Masechet Sanhedrin opens by discussing the court system, and how different cases required specific courts that varied with the number of judges. One interesting case (1:2) is ibur ha'shanah; where the court determined whether a month must be added to the year. It is unique because, according to R' Shimon ben Gamliel, the case "starts with three [judges], is deliberated upon with five and concludes with seven." He adds that if they concluded with three judges then it is valid.
The Bartenura explains that three judges would sit to determine whether the year required an extra month. If two felt it was unnecessary, then they would stop. If two however thought it was required and one disagreed, then they would add another two judges. Once again, if a majority felt it was unnecessary, it would end the case. If three however felt it was necessary, the number of judges would be increased to seven. If a majority in the negative was enough to end the case, why does a positive majority require additional judges?
The Tosfot Yom Tov cites the Mefarsh (Kiddush HaChodesh 4:10) who explains that with the additional month, the year is being taken out of its normal cycle, which is like finding one guilty of a capital offence.1 That being the case, we require a majority of two judges when ruling "guilty". The Tosfot Yom Tov notes that this would mean that even once they have seven judges, a simple majority would be insufficient until there are five who maintain that an extra month is required. Based on the Tosfot Yom Tov's deduction, it would follow that the a point that there were five judges, if four maintained that the year needed an additional month, then the case could be concluded based on there being a majority of more than one.
The Tosfot Yom Tov however prefers to explain that the reason why a majority was insufficient, is because the Chachamim specifically instituted that the judgement should be executed in this three-five-seven pattern.
Before explaining the necessity of the pattern, this debate appears to be connected to another one. What would be the ruling if in the first instance all the three judges agreed that an additional month was required. The Yad Rama understands that no further judges are required – they have reached agreement. This appears to be consistent with the opinion of the Mefaresh that the reason why judges are added is because a simple majority was insufficient to conclude the case. The Ran (10b) however argues that even if all three agreed, additional judges would still be added. This appears to be consistent with the Tosfot Yom Tov who explains that the three-five-seven pattern was critical to ibur ha'shana. Why? One explanation in the Gemara for the pattern is that it matches the pattern of the words in birkat kohanim. How does this relate to ibur ha'shana?
The Yad Rama explains that with birkat kohanim, one beracha should be sufficed. Nonetheless, since Am Yisrael is dear to Hashem, birkat kohanim included three berachot. Consequently, we imitate Hashem and replicate that when fulfilling Hashem's will of performing ibur ha'shana and unnecessarily add additional judges in the same pattern.
The Tosfot Yom Tov explains that since part of the motivation of ibur ha'shana is that the spring, produce and gathering should be at the right time, we attempt to arouse the berachot contained in birkat kohanim.
Finally, the Ben Yohayda (second explanation) explains that there is a strong parallel between ibur ha'shana and birkat kohen. Chazal explain that the light of the shechina would preside on the hands of the kohanim when they recited birkat kohanim indicating that Hashem agreed to the berachot. He explains that the same thing would happen when the Beit Din decided to add an extra month. The light of the shechina would fill the Beit Midrash indicating the Hashem agreed with their decision. Both of these, human activities with a profound worldly impact that Hashem ultimately showed his agreement.
1 The Rashash explains that the Mefaresh's opinion appears to be motivated by the Rambam's opinion that for ibur ha'shana we open with the most junior judge, like in capital cases. He suggests that perhaps the reason is that the addition of an extra month can have implications for capital cases, as it would delay when a child would be defined as a bar or bat mitzvah (or nine or three for cases of arayot).
One might find this explanation difficult since by adding the additional month, if it affected a change in status, it would result in a leniency, acquitting the accused. Furthermore, it appears from the language of the mefarash that the ruling of changing the year from it natural course is itself tantamount to a conviction. צ"ע
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