case the mathematical laws and the concepts of magnitude and causality are valid for all perceptions. Only such abstract propositions as formulate the very conditions of experience are synthetic propositions a priori. Whenever we are able to discover and express the conditions of experience we come upon propositions which are propositions of pure reason, because they are based on the pure forms of our knowledge, and which must nevertheless be valid for all experience.
The whole content of experience is conceived in space and time. Hence since pure mathematics really does nothing more than develop the laws of space and time, it must be valid for every possible content of experience, every possible perception. But this demonstration likewise involves a limitation: namely, mathematics is valid only for phenomena, i. e. only for things as we conceive them, not for things-in-themselves. We have no right to make the conditions of our conception the conditions of things-in-themselves. Time and space can be conceived only from the view-point of man.
Experience not only implies that we conceive something in space and time, but likewise that we are able to combine what is given in space and time in a definite way, i. e. as indicated in the concepts of magnitude and causality. This is the only means of distinguishing between experience and mere representation or imagination. All extensive and intensive changes must proceed continuously, i. e. through every possible degree of extension and intensity, otherwise we could never be certain of having any real experience. Gaps and breaks must be impossible (non datur hiatus non datur saltus). The origin of each particular phenomenon moreover must be conditioned by certain other phenomena,—analogous to the way in which
