Plato’s dialectic as the exercise of pure thought

The mathematical sciences studied by the apprentice philosopher in The Republic are only a prelude to the crowning stage of the philosopher’s education, namely, the study of dialectic, leading to the intellectual apprehension of the Form of the Good. Mathematics is, indeed, the indispensable tool if students are to rise above a transient physical world and the partial information they can derive from delusive senses. Through the study of geometry, the mind reaches a conceptual understanding of plane and solid ...