"they are to be introduced to various levels of mathematics and thoroughly schooled in them in order to train them intellectually so that they may become adept at abstract thought."
Not how abstract thought works. It either happens or it doesn't. Training, and especially teaching, likely makes no difference at all.
"Socrates suggests that the studies should move from the simplest to the most complex in this order: arithmetic, plane geometry, solid geometry, astronomy, and harmonics."
This is likely true but the levels are wrong. Should a real school ever appear, it will have to pray to Gnon and ask which levels go first and why. Figure out the most important thing for students to know, then work backwards to figure out the most efficient path.
It is possible the most efficient path is discarding optimization. Do set 2s until your daemon can just tell you what to investigate next.
"and we are reminded again that these young candidates must be of high moral character and industry."
Personnel is policy. If you have a ruling system (Exit) which selects for high moral character, you will have a good polity, regardless of how they're educated. If you don't, you won't.
As we now know, most cognitive traits are nearly 100% genetic. Like height, you will reach your maximum intelligence/virtue as long as you're not actively malnourished or otherwise injured. (The epistemic sets appear to be an exception, but almost everyone who can use them will invent the sets themselves.)
"but the intellectual studies are to be lightly enforced. Socrates argues that rigorous training does not harm the body at this age, but enforced intellectual studies may cause the learner to rebel."
Turns out Plato is not an entirely incompetent pedagogue.
Blind squirrel? Why does Plato know these things?
Though "lightly enforced" a fortiori. Scholars learn even if you try to stop them, never mind what's enforced. It's helpful to give a few hints here or there, or let them know which quagmires to skip, to save time. Their daemon knows roughly 10,000% more than you do about what they need to know.
"At this stage, the best of the students will be selected to further their education in a strict regimen of physical and military training (discussed earlier). "
Busybody. The students ought to select themselves. Sink or swim. See also: Exit. Have several trainers. Let the students who pick bad trainers with bad training regimes fail - then leave for the good, effective trainers. This is how you pray to Gnon to grant you good training.
Separate trainers and hiring, in general. There is no reason the hiring lord needs to know why you can do what you can do - only that you can do it.
"This physical and military training will be rigorous, and the students will have no time for intellectual pursuits."
Foolish. You must rest your body. Resting the body is an opportunity to study.
Foolish. The mind works poorly if the body is neglected. A physics education should involve duelling, horseback riding, or at the very least warehouse work. Ideally every day.
Matter and mind are not genuinely separate. The brain is a physical organ, morons.
"the young students will be tested, and a further selection will be made. The best students will be given the advanced studies in mathematics (discussed earlier); the course in mathematics will last for 10 years."
Bullshit. Again, let the students themselves decide what they want to learn. Don't forget the street runs both ways. If they can't find anyone willing to teach them, normally that's because they're dumb. This problem solves itself. Don't be a control freak.
"Part 5: When they are 35, having now become trained philosophers"
I reached grandmaster of philosophy at 29, and I trained myself. Imagine how much faster I could have managed it if I could have apprenticed instead of having to re-invent literally every wheel.
"It's hard." It's not actually that hard. You just want an excuse for not doing it, because you don't want to do it. Training someone who doesn't want to be a logiomancer doesn't take until 35 - it takes until they're 100,000. Possibly longer.
Instead, reject control freakery. It's illegitimate. They don't want you to learn either. They want you to be oppressed.
You can force someone to destroy but you can't force someone to grow. See also; creation, love, initiative, etc. It's logically impossible.
"Now that they know Goodness"
Plato's Goodness is probably just Badness. Coercion, anti-nihilism.
However, it is true that peasants can't understand. That's why they need lords. They can't figure it out. If they don't want to be wrecked by Gnon, they have to obey and only obey. To them, it looks like a bunch of random, unconnected instructions.
Sadly those who don't see can't deal with unexpected situations. Too often they can't even recognize the situation as different and thus unexpected. They need to be supervised.
Perhaps we can hope that, with wise supervision, the peasant might slowly (by age 50, perhaps) start to understand the principles behind the instructions they're given, and need less supervision. Perhaps even give them a raise, since they're less expensive. Like they have seniority or something silly.
Gonna have to ask Gnon about that one, though. Try it several ways and pay attention to Gnon's answers.