Socrates claims he's answered the original challenge (to show why justice is worthwhile for its own sake) - and shown justice to be preferable under all imaginable conditions.
The rewards of justice in this life - and/or after it!
Socrates, despite banishing the poets, proceeds to tell a poetic myth, to suggest that the soul (or personality, see Part 5) is immortal, and is rewarded after death - as he claims is "proved" by the strange tale of Er. Er was a man who was thought to have died on the battlefield - but after his soul had been to the Underworld and seen the rewards and punishments dealt out to the good and the bad he was revived - and could tell the tale.
We aren't expected to believe this as history - it's rather Plato's attempt to persuade us by poetic means (!) to the truth which he's tried to prove by logical means in the rest of the book.
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The Warner Brothers film The Matrix (1999) is a modern reworking of Platos's Cave. Read the essay by John Partidge?
This ends our quick tour of the Republic. Return to the start?