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This chapter concentrates on the recognizable uses of Pythagorean material in Plato's own writings. The Socrates of the Gorgias and Republic differs from the Socrates of earlier dialogues in having a definite conception of what is properly beneficial for humans as such and thus of what constitutes human well-being. Earlier in the Gorgias, Callicles had ridiculed Socrates' suggestion that individuals capable of governing their own appetites and pleasures are regarded as superior and worthy of governing others. In the Gorgias Plato had focused on reason's control of the body's irrational desires, while in the Phaedo he emphasizes reason's impulse to fulfill its own proper desire. These two views coalesce in the Republic. The vision of the beautiful order of the cosmos itself as based upon mathematical principles deeply attracted Plato. Although there are intimations of such view in the Republic, it finds its fullest expression in the Philebus and Timaeus.
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