Republic Book 4, All Sections

"The happiness of the state, Socrates reiterates, consists in the happiness instilled in each individual member of the classes from his having functioned well at his appointed task, performing his job well."

No rulers, only followers.

Except Plato, of course. He gets to tell you what your job is. 

Also note the Prussian-school-like ritualization. If happiness is a job well done, okay, but what is a job well done? Why not assign trivial jobs and then everyone can be trivially happy? Contra Plato, Gnon indeed exists. If you get satisfaction from the doing the wrong job - the deadly sin of falsehood - then Gnon will condemn you.
Plato doesn't know which jobs need to be done, and it's largely none of his business. Conquest #1 => the person doing the job normally does know which jobs need to be done. If you want more of a job done, do the responsible thing and pay more to get more.

"They should not be permitted to suffer either from extreme wealth or from extreme poverty. Socrates explains that extreme wealth will cause the craftsmen to become lazy and lax in their duties. They may refuse to work."

wut iz suplae end daymand

When craftsmen retire, supply goes down, which mean prices go up, which entices more to take up craftsmanship. If they can't get paid it means they're not producing wealth and should stop. In either case it's none of Plato's business. 

Scholar trying to bully merchants. If they get away with it, all that happens is everyone gets poor and nobody can supply the warriors...

 

"We will not, Socrates says, require many laws in the ideal state; too many communities suffer from an overabundance of too many laws"

True, but again none of Plato's business. It's caused by the irresponsible and unjust unilateral imposition of laws. It's not even the overabundance per se that's the problem, but the fact the laws are designed to profit the lawgiver at the expense of the lawtakers. The lawgiver sees no reason not to, and frankly, if the lawtakers are dumb enough to sit there and take it, neither do I. Weakness is a sin and ought to be punished. 

"The true way to achieve that general truth lies in the program we have already established for the Guardians: education and nurture."

Pedagogue tells us that pedagogy is the highest, purest task. 

Slave, go back to leading dumb children. Spare us this self-serving nonsense. 

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"Socrates proceeds to try to determine the essential virtues that may be said to characterize it (the Four Cardinal Virtues): wisdom, courage, temperance, and justice."

Coincidentally already BTFO by my last post. 

 

"he argues that a choice example of injustice would ensue if members of a given class, or classes, should by force attempt to seize the "rights" of some other class."

If it can happen it will happen. A logiomantic State plans on what to do after it happens, rather than dying instantly if it cannot prevent the problem.

Of course, the answer is Exit. The property of others will be unjustly seized. Once this starts occurring, revoke your consent. If a State doesn't have a formal, simple, and cheap consent revocation procedure: run, don't walk. Never get involved in the first place. 

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"It is a given proposition (a self-evident truth) that a given physical body "
"From this, we may deduce that there exist two parts of the human mind"

The mind, however, is all weird. Our understanding of it is impoverished.

Due to the nature of subjective ontology, a single mind is all one unitary thing. Also, at the same time, a typical human mind is somewhere near the quarter-megabyte range. The single state has complexity to it - and not one or two degrees of freedom, but at least half a million. How is this possible? I dunno. However, these two facts are unassailable, so they must be reconcilable in one way or another.

"Thus the essential aspects of the mind follow: (1) reason; (2) emotions or the "spirited" element; and (3) desire, or passions. These aspects of the mind correspond to the three classes of the state"

Plato/Socrates goes off track here. I think they didn't have enough background at the time. 

Intuiting. The trifunctional caste system is based on a pre-human logical fact: dominance may be physical, intellectual, or social. 

Plato wants warrior-monks in charge (emphasis on the monk), with pure warrior auxiliaries, ruling over a mass of merchants. In reality there is no universal solution. Further, it's clear by inspection that the king needs to be a proper member of all three castes. A warrior-priest-merchant. Ideally, the king is the best fighter or strategist, the wisest scholar, and the shrewdest merchant. However, they only need to be the best at one thing, and merely competent enough to overcome Dunning-Kruger in the others.