This article accompanies the fable
Borges is interested in the idea that transmigration was a respectable concept in ancient Greek thought and is still an under-appreciated thought in the West today. He cites Pythagoras who recognized the shield he fought with in the Trojan War. And then there was Plato:
"In the tenth book of Plato's Republic is the dream of Er, a soldier who watches the souls choose their fates before drinking in the river of Oblivion. Agamemnon chooses to be an eagle, Orpheus a swan, and Odysseus - who once called himself Nobody - chooses to be the most modest, the most unknown of men."
Anonymity is bliss...