ever enacted prohibiting fasting on the days before and after.
Asked the Shaagas Aryeh [101] - If it is correct that one may fast on Rosh Hashana, or that it is even a mitzva to fast on Rosh Hashana, then how can the Gemara ask that we should derive the prohibition against fasting on the second of Tishrei from the fact that it is the day after Rosh Chodesh?? This Rosh Chodesh is DIFFERENT from all of Roshei Chodesh insofar [three words for the price of ONE!!:-)] as that it is permitted to fast. So how can the day following Rosh Chodesh be forbidden to fast when Rosh Chodesh itself is permitted??!!!
The only way the Gemara's question makes sense is if we say that it is forbidden to fast on the first day of Rosh Hashana and thus the second day will also be forbidden?!
