divided line one of three analogies (with the sun and cave) offered in Plato’s Republic (VI, 509d– 511e) as a partial explanation of the Good. Socrates divides a line into two unequal segments: the longer represents the intelligible world and the shorter the sensible world. Then each of the segments is divided in the same proportion. Socrates associates four mental states with the four resulting segments (beginning with the shortest): eikasia, illusion or the apprehension of images; pistis, belief in ordinary physical objects; dianoia, the sort of hypothetical reasoning engaged in by mathematicians; and noesis, rational ascent to the first principle of the Good by means of dialectic. See also PLATO, SOCRA- TE. W.J.P.