Republic Book 10

In a way, Book 10 is an odd addendum to the Republic.  The main problem of the dialog appears to have been thoroughly solved.  We know that justice (in a city or a soul) is each part doing only the thing that it is naturally suited to, with the rational part ruling and harmonizing all the others, as befits its essential nature.  And we know that the just man is happy, and the unjust man miserable simply because of the way they are constituted, irrespective of what their worldly reputations might be.  So why, for his finale, does Socrates return to the denunciation of "imitative" poetry that he already covered in Book 3?  And why does he follow this with a discussion of the logic of models and copies he touched on in Book 6?  Finally, what does all this have to do with the immortality of the soul, a topic which hasn't been discussed and seems irrelevant, and the elaborate metempsychosis of the myth of Er?  

I think the key question that holds the conclusion together is: what is justice good for?  How does it benefit us?  While it's tempting to say that Socrates has already answered this question -- it makes us happy -- this isn't how it was presented.  It's not happiness, but the Good, that is the ultimate criterion of judgement.  We weren't counseled to be just because it would make us happy.  That was merely a byproduct of a justice that was valued in itself, even if all its consequences were invisible (359e9).  We might also be tempted to say that Socrates has provided another answer to this question by constantly showing us how the unjust soul is at war against itself.  Only the just man quells the civil war within his own soul.  But this too is merely a consequence of justice, and anyhow begs the question of why peace is good.  So if the ultimate purpose of justice is not to provide peace and happiness, then what are we supposed to use it for?

We use justice to select.  The purpose of justice is to enable us to choose the Good.  If Beauty is first among Forms because it inspires an increasingly abstract love within us, Justice is like the last Form because it enables us to distinguish the essential natures of things.  In other words, by enabling us to know what each thing is naturally suited to and how things fit together, Justice gives us a vision of the realm of Forms.  Justice is knowledge of order.  It's the knowledge of what Forms structure reality, what abstract parts it breaks down into.  This knowledge is useful, practical, and directly moral, not merely theoretical.  The world is a confusing place, filled with a multicolored clamor.  If we are to choose a life that's good for us, we need justice to act as a guide that uncovers the true Forms that organize all the appearances of experience.  Starting in Book 2, the construction of the 'luxurious city' emphasized that experience comes to us as a mixture, and that Justice purifies this mixture by showing us what metals compose the alloy.  Once we know the components of any mixture, we can separate better mixtures from worse ones.  In short, Justice gives us the tools to make a practical moral choice about how to live better amidst the confusion of this world.

This is precisely the logic of a model and its degraded or mixed copies.  We can't select a better copy without knowing what the model looked like.  Justice, then, is the knowledge of models.  The benefit of knowing the models, the Forms, is that you can see what each copy or thing is composed of.  This statue is 98% pure gold, it just got a little scuffed up.  Knowing the compositions of things allows you to choose the best one.  My reading of this naturally owes a lot to Deleuze.  He pointed out that the seemingly central distinction between Form and thing, model and copy, in Plato is actually a secondary matter.  That metaphysical distinction is important only because it serves a moral purpose -- it enables us to distinguish the better and worse copies.  The core distinction between better and worse copies explains why the Republic concludes with the curious myth of Er.  The point of the myth is to show the true benefit of Justice.  It can't help you rest in the pure realm of Forms, but it can help you choose a new life for your next spin of the wheel.  

The first half of this chapter revisits the dispute between poets and philosophers we saw in Book 3 only as a way of again illustrating the distinction between the model versus the copy we first saw in Books 6 and 7.  Poets are condemned as mere imitators, mere producers of images.  Socrates illustrates this by hypothesizing the famous Form of a table (or bed) (506b).  He doesn't seriously believe that there is a Table; this is just a pedagogic device.  But, presuming there is a form of a table, then a particular real table will be an imitation of that form, and a painting of table will be an imitation of that imitation.  Poets and other artists then deal only with reflections of reality (596e), with images of images that come in third place relative to the 'things that are'.  

Why does Plato harp on poetry  though, as the representative of art?  I think he chooses poetry specifically because of the central role of Homer in Greek culture.  As we saw in our discussion of Meno, Plato is right on the cusp between an oral and a written society.  Most of the knowledge of an oral society is stored in the form of tales and stories that are told and retold, preserved but also modified by accretion.  So, fundamentally the question is whether we should look to philosopher's or poets, Homer or Plato as an authority.

Then, we must consider tragedy and its leader, Homer. The reason is this: We hear some people say that poets know all crafts, all human affairs concerned with virtue and vice, and all about the gods as well. They say e that if a good poet produces fine poetry, he must have knowledge of the things he writes about, or else he wouldn't be able to produce it at all. Hence, we have to look to see whether those who tell us this have encountered these imitators and have been so deceived by them that they don't realize that their works are at the third remove from that which is and are easily produced without knowledge of the truth (since they are only images, not things that are), or whether there is something in what these people say, and good poets really do have knowledge of the things most people think they write so well about. (598e)

This echoes the discussion in Ion about what a poet or a rhapsode really knows.  In the end, these artists just incite people with words, without any knowledge of what they're talking about at all.  They're just 'painting pictures', as it were, of different subjects.  And like someone painting a bed, they needn't concern themselves with how to actually build one.  

And in the same way, I suppose we'll say that a poetic imitator uses words and phrases to paint colored pictures of each of the crafts. He himself knows nothing about them, but he imitates them in such a way that others, as ignorant as he, who judge by words, will think he speaks extremely well about cobblery or generalship or anything else whatever (601a)

This observation is pretty obvious to the modern mind, but I suspect it was much less so when the idea of a book was just getting off the ground.

So poets are just imitators.  They are makers of images of real things, which are themselves just images of the Forms.  Their craft (or knack as Socrates puts it in Gorgias) has nothing to do with true knowledge, but merely with appearances and opinions about appearances (602a).  It's for this that they got kicked out of the Republic in the first place.  Instead of knowing about the Form of a bed, or at least having a right opinion about how to make a working copy of a bed, they just paint something which others think appears like a bed.  Makers of images of images are locked in a kind of hall of mirrors.  Like the contestants in Keynes beauty contest, they only have opinions about the opinions of others (602b).  

Socrates goes on to give several more reasons why the poets have to go, but in the end all these amount to the same complaint --  poets don't know, or even try to approach, the Forms of Courage, Temperance, etc ... which serve as models of behavior.  They therefore don't appeal to the rational and knowing part of the soul, but to the appetitive and emotional part (603).  What's worse, poetry doesn't even confine itself to producing images of good, moderate, rational lives, but actually delights in depicting all kinds of extreme and variable characters (604e).  In fact, this is exactly what gives poetry such dangerous influence over even the good and rational souls.  Since all souls have an appetitive part, the imagination makes anyone susceptible to empathizing with the images the poets depict.  As a result, after watching all this violence on TV, it's easy to lose sight of the philosophic life we know is good for us.  In short, the problem with people who make images is that they can mix together any stories they want to make compelling images of anything.  So if we're trying to train people to separate the good life from the bad, people who don't concern themselves with the true Forms at all will have to go.

Socrates knows this condemnation of poetry sounds harsh (607b), but then again, it's the health of our immortal soul that's at stake.  The next section of the chapter gives a brief (and pretty unconvincing) proof of the immortality of the soul along different lines than those we saw in Phaedo.  The basic argument is that things can only be destroyed by whatever 'natural evil' corresponds to their essence.  So if we find that the natural evil proper to the soul nevertheless does not destroy it, then we'll have to conclude that it is immortal and indestructible.  Injustice is the natural evil that undoes the harmony of the soul.  However, being unjust does not literally kill us.  Therefore, the soul is immortal.  QED.  I don't know who this is supposed to convince.  But it certainly reinforces the notion that the world is divided into certain forms, and that the key moral question is finding what is naturally healthy or unhealthy for that form. 

Anyhow, the discussion of the immortality of the soul is really just a prelude to the discussion of how the soul benefits from justice.  Throughout the dialog, Socrates has insisted on judging justice itself, even if its appearance were invisible (612b).  Now, however, having defended justice in itself, he wants us to see that in fact it has lots of benefits and rewards, both in this life and, since the soul is immortal, after we die (614).  The biggest of these benefits, what ultimately makes justice good for us, is the way it gives us the knowledge to choose a good life the next time we are reincarnated.  Justice is really a knowledge of types of lives, types of constitutions in their pure form, that is invaluable when it comes time to select a new life.  This is the punchline of the Myth of Er that concludes the dialog.  

The basic outline of Er's return from the land of the dead is the same as the other myths of metempsychosis we've seen in Phaedo, Gorgias, and Phaedrus.  They all have some element of moral judgement that describes punishment for bad people and rewards for good people (615b).  But these aren't Christian myths and I don't think this eschatalogical aspect is the most important part.  Indeed, the notion of a 'final judgement day' is foreign to Plato since he doesn't conceive of any of these judgements as final.  The point of the myths seem to be that the endless turning of the universe prevents any judgement from being final.  Plato's idea of time seems to be entirely cyclical.  All the imagery is of elaborate circles within circles that produce a constant motion that never goes anywhere at all, much less to the final judgement at the end of time.  So while Er speaks of heaven and earth and even a sort of hell made especially for tyrants, mostly souls just seem to rotate through the apparatus, doing time on earth, then a stint in heaven, and perhaps landing in Tartarus (permanently?) if they're particularly nasty.  There's no real principle of ascension to the mechanism.  There's no final goal, no permanent resting place.  The wheel of samsara just keeps turning indefinitely, and there's no way off the merry-go-round, regardless of how much karma you build up.

But then, what is Plato's moral point with this myth?  Unlike the other versions, the myth of Er explicitly adds an element of chance and choice to the metempsychosis.  The souls waiting to be reborn draw lots in a lottery that determines the order in which they choose their next life from the set of all possible lives.  Yet chance never makes the final determination, as even the last to choose can select a satisfactory new soul -- if, that is, they are capable of recognizing a good life when they see it (619b).  If we know the Form of Justice, we can recognize which sorts of lives correspond to which sorts of constitutions.  Then we can avoid choosing the life of a tyrant or some other soul that will fare miserably on earth.  So, actually, our problem in the lottery of the afterlife is not so different than our problem here on earth.  All the various lives are mixed up in front of us.  We want to try and select a good life, and the first step in this selection is knowing how different types of souls will fare.  Justice knows what properly belongs to each soul, which makes it a perfect tool for this selection.  The elaborate circular mechanism of the afterlife seems to do nothing more than stir the pot, mixing all the lives and Forms together.  As always, our moral imperative is to purify our thinking so that we can make a choice between the various imperfect, mixed, options in front of us.  Perhaps in this sense we might read Plato as a sort of existentialist -- Forms are a hypothesis, while the need to make a choice is apodictic, a certainty beyond hypothesis.  More plausibly, the certainty in Plato is simply the existence of the Good, the commonsensical idea that there is a true good and a bad beyond the confused opinions of men.  That at least, seems to me to be the conclusion of the Republic, even if Parmenides perhaps undermines it.

Republic Book 9

But what about the tyrant, you ask?  Book 9 cleans up the last piece of the structure set up in Book 8 and discusses the constitution of the tyrannical man, the unjust man who stands opposite the philosopher king.  You probably won't be surprised to learn that the tyrannical man, and especially an actual tyrant, is a walking civil war.  His soul is torn apart by an addiction to all his various appetites.  These enslave him, and in this sense the tyrannical man and even an actual tyrant are nothing but victims and slaves.  This answers the other part of the question that the dialog began with.  Just as the most just man was the happiest, the most unjust man is also the most miserable.  No matter how much honor, money, or freedom he may appear to possess, his greatest tyranny is over his own soul.  

The most interesting aspect of this chapter is the way that Plato attempts to judge the tyrant immanently, that is, only on the basis of what it feels like to be tyrannical (577a).  It's important to emphasize this lest we slide into interpreting Plato through a christian lens.  No doubt, there are many points of overlap, but Plato has no notion of sin and judgement before God.  So when he tells us that the tyrant's waking life is like a nightmare (576b) and that he is completely possessed by the anarchic desires most of us only experience in dreams (574e), this isn't to suggest that the tyrant has sinned or that his desires are even fundamentally different from a just man's.  The problem with the tyrant is instead that his inner constitution lacks any ruler beyond the momentary gratification of pleasure and avoidance of pain.  Tyranny, ultimately, is just an internal anarchy.  The tyrant merely bounces between his various unsatisfiable lusts and his fear that others will prevent him from gratifying them.  Plato sees this disorganized state, constantly at war with itself and everyone else, as inherently miserable, regardless of what outcome it produces in the world.  In fact, the more real world power and wealth the tyrant amasses, the greater his greed and paranoia grow, so that the worst thing that can happen to the tyrannical soul is that it successfully becomes a true political tyrant (576c)!   This immanent form of judgement doesn't require any agreement about what specific actions are right and wrong, moral and immoral.  It only requires Plato's assumption that an ordered harmony feels better than discord.  

Socrates isn't content to leave the judgement there though, and instead tries to insert two more immanent proofs that: 

... the best, the most just, and the most happy is the most kingly, who rules like a king over himself, and that the worst, the most unjust, and the most wretched is the most tyrannical, who most tyrannizes himself and the city he rules (580c)

Unfortunately, each of these introduces another assumption that the modern eye recognizes as an injection of transcendent value.  

First, he contends that the philosopher is the only one that experiences the unique pleasure that corresponds to each part of the tripartite soul (581e).  Those ruled by their appetitive part (eg. a money-maker) never know the pleasures of honor or philosophy.  Likewise, those ruled by their spirited part (eg. honor-lovers) don't admit the value of money and reject philosophy as "smoke and nonsense".  The philosopher, while he values the pleasure of learning above all, nevertheless admits that money and honor are both necessary and can also be pleasures.  Naturally, each type of soul thinks that the particular pleasure that corresponds to itself is the most valuable.  But only the philosopher has experienced all three pleasures, which puts him in the best position to judge between them.  This would have been a relatively convincing stopping point in the argument.  But Socrates, perhaps under pressure from his own contention that experience alone can never by the basis of philosophy, mars the immanent criterion by introducing the idea that judgement must also involve reason and argument (582a).  Of course, these belong solely to the philosopher, and constitute a special kind of experience we call knowledge.  So the argument which at first appeared an immanent comparison of actual experience ends up invoking a transcendent experience, and we conclude that:

A person with knowledge at least speaks with authority when he praises his own life. (583a)

Second, Socrates tries to convince his companions that only a philosopher knows the true definition of pleasure.  Sure, every type of soul thinks that its particular pleasure is the most delicious.  But much of what the appetitive or spirited souls take to be pleasure is simply the absence of pain (584c).  Which is to say that most people operate with a relative hedonic scale.  Pleasure, for these souls, is just the temporary satiation of some painful urge, like hunger or thirst.  By contrast, the philosopher operates with an absolute hedonic scale, and knows that true pleasure, a pleasure which never wears off, lies in being filled with knowledge (585c).  Again, this argument is meant to present an immanent criteria of happiness as more, and more lasting, pleasure.   But we can all see that Socrates has smuggled in the transcendence of knowledge and truth, as well as the transcendent supremacy of being over becoming, the permanent over the evanescent.  

In the final analysis, I don't think there is one particular value that's transcendent in Plato.  Justice, harmony, unity, truth, knowledge, pleasure, the fine -- these are really all synonyms who point to the underlying unity of analogy that constitutes the form of the Good.  In a sense, the Good is nothing but the ever-extending analogy that lets us see one good quality after another.  This is perhaps why the Good is so difficult to explain.  An analogy has no true root.  There's not one thing which is the "most analogous" among analogs.  All we can do is construct pairwise correspondences.  And yet, when we have amassed enough of these, we feel we've isolated some abstract central term which is the essence of the analogy, just like we feel we have extracted the number 5 from many analogous collections of fingers and toes.   The Good has the same type or level of reality as a number.  At its best, a calculus of the Good would found a science of quantitative comparison of ways of living.  That's the only way we can calculate how much better and happier the just man is than the tyrant: 3^2^3 times.

Then, turning it the other way around, if someone wants to say how far a king's pleasure is from a tyrant's, he'll find, if he completes the calculation, that a king lives seven hundred and twenty-nine times more pleasantly than a tyrant and that a tyrant is the same number of times more wretched. (587e)

Republic Book 8

Book 8 returns us to the main argument of the Republic as it stood at the end of Book 4.  To recap: after a prelude where he problematizes some common definitions of justice, Socrates companions insist that he come up with one of his one.  To do this, he suggests imagining a just city.  Once we understand justice in a city, we can characterize justice in an individual by analogy.  At first, Socrates describes a truly just city as a small simple place where everyone makes a spartan living doing the one thing they are best suited for.   It appears to be a sort of anarcho-capitalist paradise where some invisible hand makes a ruling class unnecessary.  The description, however, is a bit too theoretical for Socrates' companions, and they insist he describe justice in a more realistic, more luxurious, city.  It's at this point that he launches into his description of the different classes that would compose this larger city, and begins to describe the education and upbringing of a guardian class.  The role of the guardians is to organize and purify the different classes needed to run a complex city so that it most closely approximates the theoretical city he described earlier, where everyone does exactly and only what their nature suits them to.  The whole description climaxes in the myth of the metals towards the end of Book 3.   This same definition of justice serves by analogy for the individual, whose soul has the same three part class structure -- appetitive craftsman, spirited warrior, and rational guardian.  So by the end of Book 4, Socrates has completely answered the original question of the dialog: "what is justice?"

Then, isn't to produce justice to establish the parts of the soul in a natural relation of control, one by another, while to produce injustice is to establish a relation of ruling and being ruled contrary to nature? (444d)

After that he proposes to go and and classify the main forms of injustice into 4 categories that will correspond to 4 increasingly unjust city constitutions.  Book 8 returns to this point and describes the 4 types of constitution (and corresponding types of individuals) he had in mind -- timocray, oligarchy, democracy, and tyranny.

Since it was actually the most interesting part, let's pause for a moment to remember how we got onto the tangent in Books 5, 6, and 7, the one which culminated in the cave allegory in Book 7.  At the beginning of Book 5 Socrates companions insist that he explain a remark he made in passing while he was describing the type of life the guardians lead.  He claimed the ruling guardians would share all possessions in common, including wives and children.  This was obviously pretty surprising and scandalous, and Socrates has to go back and defend the fact that there even are female guardians in the city, as well as these shocking communal relations.  As a result, it becomes clear just how far his just city is from the current one, and how different its practices are from common moral opinion.  This brings up the question of how in practice we would ever build such a city.  Midway through Book 5, Socrates drops his final shocking conclusion; to actually create a just city, we have to put the philosophers in charge.  Books 6 and 7 then get into why philosophers are so important to the city, why they are so often misunderstood or corrupted, and how they can be trained to be the best citizen rulers -- the most just individuals in a just city.  Overall, we might characterize these books as answering the question: "who is a philosopher?"  Basically, it's someone who crawls out of the cave to see the light of the sun Good, but goes back to help his troglodytic mates.

With Book 8 we return to what we would these days call political philosophy.  Of course, since Socrates sees a strict analogy between the constitution of a city and that of an individual, he probably wouldn't characterize it quite that way.  Indeed, his assumption of a connection between the political and the moral turns out to be even a little stronger than the word analogy may suggest.  Not only are there 5 types of soul to correspond to the 5 types of constitution, but cities will tend to take on a political  constitution that matches souls of the majority of their rulers, and of course the soul of the rulers will be influenced by the constitution of the city they grew up in (544d).  As a result, he organizes his examination of the constitutions as the story of a fall from the most perfect aristocratic one he described before -- the just city and the philosopher king.  At each step of decay, Socrates describes an internal civil war within the polis as well as within the corresponding soul. This civil war corrupts the higher constitution and gives rise to the next in line.  So the chapter is broken into 4 sections that each have the same structure.  First, Socrates explains how each lesser political constitution emerges from its better -- timocracy from aristocracy, oligarchy from timocracy, democracy from oligarchy, and tyranny from democracy.  Then he describes the character of the resulting constitution and the matching individual soul.  Finally he observes what effect the new political constitution will have on the upbringing of the offspring of the old rulers, creating within each soul a corrosive civil war that reproduces on the individual moral level the same mechanism of decay he described at the political level.  

Socrates' final 3 transitions in this series straightforwardly and insightfully describe both the political and psychological changes that can happen in a city/soul.  But the first transition -- from the perfect aristocratic constitution with its class hierarchy based strictly on 'virtue' to the timocratic constitution defined by its love of victory and honor -- poses a special problem.  If the philosopher kings' paradise is really so perfectly harmonious and virtuous, why isn't it also perfectly stable?  So Socrates is forced to come up with a pretty weird numerological explanation of why even a philosopher king can sometimes misculated the correct population distribution and accidentally create some intermixing of the metals (546).  His explanation of the birth and education of the timocratic soul is equally odd -- basically, it's all mom's fault (549d).   Aside from the peculiarity of the transition though, his description of the timocratic constitution is carefully aimed.  He's describing Sparta.  The timocratic constitution is obsessed with honor and victory in battle as a stand in for the true virtue which defined the aristocratic.  The result is an overly spirited, less rational polis and person.

The degeneration progresses when love of honor starts to be replaced by the love of wealth that defines an oligarchy.  At this point the caste hierarchy of the true Republic becomes the economic class hierarchy we are all too familiar with.  And this division of society is mirrored in the unbalanced olgarchic soul who establishes a love of money as its reigning appetite to enslave its spirited and rational parts (553d).  Oligarchy introduces another element that seems a bit random here but which Socrates will make use of later; drones are formerly wealthy individuals whose dissolute ways have landed them in the poor house (552c).  These come in two classes, 'stingless' and with a string, beggars and thieves.  

The trail of tears continues when oligarchy's inherent class division reaches a tipping point and the poor revolt to create a democracy.  Socrates even proposes a plausible description of the exact moment at which this occurs.  If fat, luxury loving merchants are forced to fight a war side by side with lean, fit farmers and blacksmiths, the latter aren't going to remain impressed with the value of rich men (556d).  ¡Que viva la revolución, carajo!   After the revolution, the new democratic constitution makes everyone free and equal, and no longer prises money or honor as the means of selecting the ruler.  Indeed, for Socrates, the real problem with democracy is that it doesn't do any selecting at all (561c).  The ideas of freedom and equality simply level everything off, the variety they inspire mix everything up and prevent the city from organizing itself on any basis beyond this content-less love of freedom.  Say what you want about the tenets of timocracy or oligarchy, they may substitute some inferior value for the Good, but at least it's an ethos.  In Socrates' eyes, selecting freedom is really a non-selection.  It's what happens when an oligarch's thrifty son comes across one of those drones, who turn him on to every imaginable pleasure his father prohibited him (559e).  The Good here is reduced to mere immediate gratification.  

Eventually, this love of freedom for its own sake, a freedom from everything but to nothing (563e), sets up the downfall of democracy and the birth of tyranny.  The drones turn out to be central to Socrates' account of the final step of political degeneration, and their two types are revealed to be basically politicians and their sycophants.  

You asked what was the disease that developed in oligarchy and also in democracy, enslaving it.
That's true.
And what I had in mind as an answer was that class of idle and extravagant men, whose bravest members are leaders and the more cowardly ones followers. We compared them to stinged and stingless drones, respectively. (564b)

...

In an oligarchy it is fierce because it's disdained, but since it is prevented from having a share in ruling, it doesn't get any exercise and doesn't become vigorous. In a democracy, however, with a few exceptions, this class is the dominant one. Its fiercest members do all the talking and acting, while the rest settle near the speaker's platform and buzz and refuse to tolerate the opposition of another speaker, so that, under a democratic constitution, with the few exceptions I referred to before, this class manages everything. (565e)

The democratic city contains three classes of folks -- the drones, the rich, and what we would call the middle class craftsmen.  The drones seize power in a democracy by exploiting the class tension that defined oligarchy.  They go after the remaining rich and fool the middle class into believing it benefits them.  Of course, in the end, most of the honey from this redistribution ends up enriching the drones (565b).  Seems that tyranny began with exactly this triumph of corrupt populism even 2,500 years ago.  Once the drone class eats the last of the rich they choose a champion and set him up as a tyrant.  And the tyrant finishes the process of political and moral degeneration.  Constantly paranoid of losing power, he constantly stirs up war (567b) and eliminates anyone of competence who might challenge him (567d).  In the end, he even turns on the middle class that fathered him, upending even the most basic rules of family order and enslaving the people who created him (569a).  Here ends the degeneration of organizing political principles -- from the Good, to honor, to wealth, to freedom, to slavery and the Bad.

Republic Book 7

This must be the climax; Book 7 is all about the cave allegory.  In fact though, the cave allegory is just a dramatic retelling of the division between the "conditions of the soul" that we saw in Book 6.  The shackled prisoners who can't turn their heads and who can therefore only see shadows on the cave wall are stuck in subsection 4: "imaging".  Those who can turn around and see the statues that cast these shadows as well as the visible light of the fire are in subsection 3: "belief".  Once a freed prisoner is forced out of the cave and into the bright light of day to discover real objects in the above ground world they move into subsection 2: "thought".  And when they are finally able to look at the One-Good of the sun itself, they reach the highest level of philosophy, subsection 1: "understanding".  The allegory just gives us a simple image for each level and makes explicit the idea that, relative to the intelligible, the visible world is underground. 

The rest of the chapter unpacks various aspects of the allegory.  For example, the fact that the philosopher must rise up from the darkness to the light, but then subsequently return to the cave to help the other prisoners, accounts for why he can seem so strange and useless to them.  

... the eyes may be confused in two ways and from two causes, namely, when they've come from the light into the darkness and when they've come from the darkness into the light. (518a) 

The round trip aspect of the allegory also explains why the philosopher king isn't much interested in ruling and does it only from a sense of duty (520e).  How are you going to keep them down on the farm once they've seen Karl Hungus? 

The allegory also implies that everyone has the innate capacity to see the light.  They simply need to be freed from their shackles.  So education isn't about giving people the capacity to see or think, nor is it about filling their heads with some specific knowledge. Instead, it's about changing our habits, about a practice that turns our whole body towards the light.

Education isn't what some people declare it to be, namely, putting knowledge into souls that lack it, like putting sight into blind eyes.
They do say that.
But our present discussion, on the other hand, shows that the power to learn is present in everyone's soul and that the instrument with which each learns is like an eye that cannot be turned around from darkness to light without turning the whole body.
...
Then education is the craft concerned with doing this very thing, this turning around, and with how the soul can most easily and effectively be made to do it. It isn't the craft of putting sight into the soul. Education takes for granted that sight is there but that it isn't turned the right way or looking where it ought to look, and it tries to redirect it appropriately. (518c) 

While Plato assumes that everyone will recognize the truth when they are able to see it, revealing this turns out to be a more complex process than simply telling them about it.  Learning, he seems to imply, has to actually create some sort of qualitative change in the soul.  It is not just the change from the absence to the presence of knowledge.  

This turns out to be an important consideration in the final phase of the philosopher's education he goes on to describe.  After the compulsory study of music and poetry and physical training he laid out in Book 3, comes the voluntary study of mathematics and ultimately dialectics.  These latter subjects must be studied out of a sense of curiosity and play (536e) and by means of problems (531c), and not simply because they contain some true and useful empirical facts (520b).  They are meant to cultivate a taste for learning and understanding, which, we'll recall, goes beyond thought and mental images.  They should, "draw one towards being" (523a).  

The way Socrates describes the goal of this final phase of the philosopher's education is interesting because it explicitly contrasts the model of education as recognition with one of education as puzzlement.  He claims that some experiences lead us towards understanding, whereas others do not.

I'll point out, then, if you can grasp it, that some sense perceptions don't summon the understanding to look into them, because the judgment of sense perception is itself adequate, while others encourage it in every way to look into them, because sense perception seems to produce no sound result.
You're obviously referring to things appearing in the distance and to trompe l'oeil paintings.
You're not quite getting my meaning.
Then what do you mean?
The ones that don't summon the understanding are all those that don't go off into opposite perceptions at the same time. But the ones that do go off in that way I call summoners—whenever sense perception doesn't declare one thing any more than its opposite, no matter whether the object striking the senses is near at hand or far away. (523b)

He goes on to give an example of both adequate and inadequate sense perception.  Recognizing that someone is holding up three fingers falls into the first category (523d) while perceiving the bigness/smallness, thickness/thinness, or hardness/softness of the same fingers falls into the latter category.  In these cases it isn't as if we're fooled into having an erroneous perception of something.  Instead, when we experience a relative quality, we become puzzled as to what we really mean by hard and soft, small and large.  How can something be hard (with respect to X) but simultaneously soft (with respect to Y)?  We don't know what perception to have at all.  When we don't simply recognize that something is what it is, we are forced to think about what it is.  We saw this same structure back in Book 5.  It was used as a way of justifying the idea that the Forms are the only true objects of knowledge because they are the only "things that are".  When we experience a beautiful thing, we also realize that it is actually ugly relative to some even more beautiful thing (479a).  That is to say that no thing is ever purely beautiful or purely ugly, but keeps flipping back and forth between these depending on how we look at it.  Only the Form of Beauty would always and only be beautiful.  While these impure mixtures, since they are between being and not-being, can only be objects of opinion and never knowledge, it turns out that they can be useful in spurring us towards knowledge.  Basically, they are puzzles or paradoxes that set up a problem.  And these problems "draw us towards being", towards the Forms, and especially towards the Good as first amongst Forms.  

At first it's not at all obvious how studying mathematics is going to involve us in situations with puzzling relative qualities.  But for Plato, we should puzzle over the very concept of number.

If the one is adequately seen itself by itself or is so perceived by any of the other senses, then, as we were saying in the case of fingers, it wouldn't draw the soul towards being. But if something opposite to it is always seen at the same time, so that nothing is apparently any more one than the opposite of one, then something would be needed to judge the matter. The soul would then be puzzled, would look for an answer, would stir up its understanding, and would ask what the one itself is. And so this would be among the subjects that lead the soul and turn it around towards the study of that which is. (524e)

Since we never have a direct sense experience of the concept one but only encounter it through the many ones we find in the world, it defines a paradoxical problem for us.  With it and all the other numbers, we have to somehow separate out or abstract the essence of the number from the counting of particular items set in front of us.  In other words, when we do mathematics we get at the number in itself, we purify it of its mixture with particular things.  Learning to purify a mixture like this trains us to see the Forms or find the golden guardians mixed in with the other metals.  So Socrates values math not really because of its truth, its certainty, or its rationality.  Remember, mathematical forms are still images of thought, not the objects of understanding itself. Math isn't valuable because of its conclusions, but because it teaches us how to take up a problem, to purify the world into intelligible essences.  So while he admits that arithmetic (525c) and geometry (527b) and astronomy (527e) may all be useful to the ruling philosopher king, the axiomatic truth and empirical success of these sciences is entirely beside the point.  In fact, he chides Glaucon for defending their study on that basis (527e).  An astronomy that merely correctly predicted the movements of the planets would be little more than the study of some elaborate toy mechanism designed by the gods (530a).  Since it is descriptive, it wouldn't ever explain to us why the various parts move as they do.  It wouldn't ascend to the level of problems (530c).  It wouldn't force us to contemplate a pure and invisible ideal world that governs this one from above.  Note that Plato obviously has in mind the astronomy of his day, whereas modern astronomy would come a lot closer to fitting his definition.

However, the study of all these sciences is just preparation for studying the queen of the sciences, the dialectic (534e).  The reason the dialectic is so important is that it fulfills the criteria Socrates set out for true knowledge at the end of Book 6.  Instead of taking its hypotheses as unqiestioned first principles or definitions, it takes them as stepping stones to reach an un-hypotetical, necessary or apodictic, first principle.  The dialectic takes the Forms as hypotheses only to reach the certain conclusion that there is a natural light which illuminates them: the Good.  So instead of producing the universal agreement of opinion that arithmetic or geometry inspire (we all agree that if X then Y), it reaches the self-evident certainty of knowledge.

And as for the rest, I mean geometry and the subjects that follow it, we described them as to some extent grasping what is, for we saw that, while they do dream about what is, they are unable to command a waking view of it as long as they make use of hypotheses that they leave untouched and that they cannot give any account of. What mechanism could possibly turn any agreement into knowledge when it begins with something unknown and puts together the conclusion and the steps in between from what is unknown?
None.
Therefore, dialectic is the only inquiry that travels this road, doing away with hypotheses and proceeding to the first principle itself, so as to be secure. And when the eye of the soul is really buried in a sort of barbaric bog, dialectic gently pulls it out and leads it upwards, using the crafts we described to help it and cooperate with it in turning the soul around. From force of habit, we've often called these crafts sciences or kinds of knowledge, but they need another name, clearer than opinion, darker than knowledge. We called them thought somewhere before. (533c)

 

It may seem odd, but Socrates doesn't actually spend a lot of time discussing how the dialectic works.  We can infer from Plato's whole oeuvre that it always proceeds by question and answer, as well as by separating and unifying (as we saw in Phaedrus).  Socrates explicitly makes both of these points here (435e and 537c5).  To go beyond these hints though and really describe the dialectic in detail, Socrates would have to claim that he knows the Good itself, which organizes the whole dialectic.  But of course, Socrates only knows that he knows nothing, so he can't claim to explain how the dialectic works -- though since he knows that he knows nothing, he can claim that it exists.

So tell us: what is the sort of power dialectic has, what forms is it divided into, and what paths does it follow? For these lead at last, it seems, towards that place which is a rest from the road, so to speak, and an end of journeying for the one who reaches it.
You won't be able to follow me any longer, Glaucon, even though there is no lack of eagerness on my part to lead you, for you would no longer be seeing an image of what we're describing, but the truth itself. At any rate, that's how it seems to me. That it is really so is not worth insisting on any further. But that there is some such thing to be seen, that is something we must insist on. (533a)

Similar to what we saw in Meno, the early Socrates' catchy claim to fame is here transformed into a whole philosophical method.  His questions and answers about courage and friendship and love and justice are designed to set up problems that lead us into the confusion of contrary perceptions.  From these problems we can move towards the Forms that resolve the mixture of a problem into its elements.  In fact, the paradox of Socrates' motto sets up the most fundamental problem of all.  How can he know and not know at the same time?  This is much tougher than the paradox of the big, thick, hard ... finger (524a).  But it is 'resolved' in the same way.  The question itself makes us realize that there must be a difference between knowledge and ignorance, the two opposed Forms that structure knowing and not-knowing.  And in the middle, we have the muddle of opinion.  The Socratic method of inquiry, when it takes the paradoxes it uncovers seriously, and not as refutations in some rhetorical game (539b), exemplifies the dialectic.  

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In another Deleuzian aside, the passage at 523b where Socrates distinguishes between perceptions that "summon" the understanding and those which do not is reproduced on page 138 of D&R.  I actually think he uses the quote there as a sly form of humor, since the subtlety of a thought-without-image is as easy to misinterpret as Socrates' idea is for Glaucon.  Deleuze goes on to make great use of the concept of problems in the rest of his book.  But first he spends a few pages (up to 143) critiquing Plato's construction of that concept.  Basically, while Plato clearly values problems, he ultimately expects them to be solved.  In fact, the Forms are precisely the solutions to problems, the elements that allow us to resolve a mixture into its pure components.  Likewise, the Good is the solution to the problem of knowledge posed by Socrates' tag line.  In Plato, we resolve the problems by remembering the Forms we saw prior to our (latest) birth.  Deleuze points out that this kind of remembering is precisely not 'problematic' in Plato's own sense -- it's just a form of recognizing some identity we've seen before we were born.  So I guess my point here is that learning more about Plato's use of the term doesn't actually help us understand the way Deleuze employs it, unless this is by way of contrast.  For Deleuze, problems are not about relative qualitative oppositions, and they are not meant to be solved but to be preserved as problems so that we are able to move completely beyond modeling thought upon the experience of recognition.  It's only in this sense that he agrees with Plato -- thinking (or understanding as Plato calls it) starts only when recognition stops. 

Republic Book 6

As we move past the midpoint of the Republic, Socarates seems to finally leave behind his description of the rules of the just city and move into more interesting territory.  Book 5 finished the thought experiment by concluding that the most important rule for bringing the just city into existence was to put the philosophers in charge.  Book 6 is mostly devoted to answering the obvious objection -- most folks don't think of philosophers as particularly useful people who would make good rulers.  In fact, even Socrates agrees (487e) that most people who study philosophy end up somewhere between useless and downright bad.  However, he explains that this happens because their noble natures are planted in the barren soil of the corrupted city.  Philosophy's quest for truth can never thrive under pressure from the masses, it is an inherently aristocratic endeavor.  

Towards the end of the chapter, this discussion of the rarity of the philosophic nature leads Socrates to describe the most stringent and important test for it -- the ability to understand the Form of the Good.  Beyond possessing all the virtues like courage and wisdom and justice, the true philosopher needs above all else to understand how these virtues can benefit us.  He needs to know why they are good for us.  Is something good because it brings us pleasure or imparts knowledge (505b4) or is there some other explanation?  The philosopher king needs to be able to pass beyond the many good virtues and understand what makes something Good in itself.  The Form of the Good brings us to another level of abstraction, since the many goods it encompasses are themselves Forms.  And since its definition takes us beyond pleasure and even knowledge, it introduces another power (477c) beyond both opinion and knowledge -- understanding.  While Socrates isn't really able to describe the Good or 'understanding' very exactly, he tells us that it is like the sun -- not only a brilliant object in its own right, but the source of the natural light that lets us perceive all the others.  

The initial part of this book simply recapitulates what we heard in book 5 about the many virtues of the philosopher.

Is there any objection you can find, then, to a pursuit that no one can adequately follow unless he's by nature good at remembering, quick to learn, high-minded, graceful, and a friend and relative of truth, justice, courage, and moderation?

Not even Momus could find one.
When such people have reached maturity in age and education, wouldn't you entrust the city to them and to them alone? 

(487a2)

While Socrates may have convinced all his companions with his reasoning, this image of the philosopher, and the idea of putting him in charge of a city, runs so counter to popular opinion that Socrates is obliged to explain why the public so misunderstands philosophy.  One part of the problem is that the masses don't know what they are talking about.  Socrates likens them to the strong but not too bright owner of a ship who has to pick a captain (488).  Many sailors clamor to be in charge, and the ones who succeed are the ones who are best at convincing the owner to put them in charge, not necessarily the ones who are best at sailing.  By contrast, a truly good sailor, who would make a great captain, spends his time studying the water, the sky, and the craft of sailing, all of which appear completely beside the point both to the other sailors clamoring for the position, as well as to the dullard owner.  The story parallels the description of politicians and orators as the pastry chefs of the soul we saw in Gorgias.  So the reason the common man considers the philosopher so useless is because he has a bunch of opinions, but no real knowledge of what's good for himself.  He is, to use a metaphor Plato is fond of, like a sick man who doesn't even realize that he needs a doctor (489c).

While the ignorance of the masses may explain the philosopher's image as a useless "stargazer, babbler, and good-for-nothing", it doesn't explain why so many who study philosophy end up downright mean.  I don't know how mean we consider philosopher's today, especially given that our current image depicts them as mostly harmless academics.  But we're certainly still familiar with the general problem of how 'high-minded' folks can often be more vicious than the common man.  Just ask your local catholic priest.  So what is it that corrupts these people who Socrates has argued begin with such a panoply of virtues?  The problem turns out to be, again, the ignorant masses.  In fact, the virtuous philosophic soul, when planted in the degenerate soil of the luxurious city, is the most easily corrupted thing of all.  The greatest virtues are converted into the greatest vices because everyone wants to use the philosopher's strength to their own advantage; they praise him for his virtue only so long as he uses it to achieve things valuable in the opinion of the masses.  This is actually kind of a clever argument that reminds me of Nozick's explanation for why so many academics dislike capitalism.  Socrates observes that in the impure city that exists today, these talented philosophic souls receive consistent praise using those talents to get ahead in conventional ways, and consistent scorn for pursuing some supposed higher truth at odds with the common value placed on money, honor, and fame.

When many of them [the masses] are sitting together in assemblies, courts, theaters, army camps, or in some other public gathering of the crowd, they object very loudly and excessively to some of the things that are said or done and approve others in the same way, shouting and clapping, so that the very rocks and surroundings echo the din of their praise or blame and double it. In circumstances like that, what is the effect, as they say, on a young person's heart? What private training can hold out and not be swept away by that kind of praise or blame and be carried by the flood wherever it goes, so that he'll say that the same things are beautiful or ugly as the crowd does, follow the same pursuits as they do, and be the same sort of person as they are? (492b4)

Even Plato believed that incentives matter, it seems.  Everything that makes the noble philosophic soul great simultaneously increases the pressure of this tyranny of expectations.  Which goes a long way to explain why Socrates spent so much time discussing the education and upbringing of the guardians back in books 2 and 3.  

Given this incentive structure, you might think that Socrates has worked himself into a corner.  If a philosophic nature is inevitably corrupted by a degenerate society, how are we ever supposed to raise a philosopher king who would have the wisdom to institute the thoroughly contrarian constitution that Socrates has described?  If there's no chicken, how do we get good eggs?  In short, we don't.  Unless, that is, we get lucky.  Remember, Socrates only wants to establish that it's possible to create this best of cities, not that it is likely or easy.  To establish this minimum he suggests a few lucky scenarios that might produce an uncorrupted philosophical soul -- an exiled noble, a great man living in a small city, a brilliant intellect with a sickly physique, or Socrates own case, where his daemon holds him back from getting embroiled in the affairs of other men (496b).  Of course, if these accidents happen in the barren soil of the corrupt city, the philosopher produced will understand the pointlessness of entering public affairs and will follow Socrates example and lead a quiet life, "free from injustice and impious acts and depart from it with good hope, blameless and content" (496d9).  It would take even a further miracle for a seed of this nature to be planted in a soil where it would thrive and reproduce itself, where it would be given power over a city, allowed to set its constitution and provide for the upbringing of future philosopher kings.  This would truly be a moment of divine intervention (492e8).

If this rare flower of philosophy is to benefit the city despite the opposition between the public's beliefs and his knowledge, then the philosopher must truly know what's really good for the city, not merely what appears to be good to its masses.  The inherently aristocratic nature of philosophy means that the philosopher must know the very Form of what makes something Good.  This is the only way he can understand why some particular thing is truly good and who it is good for.  At this point, the up to now fairly rationalist theory of the Forms seems to begin to shade into mysticism.  Yet at the same time, we can clearly see the most concrete moral question that has animated Plato's theory from the very beginning -- how do we live the good life?  The theory of Forms always had a moral dimension beneath its metaphysical one, but now this becomes explicit.  The Good is a sort of meta-Form that illuminates and organizes all the others.  After all, Plato came up with the theory primarily as a tool for selecting, not just describing, what we should consider truly Beautiful, or Courageous, or Just.  If we were only to know those other Forms, without being able to act on that knowledge, how would we benefit from them? 

And you also know that, if we don't know it, even the fullest possible knowledge of other things is of no benefit to us, any more than if we acquire any possession without the good of it. Or do you think that it is any advantage to have every kind of possession without the good of it? (505a)

What is the Form of the Good though?  In keeping with his knowing nothing, it turns out that Socrates really isn't able to answer this question, and is forced to approach it only by analogy.  First though, he dismisses the two most obvious candidates for the god -- pleasure and knowledge.  Gorgias already provided an extended critique of the latter identification, so the argument is not reprised here.  And Socrates immediately observes that while it sounds more sophisticated to equate the good with knowledge, this results in a circularity.

Furthermore, you certainly know that the majority believe that pleasure is the good, while the more sophisticated believe that it is knowledge.
Indeed I do.
And you know that those who believe this can't tell us what sort of knowledge it is, however, but in the end are forced to say that it is knowledge of the good. (505b)

Socrates insists that the best he can do (beyond clearing the field of false definitions) is to tell us what the good is like, to tell us about, "what is apparently an offspring of the good and most like it." (506e2).  And the Good turns out to be like the sun.  It is the light that illuminates the other intelligible objects in the same way that the sun illuminates visible objects.

What the good itself is in the intelligible realm, in relation to understanding and intelligible things, the sun is in the visible realm, in relation to sight and visible things. (508c)

 

This may seem fairly straightforward at first, but it raises a host of interesting questions about the role of the Good.  For one, while Plato isn't explicit that he's referring to their earlier definition (477c), he has introduced some new power that is neither opinion nor knowledge.  He's going to name this new power, that operates like a mental sun, "understanding".  This is the power by which we are able to come to know.  Since knowledge was already a power, this makes understanding a kind of meta-power.  

So that what gives truth to the things known and the power to know to the knower is the form of the good. And though it is the cause of knowledge and truth, it is also an object of knowledge.  Both knowledge and truth are beautiful things, but the good is other and more beautiful than they. (508e)

At the same time, the Good not only provides for the possibility of knowledge, but is also itself an object of knowledge, just as the sun is itself also a visual object.  So the Good even has a sort of self-illuminating quality to it.  Socrates pushes the metaphor even further by noting that the sun doesn't just illuminate things, but also nourishes them and makes everything grow.  Analogously, the Good is responsible for our knowledge of things, but also for the very being of the things themselves.

Therefore, you should also say that not only do the objects of knowledge owe their being known to the good, but their being is also due to it, although the good is not being, but superior to it in rank and power. (509b)

The Good has a Form, and constitutes a power, but it is beyond the other Forms, and beyond even being itself (note this latter fact in relation to Parmenides).  Basically, it's the power to understand the other Forms.   

Finally, Socrates concludes the chapter by formalizing the analogy between the visible and the intelligible.  He describes a line divided into four unequal pieces.  First, in keeping with the analogy between the Good and the sun, the whole line is divided unequally between visible and intelligible.  Next, each of these parts is again divided unequally (though in the same proportions to one another and to the division between visible and intelligible) into images and the originals which produced these images.

1) Imagination: The lowest rung, so to speak, will be occupied by images of visible objects. 

"And by images I mean, first, shadows, then reflections in water and in all close-packed, smooth, and shiny materials, and everything of that sort" (509e)

2) Belief: Next will come the real visible objects that produce these images.

In the other subsection of the visible, put the originals of these images, namely, the animals around us, all the plants, and the whole class of manufactured things. (510a)

So far, so good.  Things take an interesting twist though, with the second section of the line, the intelligible.  

3) Thought: The images that occupy the lower subsection of the intelligible turn out to be mathematical objects like circles and triangles.  Socrates makes clear that he does not mean visible drawings or representations of those objects (which would be classified in 2), but the actual triangle as an object of thought, a 'mental image' (510c).  So while subsection 3 is filled with intelligible images, these images serve as originals with respect to the visible images of them (eg. a circle drawn in the sand) that were in subsection 2.  Like the definitions of geometric figures, the intelligible objects of subsection 3 serve as hypotheses.  They are first principles that the mind takes as given, and that allow it to deduce other conclusions.  

In one subsection, the soul, using as images the things that were imitated before, is forced to investigate from hypotheses, proceeding not to a first principle but to a conclusion. (510b) 

...

I think you know that students of geometry, calculation, and the like hypothesize the odd and the even, the various figures, the three kinds of angles, and other things akin to these in each of their investigations, as if they knew them. They make these their hypotheses and don't think it necessary to give any account of them, either to themselves or to others, as if they were clear to everyone. And going from these first principles through the remaining steps, they arrive in full agreement. 
I certainly know that much.
Then you also know that, although they use visible figures and make claims about them, their thought isn't directed to them but to those other things that they are like. They make their claims for the sake of the square itself and the diagonal itself, not the diagonal they draw, and similarly with the others. These figures that they make and draw, of which shadows and reflections in water are images, they now in turn use as images, in seeking to see those others themselves that one cannot see except by means of thought.
That's true.
This, then, is the kind of thing that, on the one hand, I said is intelligible, and, on the other, is such that the soul is forced to use hypotheses in the investigation of it, not travelling up to a first principle, since it cannot reach beyond its hypotheses, but using as images those very things of which images were made in the section below, and which, by comparison to their images, were thought to be clear and to be valued as such. (510c-511a)

4) Understanding: Finally, subsection 4 contains ... well, it's not completely clear.  By analogy, it should contain the originals, of which the contents of subsection 3 are just mental images.  However, it's not totally clear what that would mean in terms of the mathematical example, and this isn't quite how Plato describes it anyhow.  Instead, it may contain only the first principle that allows one to deduce the things that were acceptable as provisional hypotheses in subsection 3.  In the present context, this is obviously the Good, which is like a meta-Form that illuminates all the others.  

... by the other subsection of the intelligible, I mean that which reason itself grasps by the power of dialectic. It does not consider these hypotheses as first principles but truly as hypotheses—but as stepping stones to take off from, enabling it to reach the unhypothetical first principle of everything. Having grasped this principle, it reverses itself and, keeping hold of what follows from it, comes down to a conclusion without making use of anything visible at all, but only of forms themselves, moving on from forms to forms, and ending in forms. (511b)

A drawing should help clarify all this.  I think my version improves on the one given by the translators.  While Plato doesn't explicitly say that the 'lower' or image side of the division is larger than the 'higher' or original side, the fact that the One-Good belongs in the top subsection suggests to me that this should be the smallest and the base of the ratio R used in the divisions.  My diagram also makes clear that the math implies the size of subsection 2 must equal subsection 3, which implies that every real thing in the world will have a corresponding mental image.

The most interesting question here is how Plato conceives of the individual Forms as hypotheses.  He introduced them in exactly this way back in Phaedo (100b).  And as we've pointed out many times, in that case as well as any other, the Forms are introduced as a tool to help us figure out how to live the good life.  In this sense they have always been hypotheses about "things that are" that would help to guide our actions.  Now, however, he wants us to move in the opposite direction, from the Forms as hypotheses to some central moral principle that would be self evident and certain, not merely hypothetical.  As if even to be able to entertain the truth or falsity of the hypothesis would require a certain presupposition that would be necessarily true.  The Good seems to fulfill this role by being the natural light that allows us to see and understand anything at all.  If we can even think of the Forms as a hypothesis, we must be able to understand the Good.  But I don't think this idea is clear yet, so we'll have to see how Socrates develops it.

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As an aside, this is certainly the passage that Deleueze must be thinking of when he characterizes the unity of philosophy as the movement for the hypothetical to the apodictic.

From Plato to the post-Kantians, philosophy has defined the movement of thought as a certain type of passage from the hypothetical to the apodictic. Even the Cartesian movement from doubt to certainty is a variant of the passage. Another is the passage from hypothetical necessity to metaphysical necessity in the On the Ultimate Origination of Things. Already with Plato the dialectic was defined in this manner: depart from hypotheses, use hypotheses as springboards or 'problems' in order to attain the an-hypothetical principle which determines the solution to the problems as well as the truth of the hypotheses. The whole structure of the Parmenides follows from this, under conditions such that it is no longer possible to see therein a propaedeutics, a gymnastics, a game or a formal exercise, as has nevertheless been done ever so delicately. Kant himself is more Platonic than he thinks when he passes from the Critique of Pure Reason, entirely subordinated to the hypothetical form of possible experience, to the Critique of Practical Reason in which, with the aid of problems, he discovers the pure necessity of a categorical principle. Even more so the post-Kantians when they wish to transform hypothetical judgement into thetic judgement immediately, without changing 'critiques,. It is not illegitimate, therefore, to summarise in this way the movement of philosophy from Plato to Fichte or Hegel by way of Descartes, whatever the diversity of the initial hypotheses or the final apodicticities. There is at least something in common: namely, the point of departure found in a 'hypothesis' or proposition of consciousness affected by a coefficient of uncertainty (as with Cartesian doubt) and the point of arrival found in an eminently moral apodicticity or imperative (Plato's One-Good, the non-deceiving God of the Cartesian Cogito, Leibniz's principle of the best of all possible worlds, Kant's categorical imperative, Fichte's Self, Hegel's 'Science'). (D&R 196)

 I don't yet grasp the full implications this idea has for interpreting Parmenides.  But it does seem to go in the direction I vaguely foresaw -- the One and the Many refer to the Forms, not things.  The question in Parmenides then is not the binary existential one of whether the One is or is not.  The One-Good is beyond being and not being.  That the One is and that it is not are two complementary hypotheses that are meant to lead us beyond themselves and into the realm of apodictic certainty.  This casts the final line of the dialog in a new light.

... whether one is or is not, it and the others both are and are not, and both appear and do not appear all things in all ways, both in relation to themselves and in relation to each other. (Parmenides 166c)

 

What if we substitute, "Whether the Good is or is not, the other Forms both are and are not, etc ..."?  The hypothesis of the being and the hypothesis of the non-being of the Good together allow us to reach the certainty that ... ???  This is the problem.  The conclusion of that sentence should tell us something about the self-evident nature of the Good, that powerful sun beyond the other Forms and beyond even being.  Yet it just seems to say, "everything".  And it doesn't even say that very clearly.  So whatever apodictic principle Parmenides has shown us is still a mystery to me.