How do we know that the Destruction of the Second Temple occurred on 9 Av?
** Here's what we know:**The Books of Jeremiah gives one date (10 Av) for the destruction of the First Temple, while the Book of Kings gives another. (7 Av)
Josephus, in his book, says that Second Temple was destroyed on 10 AV
The Mishna says both buildings were destroyed on 9 Av.
The Talmud (Tannit 29) reconciles the discrepancy between Jeremiah and Kings with and justifies the Mishna's date for the First destruction with a sevarah
The Talmud (Tannit 29) justifies the Mishna's date for the Second destruction with a second sevarah
**Observations**(1) We cant establish a historical fact via sevarah. A legal fiction, however can be established via severah.
(2) It seems rather unlikely that any of the Tannaim who were alive in 70 CE would have known exactly when the Second destruction occurred. Most Tannaim were already stationed in Yavna, and they got their news via messenger. It seems unlikely that establishing the precise date of the destruction would have been their first order of business once the messenger arrived.The precise position of the sun when the Temple was set on fire would likely not have mattered to them, and the messenger himself may not have known.
(3) Even before the destruction of the Second Temple, the ninth of Av was considered a "bad date" because simple math demonstrated that several biblical tragedies occurred on that date.
(4) After the destruction, the tragedy was commemorated and gradually, over time, the date for that commemoration settled on 9 Av.
**Tentative conclusions**(4) When the Mishna was written, no one really knew exactly when either Temple was destroyed. However, they knew 9 Av was a bad date and they knew people were commemorating the destruction on 9 av, so they codified it.
(5) The debate the Gemarah records provide the post-facto justification for the date the Mishna codified, which itself is based on the date of a pre-existing grass roots commemoration
I expect #2 to generate the most disagreement. You might find it hard to believe that knowing the exact date of the destruction would have been unimportant to the Rabbis of Yavnah. But I think they they were probably more worried about friends and relatives, property that was left behind and the Roman army's next move. The fact that the destruction was such a huge event is precisely why I am arguing that something unknowable and unverifiable like the date wouldn't have captured too much of their brain space. And even if they did care, it doesn't follow from this that they knew the correct date or that the later commemorations were based on their date.
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