received from sense. Nay, such a priori principles are necessary to the very possibility of our sense-experience. Otherwise, it would have no certainty, but remain a collection of contingent rules; and how could we then say, for example, Every change must have a cause? But apart from common sense, we have, in the sciences of mathematics and physics, judgments which are universal and necessary. Experience could not so stamp them. They must therefore be a priori. They are also synthetic. Neither experience nor analysis can prove, for example, that 7+5=12, or that in the communication of motion, action and reaction are always alike. Nor is the number of such propositions scanty. Mathematics is made up entirely of synthetic judgments a priori. Furthermore, not merely judgments, but even certain ideas, may claim for themselves an a priori origin. Of these it will here suffice to mention space and substance. But what is still more extraordinary is this, that we have a whole class of a priori synthetic judgments which in no way enter into our sense-experience or can be brought to any of its tests. This is metaphysics. And it is in this very kind of knowledge which transcends the world of the senses, and where experience can neither guide nor correct us, that reason finds its most important, its loftiest, and its most imperative problems. These unavoidable problems of pure reason are God, Free Will, and Immortality.
But just there is the rub. A science built on other foundation than the solid ground of experience and constructed of materials whose origin and worth no man knows, is surely a precarious edifice. But two circumstances have hitherto saved it from attack. In the first place, human reason is naturally constructive rather than critical. And, in the second place, the brilliant example of mathematics has created a presumption in favor of every kind of a priori knowledge; and the all-important point was overlooked that while mathematics deals with objects only that are capable of sense-presentation, metaphysics reaches out to objects which are beyond the grasp of any experience. But the time has now arrived to inquire whence this metaphysical knowledge is derived, and to test its truth, value, and
