Millennia ago, Jerusalem may have opened its doors to thousands of refugees from the north of the country. A new cache of First Temple bullae (sealings) discovered in an excavation at Jerusalem’s City of David shows a mixture of names from the Kingdom of Israel and Judah used on official bureaucratic correspondence dating from after the fall of Israel at the hands of the Assyrians in 720 BCE.The reasoning here more or less accurately reflects the IAA press release, which you can read here. But I do not find it compelling. They found several names that are found in the Bible only as names of northerners. But I don't think we know enough about the Israelite and Judean onomasticon (range of names) to rule out that southerners also bore them.
The dozens of clay imprints were used on letters and documents which were bound by string and sealed by wet clay pressed with the sender’s mark or name. The impressive trove was discovered at recent digs uncovering three Late Iron Age buildings frozen in time by the destruction caused by the 586 BCE Babylonian siege. The discovery was made by a team of Israel Antiquity Authority archaeologists led by co-directors Dr. Joe Uziel and Ortal Chalaf.
Among the dozens of bullae is a rare find of an intact sealing, bearing the name “Ahiav ben (son of) Menahem,” referring to two kings of Israel but found in the capital of the Kingdom of Judah, Jerusalem.
It seems likely enough that Judah accepted refugees from Israel after the fall of the Northern Kingdom. These bullae may reflect that, but I don't think we can be sure that they do.
The third paragraph could be phrased more clearly. Two kings of Israel did have these names, sort of, but the person named on the bullae was not one of these kings, or indeed any king.
Backgeound on the upcoming exhibition of these bullae is here.
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