Although a lively and thought-provoking debate is clearly underway, it's hard to see how, with so many differing opinions and personalities, this group will actually get anywhere in its attempt to understand the meaning of justice.
Finally, Socrates has the inspired idea of inventing an imaginary city as a way to organize and focus their abstract and confusing debate. And, success: their production of an imaginary city proves to be both clearer and more thought provoking than what they were up to before. Details and topics related to the city keep them occupied for the majority of the conversation.
They've imagined a city, unpacked incredibly complicated concepts, overturned their most cherished ideals, and now they finally find some peace. Maybe even more amazingly, they seem to have found some answers. Can you imagine how satisfied you'd feel knowing you'd understood the very concept of justice and goodness? Not a bad way to end a book.