Socrates adamantly denies that he can identify a single state at the time of this dialogue that might prove fruitful for the growth of a philosopher-ruler; he says that, because of his environment (the society in which he finds himself), the naturally good, budding philosopher becomes warped. But Socrates anticipates the resultant clamor from a public whom he has accused of being corrupt, and he attempts to placate that public by insisting that a philosopher-ruler would still be the ideal ruler for the ideal state.
The problem, Socrates says, for our producing a philosopher-ruler may lie in the material with which we have to work. We agree that such a ruler must be intelligent, a "quick study," ambitious in things of the mind, diligent. At the same time, the potential ruler must be disciplined, temperate, reliable. But intelligent people may be intemperate and unreliable, and they may lack courage. Reliable people, conversely, are often indolent and bored when facing intellectual tasks; such people are often ignorant and may be stupid. Citizens who possess all the qualities required in a philosopher-ruler will be in a distinct minority.
Thus it is that candidates for the capacity as ruler will have to be more thoroughly educated than we had thought; they will have to pursue a more rigorous intellectual training so that they can attain knowledge of the real.
Glaucon asks Socrates if he means that the potential rulers are to have knowledge of the Forms. Socrates replies that the rulers must possess knowledge of Goodness, for logically that is the sole way a man may recognize the goodness of, say, Justice and Beauty.
Logically, Socrates must at this juncture entertain a definition of Goodness, but we cannot accept the premise that "knowledge of the Good is Goodness"; that constitutes an invalid argument (a false tautology). And some people offer other invalid arguments for Goodness, as we may observe.
Socrates then says that he will not precisely define Goodness, but that he can elucidate the argument by arguing another analogy. Socrates' analogy involves a comparison between sight and knowledge. In order for men to see, men must be given visible objects to perceive, and men must be given light in order to perceive the objects. The source of this light is the sun. Analogically, in order for men to know anything, men must be able to think, and they must be provided objects of knowledge (the Forms). Visible objects, then, have to be in the light; objects of knowledge have to be true. Light comes from the sun; truth comes from Goodness. (This analogy has come to be known as the Analogy of the Sun.)
At this point, Plato is perhaps alluding to his first trip to Syracuse when he still had hopes of helping his friend, Dion, to persuade the young king, Dionysius II, to become a friend to philosophy and to enlighten his fellow citizens. Thus, in actuality, Plato might have, as he had hoped, produced in Dionysius II an enlightened despot, a king-turned-philosopher. But Plato's plan failed (see the Life and Background section).
When Socrates is here speaking of Plato's idea of "Goodness," Plato's meaning is "Goodness itself"; it is the supreme Form, inherent, timeless, essential; hence, the reflexive, "Goodness itself." Goodness is embodied not only in the cardinal virtues, but also in all of the universe. Earlier for Plato (and for us), Goodness might be achieved through the exercise of the virtues, resulting in the good and happy life (embracing courage, justice, temperance, wisdom). We now are to see Goodness itself manifested in the moral universe and in the physical universe (the beauty of the heavenly bodies and the order of them). We are to see this supreme Goodness itself as a manifestation of a divine Reason at work in the universe. This apprehension of a divine Reason at work permits us to see how the universe works; it leads to our "seeing" knowledge (the Forms), and the universe is thus illuminated. As illumination, Goodness itself is analogous to the sun, which sheds light upon vision and upon things made visible and is the source of all mortal life.
Socrates never in this dialogue, nor in any dialogue, defines Goodness itself. But Socrates does say that the knowledge of it may come to one in a kind of revelation after a long course of philosophical study (Jowett translation 540 A). And we know that Plato says, in the letter he wrote to Dion's friends and family, that he never wrote down a definition for Goodness itself (Letter VII 341 c, Harward translation).
We may briefly set forth the Analogy of the Sun thus: For sight, the sun is the source of light, and so makes objects visible and allows the eye to see; for Knowledge, Goodness is the source of Truth, and so makes the Forms intelligible and allows the mind to know.
Theages' bridle Scholars identify Socrates' phrase here as referring to a proverb.
the Muse of philosophy The nine Muses were mythical daughters of Memory, goddesses of the arts, who were said to watch over or inspire the practitioners of nine specific arts: Calliope, epic poetry; Clio, history; Euterpe, the flute; Melpomene, tragedy; Terpsichore, dance; Erato, the lyre (and lyric poetry); Polyhymnia, sacred song; Urania, astronomy; and Thalia, comedy. There was no Muse assigned to philosophy; Socrates is using this phrase figuratively and fancifully, and perhaps implying that philosophy is more deserving of a Muse than some of these other arts.