=Proof that the above View of Space and Time is not a mere Hypothesis, but completely certain.=[579]--The proof, which as here recapitulated and developed follows the analytic method, has already been considered in connection with A 39 = B 56. It proceeds upon the assumption that space cannot be both an _a priori_ form of intuition and also independently real. The argument as a whole lacks clearness owing to Kant’s failure to distinguish between the problems of pure and applied geometry, between pure intuition and form of intuition. This is especially obvious in the very unfortunate and misleading second application of the triangle illustration.[580] Kant’s tendency to conceive mathematical science almost exclusively in terms of geometry is likewise illustrated. “There is in regard to both [space and time] a large number of _a priori_ apodictic and synthetic propositions. This is especially true of space, which for this reason will be our chief illustration in this enquiry.”[581] =II. Paragraphs added in the Second Edition.=[582]--Kant proceeds to offer further proof of the ideality of the appearances (_a_) of outer and (_b_) of inner sense. Such proof he finds in the fact that these appearances consist solely of relations. (_a_) Outer appearances reduce without remainder to relations of position in intuition (_i.e._ of extension), of change of position (motion), and to the laws which express in merely relational terms the motive forces by which such change is determined. What it is that is thus present in space, or what the dynamic agencies may be to which the motion is due, is never revealed. But a real existent (_Sache an sich_) can never be known through mere relations. Outer sense consequently reveals through its representations only the relation of an object to the subject, not the intrinsic inner nature of the object in itself (_Object an sich_). Kant’s avoidance of the term _Ding an sich_ may be noted.[583] (_b_) The same holds true of inner sense, not only because the representations of outer sense constitute its proper (_eigentlichen_) material, but also because time, in which these are set, contains only relations of succession, coexistence, and duration. This time (which as consisting only of relations can be nothing but a form[584]) is itself, in turn, a mere relation. It is only the manner in which through its own activity the mind is affected by itself. But in order to be affected by itself it must have receptivity, in other words, sensibility. Time, consequently, must be regarded as the form of this inner sense.