Detail the Pythagorean influence on Plato's philosophy here.
Pythagorean thought profoundly shaped Plato's philosophy, particularly in the realms of metaphysics, cosmology, and education: 1. **Theory of Forms**: The Pythagoreans believed that numbers were the fundamental principles of reality. Plato extended this idea into his Theory of Forms, where abstract, immutable entities (Forms) exist beyond sensory perception. Mathematical truths, which are independent of the physical world, exemplify the perfection and permanence of these Forms. 2. **Cosmology**: In *Timaeus*, Plato describes the universe as an ordered, geometric entity, reflecting Pythagorean ideas of mathematical harmony. He explains that the Demiurge (divine craftsman) structured the cosmos using mathematical principles, including the Platonic solids, emphasizing numerical ratios as the foundation of cosmic balance. 3. **Education**: Plato's emphasis on mathematical training as a path to philosophical enlightenment stems from Pythagorean thought. In *The Republic*, he outline...