Thursday, November 04, 2004

Plato: Mathematics Would Reveal the Structure of the World

We should ask why Plato's theory is so progressive, why Aristotle's is so archaic, and why Plato is usually given so little credit for his theory. The answer to all these is the same: Plato comes up with this kind of theory because of his Pythagorean faith that mathematics would reveal the structure of the world. Aristotle had no such faith, regarding mathematics only as a calculating device (the common opinion in the Middle Ages). In turn, Plato is usually overlooked by down-to-earth philosophers and historians of science because his Pythagorean number mysticism seems to them of a piece with the rest of his philosophy, which they regard as, in general, a mysticism unworthy of consideration. Yet modern science, which is distinctively mathematical, was set on its way by just those scientists, like Galileo Galilei and Johannes Kepler, who shared Plato's mystical faith in mathematics. That is the most conspicuous in Kepler, whose flights of fancy, which included a science fiction book about life on the Moon (the Somnium or "Dream"), are found together with the most serious, hard mathematical breakthrough in the formulation of modern astronomy short of Isaac Newton's own theory of universal gravitation: Kepler's Three Laws of planetary motion.

This view of God seems to be prevalent in todays views that I have yet to produce John Baez's view, as has been previously suggested.

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