Wednesday, June 27, 2007

Philosophy of Mathematics

Socrates, in Plato's Republic, requires the guardians of the ideal city-state to study mathematics for ten years before proceeding to dialectic, philosophy, and political theory, as part of their training to become philosopher-kings. Plato reportedly ran afoul of Dionysius II, the tyrant of Syracuse, when he tried to convince the willful young ruler that to become a philosopher-king, as he was inspired by Plato's writings to do, he would first need to spend many years studying geometry. After a few impatiently received lessons in mathematics, Plato is supposed to have fled for his life to escape the tyrant's wrath. Socrates' pedagogical progression, reflected in Plato's analogy of the divided line, embodies the conviction that after their gymnastic and musical training has prepared them for serious education as soldiers and leaders, the guardians will be best able to govern if the have first grasped the Form of the Good. To attain this distant goal, the guardians must come to understand the nature of Forms generally through a recognition of other Forms, made possible through the study of mathematics. As Socrates says of mathematics in learning to grasp the Forms, the study of calculation 'draws the soul toward the truth.'

"Mathematics and Philosophy of Mathematics," Dale Jacquette
Introduction to Philosophy of Mathematics: An Anthology, edited by Jacquette

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