Lecture III

Even in such a book as his Ethics, the philosopher Spinoza placed great value on presenting his philosophical principles and postulates, if not in mathematical formulae—for actual calculations play no special part—yet in such a manner that the whole form of drawing conclusions, of deducing the later rules from earlier ones, is based on the mathematical pattern. By and by it appeared self-evident to the men of that time that in mathematics they had the right model for the attainment of inward certainty. Hence they felt that if they could express the world in thoughts arranged in the same clear-cut architectural order as in a mathematical or geometrical system, they would thereby achieve something that would have to correspond to reality. If the character of scientific thinking is to be correctly understood, it must be through the special way in which man relates to mathematics and mathematics relates to reality. Mathematics had gradually become what I would term a self-sufficient inward capacity for thinking. What do I mean by that?