10. Metaphors to Think by

Chapter Ten, ‘Metaphors to Think By: The Sun and Divided Line Analogies’, is devoted to the marquee analogies of Book VI, both of which address the Third Wave by developing the distinction between the sensible world of concrete particular things and the intelligible world of the Forms. Having suggested that the Form of the good is even more important than justice, Socrates cannot or will not say what the good is, but he does say what he thinks it is like: the good plays the same role in the intelligible world as the sun plays in the visible world. In the Analogy of the Divided Line, Socrates further develops the distinction between belief, which is appropriate to the sensible, visible world, and knowledge, which is appropriate to the intelligible world of the Forms. By exploring the role that hypotheses play in reasoning, he distinguishes philosophical knowledge from mathematical knowledge, somewhat surprisingly taking the former to be more rigorous.