Republic Book 4

With Book 4, Socrates finally returns to his main argument and uncovers a definition of justice that applies to both a city and, by analogy, to an individual.  Justice, in short, is everybody doing everything they are supposed to do and nothing that they are not supposed to do.  Each part performing only its own function, being only itself, produces a single harmonious whole.  Justice, however, is not the harmony created by the interaction of the parts.  That is moderation (431e7).  Justice is the distinction of the parts themselves, the purification of the metals that allows them to be combined into an alloyed whole.  So, basically, justice is precisely the division of labor with which Socrates began his thought experiment about founding a city.  To preserve this 'natural' division as a city grows into a confusing mixture, it must be purified into the caste system he ended up describing.  It's pretty obvious how this fits with the theory of Forms.  The Forms purify the mixtures we find in the world into elements that are only themselves, and not also, partly and in another respect, something else.  Plato's metaphysics perfectly reflect his political and moral beliefs.  They are all about re-establishing a pure aristocratic order by drawing new lines of descent that organize a tangled world.  This casts Socrates detour into a description of the 'luxurious' city in a new light.  Exactly like the myth of the metals indicated, the fundamental problem at stake is purifying a mixture.  Only after we've succeeded in finding the pure Forms can we worry about preserving them unalloyed.

In the first section of this chapter (up to 427d1), Socrates puts the finishing touches on his imaginary city.  Having gone into detail on the education of the guardians, he now pulls back to show us that there are few concrete rules that govern the city beyond those he has already discussed.  With the correct upbringing, the guardians will naturally preserve the most essential aspect of the city, its unity.  From the overarching principle that the city remain one, we can deduce most of its other aspects.  The happiness of any individual part, even of the guardians, is not as important as the happiness of the whole unit (421b3).  The city should be neither too rich nor too poor (422a1) nor should it grow so large that it develops factions (423b8).  And above all, the city should preserve the educational system that Socrates outlines (423e2).  In a sort of political dialectic, this indoctrination holds the city together while at the same time separating and purifying each of its parts.  

Once he's finally completed the description of the luxurious city that began on 372e2, Socrates returns to the original question and begins searching for the way justice arises in a city.  Though it's the climax of the argument so far, the results have been so telegraphed that it feels like a bit of a let down to discover how the city he's described is wise, courageous, moderate (sophrosune), and just.  Wisdom lies in the guardians being in charge, since they are the ones who know how to run the city.  Courage too, lies entirely with the guardian class, since they are also the ones who know "what is to be feared" (429b8), and because of their strict upbringing, are capable of preserving the ideals of the city, come what may.  Moderation, as we mentioned at the beginning, is the harmony created by each part of the whole playing its role (431e5), maintaining the relationship of ruler and ruled.  And Justice is the very distinction of parts, the creation of the classes that allow all the other virtues to get off the ground (433c4).  Socrates' final definition of Justice simplifies the four metals into three classes.

Then, that exchange and meddling is injustice. Or to put it the other way around: For the money-making, auxiliary, and guardian classes each to do its own work in the city, is the opposite. That's justice, isn't it, and makes the city just? (434c6)

Finding how Justice arose in a city was only a means to an end though; we were originally (368c) looking for the definition of a just individual.  Socrates shifted the question to the political sphere by suggesting we should look for large print versions of the letters we wished to learn.  In the end (as Abrams described) it doesn't matter how big or small the print is, or even what typeface we use, since a letter preserves its symbolic form despite all these transformations (435a5).  All we need to do, then, to uncover justice in an individual, is to find an analogy with the way a just city works.  So Socrates spends the rest of the chapter establishing that the individual soul is composed of three parts -- rational, spirited, and appetitive -- that interact just like the three classes -- guardian, auxiliary, and money-maker -- do in the just city.  Again, with all this setup, the conclusion is pretty anticlimactic.  Like the just city, the just individual keeps the three parts of his soul distinct yet complementary, separated apart yet gathered together.

One who is just does not allow any part of himself to do the work of another part or allow the various classes within him to meddle with each other. He regulates well what is really his own and rules himself. He puts himself in order, is his own friend, and harmonizes the three parts of himself like three limiting notes in a musical scale—high, low, and middle. He binds together those parts and any others there may be in between, and from having been many things he becomes entirely one, moderate and harmonious. Only then does he act. And when he does anything, whether acquiring wealth, taking care of his body, engaging in politics, or in private contracts—in all of these, he believes that the action is just and fine that preserves this inner harmony and helps achieve it, and calls it so, and regards as wisdom the knowledge that oversees such actions. And he believes that the action that destroys this harmony is unjust, and calls it so, and regards the belief that oversees it as ignorance. (443d1) 

Since the analogy with the city makes the conclusions of this section repetitious, the only thing really interesting here lies in the way that Socrates goes about establishing that the analogy holds.  It's not obvious that the individual soul should have three parts nor that they should be organized as ruler, helper, and ruled (436a6).  In order to establish the analogy, Socrates has to, in effect, purify the concept of the individual soul into these three forms.  He goes about this in an interesting way.  First, he gives us a general principle of purification that asserts:

It is obvious that the same thing will not be willing to do or undergo opposites in the same part of itself, in relation to the same thing, at the same time. So, if we ever find this happening in the soul, we'll know that we aren't dealing with one thing but many. (436b7)

Notice the repeated use of "same" here.  If we purify something to the point where it is 'the same as itself' in every respect, if we find the thing in-itself, then it will not be pulled in two directions at once.  Once purified, each thing is unitary, and has a single state at any given time.  After this purification of a thing in itself, context can be added back and new relations and changes can be considered that appear to make the thing swing between opposites.  Socrates introduces this abstract principle in order to assert that thirst, in itself, only desires drink, in itself.  This thesis is meant to contradict the idea that we don't thirst in the abstract, but we thirst for something particular, namely, whatever particular thing we feel like would be a tasty beverage.  All this is laid out in an interesting passage where Plato seems to explicitly acknowledge that he is contradicting the way he defined power as the power to do something good for oneself in Gorgias (438a7).  So it seems like Plato feels this is a vulnerable point in his argument.  If our appetites like thirst are for something concrete, if they don't exist in a vacuum based on a set of abstract needs but always already as part of some contextual assemblage, then we don't need to invoke a complicated multi-part theory of the soul to explain why we're thirsty, but not for that shit.  In which case the logic Socrates uses to prove that there is a rational part of the soul which governs a purely animalistic appetitive one would fall apart.

Therefore a particular sort of thirst is for a particular sort of drink. But thirst itself isn't for much or little, good or bad, or, in a word, for drink of a particular sort. Rather, thirst itself is in its nature only for drink itself.
Absolutely.
Hence the soul of the thirsty person, insofar as he's thirsty, doesn't wish anything else but to drink, and it wants this and is impelled towards it.
Clearly.
Therefore, if something draws it back when it is thirsting, wouldn't that be something different in it from whatever thirsts and drives it like a beast to drink? It can't be, we say, that the same thing, with the same part of itself, in relation to the same, at the same time, does opposite things. (439a2)

So again, the crucial idea is this principle of the separation, distinction, and purification of a confusing mixed-up world.