Page:Mind (New Series) Volume 8.djvu/527

 KANT'S PROOF OP THE PROPOSITION, ETC. 513 rect, and their " relations as greater or less," etc., properly understood, but the corresponding synthetic and intuitive retranslation of the signs into the concrete was defective. In Pure Geometry, on the other hand, we certainly do work with signs " by transposition, addition or subtraction, and other operations," but we retain throughout a concrete sense representation of our process from point to point in the figure which we construct, we are continually passing from mere signs to their meaning in the figure, and therefore in this case the same difficulty does not appear. Mathematics, Kant says in fact, always presupposes synthetic processes, yet its method may be largely analytical. Now this double view of the nature of mathematics in general continues to pervade Kant's work at least down to the publication of the first edition of the Critique. In the Dissertation of 1770, where " the distinction of Sense and Intellect had come to Kant's aid," his doctrine receives a new verbal setting, but in its essence it remains unchanged. The intuitive and synthetic procedure of Mathematics is represented as characteristic of the use of the faculty of sense, intellect proceeds by analysis. " Of the objects of the intellect," says Kant, " men are given no intuition, but only a symbolical cognition, and the use of the intellect is possible to us only by means of universal concepts in abstracto and not by singular instances in concrete." This use of the in- tellect through universal concepts in abstracto is the exact equivalent of the " Metaphysics," which Kant so clearly distinguished from geometry in his Monadologia Physica of 1756 and later in many detached passages. When the Geo- metrician sets out to prove that space is infinitely divisible he constructs a figure, in which he says : Draw an " infinite" number of straight lines from a fixed point. Using this symbolical figure in concreto, he sees intuitively that the division of Space must go on without end. The philosopher, on the other hand, argues that he can, in thought, remove all composition from a material body, which nevertheless must still consist of real substance, and therefore he con- cludes that, when all composition is removed nothing but simple substances are left. Here we have neither figures constructed, nor signs introduced, but from mere considera- tion of universals in abstracto the philosopher can draw his conclusion : All composite substances consist of simple parts. Such, in short, is the essence of Kant's earlier treatment of this ' Antinomy,' but now he can give a new colouring to his older outline. Philosophic procedure is concerned with the objects of intellect, mathematics with those of sense. But 33