Book 3: Chapter 31, The Philosophy of Logical Summary and Analysis

Since Pythagoras philosophy involved thoughts inspired by mathematics on one hand, and empirical sciences on the other. Mathematical group involved Plato, Thomas de Aquinas, Spinoza, and Kant, while Democritus, Aristotle and Locke were part of empiricism. The modern school of philosophy eliminated Pythagoreanism from mathematics, while empiricism was included as part of deductive elements. Although the goals of such undertaking were not impressive, the results could be judged as solid.

In the seventeenth century, mathematicians abandoned the foundations of analytical geometry, and the infinitesimal calculus to obtain quicker results. Although Leibniz adhered to infinitesimals, and it was useful in his metaphysics, it was less functional in mathematics. Weierstrass established the calculus without infinitesimals, while Georg Cantor developed continuity theory and infinite number. Cantor thought that continuity was needed, which led to...