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Today, the second day of Rosh chodesh, we leined the קרבנות of ר"ח for the second day in a row, and likewise prayed another תפילת מוסף, although in the בית המקדש only one מוסף was brought each month.

This must be rooted somehow in a ספיקא דיומא, but that's precisely where the confusion arises. In חו''ל this year פסח was observed on Tuesday and Wednesday, necessarily the result of a ספיקא דיומא whether ר"ח ניסן ought to be on Tuesday or Wednesday. However ר"ח ניסן was observed on Tuesday only...

So how is it that following almost every חסר month we are satisfied with one ר"ח and one מוסף, even though the ספיקא דיומא element is no less than any other month?

This is especially confusing now that we have a calendar. Surely either we now know everything, or we act as if we know nothing. Why do we keep alternating?

The mishnah in ערכין פרק ב' discusses the guidelines by which beis din would decide when to set Rosh Chodesh. The ספק element is for those at a distance who don't know what beis din decided. This doubt must have ended with the advent of the calendar. For some reason the חכמים saw it necessary to maintain that, and only every other month, despite there being no danger of coming to eat חמץ on pesach (תחילת גמ' ביצה).

To be clearer, I'm not asking why months are sometimes 29 or 30 days. I'm asking why it's necessary to call any day besides the 1st of the month, "Rosh Chodesh".

To be fair, the Rambam addresses this. He writes: ואם היה החודש שעבר מלא, יהיה יום שלושים ראש חודש, הואיל ומקצתו ראש חודש , ויהיה תשלום החודש המלא שעבר.

This is very challenging to understand. Whatever it means, and I don't pretend to know, it wasn't a reason to bring two קרבנות מוסף, yet it clearly is a reason to daven twice תפילת מוסף.

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