Abstract

Elaborating the analogy between the sun and the good, Plato's Socrates tells Glaucon to divide a line αβ into two unequal segments at γ. The result is that αγ represents what is intelligible and γβ what is visible.1 Then Glaucon is to divide each of the two segments by the same ratio as he used in the original division.2 Whatever proportion he used to make the cuts γ, δ, and ε in the divided line, generating its four segments, the geometrical implication is that the two middle segments must be equal in length. As both Nicholas D. Smith and Richard Foley have emphasized, when Socrates reiterates the characteristics of the line at 534a3–5, transposing δγ and γε, there should be no doubt that Plato...