The closing passages of the myth tell first of the four great rivers of the underworld, and of their courses; after which Socrates returns to the judgement of souls. According to the merit or demerit of a man's earthly life the souls fall into one or other of five classes: the worst are incurable sinners, and suffer eternal punishment in Tartarus; the best are of course those purified by philosophy, who live for evermore wholly discarnate, in glorious habitations. Those belonging to the three intermediate classes are assigned to their several dwelling-places, where they abide until the time comes for them to re-enter human or animal bodies.

'Now in truth many are these rivers and great, and of divers natures; but four there are amongst their number of especial note; and the greatest of these, whose course is circular and outermost, is that named Oceanus. Opposite it, flowing in the contrary direction, is Acheron, whose course is through many a waste place beneath the earth, until at last it reaches the Acherusian Lake; thither come the souls of most of the dead, and after abiding there for their fated span, be it longer or shorter, they are sent forth to be born again as living creatures.

'The third river issues midway between these two, and soon falls into a vast region of blazing fire, so as to form a lake larger than our sea, seething with water and mud.