The influence of mathematics on Plato's moral theory

"In his ''Moral Theory'' Plato developed and justified views on the best way for humans to live, and to set up and regulate societies in the light of their understanding of their own needs and limitations. These views are presented in his dialogues. The study of the influence of mathematics on Plato''s dialogues, and hence on his moral theory, is not a matter of tracing the effects of contemporary mathematics on particular arguments or styles of argument. The dialogues are stimulants to thought, not presentations of finished theses in a dialectical dress. The introduction of mathematical ideas into the dialogues is to be explained on educational grounds, as contributing to philosophical understanding..."