The Metaphor of the Line

A line is cut into two unequal parts, and each of them is divided again in the same proportion. The two main divisions correspond to the intelligible world and to the visible world.

One section in the visible division consists of images, that is, shadows and reflections, and is accessed through imagination.

The other, higher section in the visible division consists of sensible particulars and is accessed through belief.

One section in the intelligible division consists of Forms and is accessed through thought, but via sensible particulars and hypotheses, as when geometers use a picture of a triangle to help reason about triangularity, or make appeal to axioms to prove theorems.

The other, higher section in the intelligible division also consists of Forms but is accessed by understanding, a purely abstract science which requires neither sensible particulars nor hypotheses, but only an unhypothetical first principle, namely, the Form of the Good.

The purpose of education is to move the philosopher through the various sections of the line until he reaches the Form of the Good.