Abstract
The similes of the Sun, Line, and Cave in the Republic remain a reproach to Platonic scholarship because there is no agreement about them, though they are meant to illustrate. I propose to analyse the form of the argument, a clue that has never been properly weighed. The Greek theory and practice of analogia and diairesis give good evidence about the method that Plato adopted; if this usage were respected, the analogical argument would not be so loosely interpreted, and the double diairesis and proportion that the Line actually is could not be mistaken for a classification. I hope also to show that Plato's terminology is definite and consistent; here too ancient usage helps to establish his meaning.