The Philosopher Ruler (497-509)

He had mentioned in Book III that the guardians-in-training are subjected to many tests so that rulers are chosen from among them. One point of the test, he told us then, was to see who was most loyal to the city. Now we see that another major point of these tests is to determine who among them can tolerate the most important subject - philosophy. 

'There's no existing form of society good enough for the philosophic nature'

'children should only tackle the amount of philosophic training their age can stand...when they are older and their minds begin to mature, their mental training can be intensified'

'there would never be a perrfect state or society or individual until some chance compelled this minority of uncorrupted philosophers, now called useless, to take a hand in politics'

Plato begins by outlining the education of the philosopher kings, and 'the studies and pursuits which will produce these saviours of our society', he reminds his reader of the test which guardians must undergo ('they must love their country and be tested both in pleasure and pain to ensure that their loyalty remained unshaken') and the qualities which all good leaders must possess and how it is rare to find theses qualities whicha are 'normally found separately', 'combine into a whole'. For the first time he explicitly states that 'Guardians, in the fullest sense, must be philosophers.'

The most important subject for a philosopher-king, it turns out, is the study of Form of the Good. It is in understanding the Form of the Good, in fact, that someone gains the highest level knowledge and thus becomes fit to be a philosopher king ('it's no use possessing anything if you can't get any good out of it' and 'The good, then, is the end of all endeavour, the object on which every heart is set').

Socrates explains that the Form of the Good is not what is commonly held to be good. Some think that the highest good is pleasure, while the more sophisticated think that it is knowledge. In fact, it is neither of these, but Socrates cannot really say directly what it is.The best he can do is give an analogy—to say “what is the offspring of the good and most like it.” This analogy is the first in a string of three famous and densely interrelated metaphors that will stretch into the next book—the sun, the line, and the cave. In the course of developing these three metaphors, Socrates explains who the philosopher is, while working out his metaphysics and epistemology.

'The sun, I think you will agree, not only makes things we see visible, but causes the processes of generation, growth and nourishment, without itself being such a process...the good therefore may be said to be the source not only of the intelligibility of the objects of knowledge but also of their being and reality; yet it is not itself that reality' 

The good is 'miraculously transcendent'