Book VII

Socrates describes prisoners in a cave who mistake shadows for reality and resist being led to the truth of the upper world.

The cave represents the visible world, the journey upwards is the soul's ascent to knowledge, and blindness can result from both entering and leaving the light.

Education is turning the soul's existing faculty of sight toward the good, and enlightened rulers must be compelled to return to the cave to govern.

Philosophers are compelled to rule for the state's salvation, as their detachment from political ambition makes them the best governors.

The education of rulers begins with arithmetic, a science that stimulates the mind to grasp abstract being beyond the confusing world of the senses.

Geometry is the second subject for its power to elevate the soul, followed by the neglected but essential study of solid geometry.

Astronomy must be studied not by observing the imperfect heavens, but by using the mind to grasp the absolute harmonies of motion through problems.

Harmonics, like other sciences, must be studied abstractly, and all these studies are merely a prelude to the higher reasoning of dialectic.

Dialectic is the supreme science that rises above the hypotheses of mathematics to grasp the first principles and true essence of things.

Rulers are selected for their natural abilities and undergo a rigorous, multi-stage education in sciences, dialectic, and practical experience before governing.

After confirming female rulers, Socrates explains the first step in creating the state, followed by a summary of the cave allegory's meaning.

Plato's philosophy aims to realize and connect universal abstractions, using the sciences of number and relation to draw the mind from becoming to being.

A modern mathematician would appreciate Plato's love for pure mathematics but also recognize his error in believing the heavens could be constructed a priori.

A metaphysical philosopher sees mathematics as a tool for education but notes Plato's Pythagorean-influenced attempt to connect it to higher moral ideas.

This unit explains Plato's concepts of vision as the mind ordering sensory chaos and of harmonics as an abstract science beyond empirical study.

The cave allegory also has a political meaning, representing the philosopher's difficult return to the narrow, practical world of politics.

A modern parallel is found in statesmen or theorists who are so absorbed by grand ideas that they cannot see contemporary politics in true proportion.

The contrasting disorder is seen in practical men of narrow experience who are blinded and confused when introduced to a wider world of ideas.

Plato's depiction of youth losing their principles when questioning doctrines is compared to modern students who are easily swayed by new, fashionable ideas.

This unit highlights several characteristic Platonic elements, including the distinction between mathematics and dialectic and the gravity with which radical ideas are proposed.