The arts in education are primarily dealt with in Book III.
Socrates concludes his attack on the "libelous poetry" that portrays his beloved virtues in so many negative lights. It is not of use to the State. Or if it is to be of use, it must be stringently didactic and partake of none of the indulgence and rhapsody common to their tradition and to contemporary poets as well.
Even Homer is indicted. Instead the citizens of the state, at this early stage they are generically named guardians, are to be nourished only on literature - broadly termed 'music' by Socrates - clearly illustrating courage, wisdom, temperance, and virtue (just behavior).
The second part of education, gymnasium, consists mostly of the physical training of the citizens. At this point Socrates' State needs rulers. Who better to rule than the best and most patriotic citizens produced by the rigorous education apparatus. These very select few are now more strictly called the guardians, while non-guardians remain citizens. The guardians will be the rulers.
The book closes with the Phoenician myth, which Socrates feels would serve as effective mythical explanation for their State.
Through the myth citizens are told they are made of a certain mix of metals, gold and silver, iron and brass, etc.
They are born like this and are to take the requisite social station because of it.
However, should a citizen of gold or silver be born to parents of an inferior metal, he will rise socially as is just; and the rule will also function in the reverse situation.
The myth provides the State with an accessible, allegorical illustration of its stable, hierarchical social organization.
