I took an honors course on Ancient Philosophy last semester in which we spent almost the entire time discussing the Republic (and a little of Aristotle's Politics in the end). It was one of the best classes I've taken at UNC so far.

He believed that, by creating a city and finding justice in it, he was looking at an individual under a magnifying glass, since a city is just a bunch of individuals. Find justice in the perfect city and you'll find what justice is in the individual.

Therefore, according to Socrates' argument in the Republic justice is when the three parts of the soul (appetitive, spirited and reasoning) work together in harmony, each doing what it is supposed to be doing. The appetitive and the spirited parts, like the workers and the guardians in the Kallipolis, are under the rule of reason (the philosopher-kings). The just individual will be so because reason rules and appetites are kept in check.

It's important to remember that δικη was not "justice" for Plato in the same way we think of it today.

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DAVIDIVS DOCTVS VTRIVSQVE LINGVAE
Husband of Emilia
Member: First Reformed Presbyterian Church of Durham (RPCNA) - Durham, NC
Currently in the process of transferring membership to an as-yet-undecided church in Chapel Hill
Student: University of North Carolina at Chapel Hill, German Literature and Classics