Aside from the issue of eiruvin, the establishment of two days of Rosh HaShana due to the uncertainty of whether witnesses will arrive who will testify about the new moon also created problems with the prayers. Rabbi Dosa ben Harekinas was concerned about saying a prayer that referred to a day as Rosh HaShana, when perhaps Rosh HaShana was truly on the next day or the previous day. Because of these concerns, he rules (Mishna 39a) that the prayer on the first day of Rosh HaShana should clearly state that it is “today or tomorrow” and on the second day “today or yesterday”. The hakhamim, who believe that the two days have kedusha ahat – “one holiness,” rule that it is unnecessary (and improper) to add those clauses.
This discussion leads the Gemara to a broad discussion about the prayers on Rosh HaShana and Yom Kippur, days that are unique on the Jewish calendar, but are not one of the Shalosh Regalim – the three pilgrimage festivals of Pesach, Shavuot and Sukkot. For example, on the Shalosh Regalim the sheheheyanu blessing (referred to by the Gemara as Zman, or time) is recited. Should it be recited on Rosh HaShana and Yom Kippur – which are one-time-a-year events as well? Or, perhaps, that blessing is restricted to the Shalosh Regalim?
One of the concerns of the Gemara is that this blessing is, ordinarily, said with a cup of wine, which cannot be done on Yom Kippur. The Gemara rejects the possibility that the blessing can be said together with a cup of wine (that would also receive a beraha of its own), which would then be given to a child, because the child may learn that he is allowed to eat and drink on Yom Kippur. This concern stems from the fact that the child under consideration must be old enough to understand what is going on, otherwise making a blessing on his behalf would be without purpose and having him drink the wine would not solve the problem of making sure that the blessing was said purposefully.
The obvious problem with this line of reasoning is that if we are concerned that a child will learn to eat and drink on Yom Kippur because he is given Kiddush wine, shouldn’t we forbid him to eat anything, since perhaps he will learn that he does not need to fast? The answer given by the Rashba and the Meiri is that we are not concerned with normal meals, as the child will understand that as an adult he will have to conform to the restrictions of the day like all other adults. The only concern is that Kiddush wine drunk on behalf of others may be perceived by the child as something special that he can continue doing as an adult.
The Gemara concludes: The halakha is that one recites the blessing for time on Rosh HaShana and on Yom Kippur, and the halakha is that one may recite the blessing for time even in the market, as it does not require a cup of wine.