As we have already noted,[472] Kant in the second edition obscures the sequence of his argument by offering in the new transcendental exposition a justification of applied as well as of pure geometry. In so doing he anticipates the conclusion which is first drawn in this later paragraph. This would have been avoided had Kant given two separate transcendental expositions. First, an exposition of pure mathematics, placed immediately after the metaphysical exposition; for pure mathematics is exclusively based upon the results of the metaphysical exposition. And secondly, an exposition of applied mathematics, introduced after _Conclusion b_. The explanation of applied geometry is really the more essential and central of the two, as it alone involves the truly Critical problem, how judgments formed _a priori_ can yet apply to objects. _Conclusion b_ constitutes, as Vaihinger rightly insists,[473] the very heart of the _Aesthetic_. The arrangement of Kant’s argument diverts the reader’s attention from where it ought properly to centre. The use which Kant makes of the _Prolegomena_ in his statement of the new transcendental exposition is one cause of the confusion. The exposition is a brief summary of the corresponding _Prolegomena_[474] sections. In introducing this summary into the _Critique_ Kant overlooked the fact that in referring to applied mathematics he is anticipating a point first established in _Conclusion b_. The real cause, however, of the trouble is common to both editions, namely Kant’s failure clearly to appreciate the fundamental distinction between the view that space is an _a priori_ intuition and the view that it is the _a priori_ form of all external intuition, _i.e._ of outer sense. He does not seem to have fully realised how very different are those two views. In consequence of this he fails to distinguish between the transcendental expositions of pure and applied geometry.[475] =Third paragraph.=--Kant proceeds to develop the subjectivist conclusions which follow from _a_ and _b_. “We may say that space contains all things which can appear to us externally, but not all things in themselves, whether intuited or not, nor again all things intuited by any and every subject.”[476] This sentence makes two assertions: (_a_) space does not belong to things in and by themselves; (_b_) space is not a necessary form of intuition for all subjects whatsoever.