Abstract

In this, the final chapter, the focus is on Socrates’ expectation that potential guardians will study mathematics for the purpose of understanding the Form of the Good. Mathematical studies contribute to this end by formulating definitions of mathematical entities that employ the notions of ratio and commensurability. As mathematicians work with visible figures and diagrams to prove their conclusions, they will come to see ratios and commensurability as a central aspect of their field. Definitions that employ the notions of commensurability then become the basis for dialectical inquiry leading to an awareness of the Form of the Good. Mathematical studies are carried on for the sake of understanding the Form of the Good in that they stimulate the formulation of definitions of mathematical entities. These definitions become the raw material for the dialectical understanding of the Form of the Good.