Plato: Republic

Socrates presents to Glaucon a figure of human enlightenment: prisoners chained in an underground den, seeing only shadows cast on a wall by a fire behind them, take the shadows for realities. He describes the release of one prisoner — the pain and dazzlement of turning toward the light, the gradual accustoming to the upper world by stages, from shadows to reflections to objects themselves, then moon and stars, and last the sun. The returned prisoner, his eyes filled with darkness, appears ridiculous to those still below, who would kill anyone attempting to free them. Socrates states the figure's application: the prison-house corresponds to the world of sight, the ascent to the journey of the soul into the intellectual world, and the idea of good, perceived last and with effort, to the author of all things beautiful and right, upon which the rational actor must fix his eye. Those who attain this vision are unwilling to descend to human affairs. Education, he argues, is not putting sight into blind eyes but turning the whole soul toward being; even clever rogues possess keen eyesight forced into the service of evil. The founders of the State must therefore compel the best natures to ascend to the good and then descend again to rule, and the State whose rulers are most reluctant to govern is best governed. Socrates then asks what knowledge draws the soul from becoming to being: not gymnastic, which concerns growth and decay, nor music, which trains by habit. He proposes number and calculation, distinguishing perceptions that suffice for sight, as a finger is a finger, from contradictory perceptions of great and small that summon thought; arithmetic and calculation lead the mind toward truth.

Socrates and Glaucon establish that arithmetic has a double use, military and philosophical, and that the guardian, being both warrior and philosopher, should study it not as a merchant but until numbers are grasped by the mind alone. Socrates praises arithmetic's elevating effect, noting how its masters refuse to divide absolute unity, and observes that those talented at calculation are quick at other studies. He names it a required subject. They turn to geometry, distinguishing its military use from its higher part, which draws the soul toward being and truth; Socrates says geometricians speak narrowly of squaring and extending, yet geometry aims at knowledge of the eternal. It is made a second subject. Proposing astronomy third, Socrates jokes at Glaucon's fear of appearing to insist on useless studies. He notes an error in ordering the sciences: solid geometry should precede astronomy, but is neglected because no government patronizes it. Astronomy is set fourth. Socrates corrects Glaucon's praise, arguing true astronomy uses the visible heavens as patterns and proceeds by problems, apprehending motions by reason, not sight. He introduces harmony as a sister science, criticizing the Pythagoreans and others who study heard sounds rather than the natural harmonies of number. When these studies reach intercommunion, they prepare for dialectic. Socrates calls the mathematical studies a prelude to dialectic, which alone reaches the first principle and the absolute good without the senses. He recalls the four divisions—science, understanding, belief, perception of shadows—and defines the dialectician as one grasping each thing's essence and the idea of good. Dialectic is named coping-stone of the sciences. They discuss who should receive these studies: natures keen, retentive, laborious in mind, lovers of truth, not half-idle or tolerant of falsehood.

Socrates states that virtues like temperance, courage, and magnificence must be tested for the true versus the bastard, since States and individuals err without such discernment. He warns that unsound pupils would bring ridicule on philosophy, and admits his own vehemence arose from indignation at philosophy's disgrace. He says Solon was wrong that the old can learn much; youth is the time for toil, so calculation and geometry should be taught in childhood as amusement, without compulsion. He recalls taking children to watch battle. He describes selecting the best after gymnastics, promoting them at twenty to see the sciences' relationship to true being, and at thirty testing them by dialectic. Socrates warns dialectic breeds lawlessness, using the parallel of a supposititious son who, discovering his parents are not real, turns to flatterers; likewise students refuted about justice abandon inherited maxims. He compares young arguers to puppy-dogs and urges caution. He proposes five years of philosophy, then fifteen years of practical office, until at fifty the survivors behold the absolute good, order the State, and depart to the Islands of the Blest. Glaucon calls him a sculptor of governors; Socrates adds governesses. They agree philosopher-kings would send out those over ten to train children, and conclude describing the perfect State.