Plato (427 BC - 347 BC)

Appeared in: Lecture 1,3.

Greek philosopher who was a student and follower of Socrates . He founded the Academy school in Athens. His works consisted of "dialogs" between Socrates and others. Like Socrates , he was interested in moral, not natural philosophy. He believed that the heads of government should be "philosopher kings" and developed a course of study stressing abstract thought for their education in the Republic. Plato advocated the "quadrivium" (the four math fields of study in the liberal arts), which starts with arithmetic, then progresses to plane geometry, solid geometry, and finally astronomy and harmonics. Plato believed that knowledge was "forgotten" at birth, and could be remembered. He saw the search for understanding as an attempt to gain pure knowledge, or "forms." In Eikos Mythos (A Likely Story), he said that cosmology is, at best, a likely account. In Timaeus, he presented his cosmology , which consisted of forms, particular objects, God the Craftsman, absolute space, and brute matter. As a craftsman, God could not make a perfect world from imperfect material.

Plato believed all substances to be composed of air, earth, fire, and water. He believed in a spherical Earth which was the center of his universe, and a motion of planets along crystalline spheres. Plato invented a theory of vision involving three streams of light: one from the what is being seen, one from the eyes, and one from the illuminating source. In keeping with his belief that philosophy should be pursued for the attainment of pure knowledge, he proposed studying astronomy as an exact mathematical science based on the assumption that motions were regular and circular. He wanted to discover the truth behind appearances, but believed that absolute truth could not be derived.

Plato also described the five regular solids, the tetrahedron , cube , octahedron , dodecahedron , and icosahedron , now known as the Platonic solids .

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Plato picture taken from MacTutor History of Mathematics Archive .

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