Page:Mind (New Series) Volume 8.djvu/537

KANT'S PROOF OF THE PROPOSITION, ETC. 523 geometrical procedure ; yet, when need be, he is able ,to draw a good analogy between the science of Space and the science of symbols. " By means of a symbolical construction of quantity," he says, "Algebra arrives at results, which discursive cognition cannot hope to reach by the aid of mere conceptions, and in this way it resembles Geometry with its ostensive and geometrical construction (of the objects them- selves)." And if there be any inequalities in Kant's analysis of Algebra and Geometry, it is perfectly clear that to the author himself they seemed unimportant. He speaks of his estimate of mathematical judgments as if he knew it to be true of Mathematics throughout and honestly proved in the case of Definition, Axiom and Demonstrated Proposition, in Geometry, in Arithmetic and Algebra alike. The various distinct steps of this proof we have already mentioned in detail, the conclusion Kant draws is summed up in the words " Mathematical judgments are one and all synthetic " ; we have decided that not a single type of mathematical judgments was left out of Kant's consideration, and we only wish that, when critics examine the fitness of the premises to produce Kant's conclusion, they would abandon the old fallacy that the view taken of Mathematics in the Critique is carelessly partial or incomplete.