CONCLUSIONS FROM THE ABOVE CONCEPTS[461]
Conclusion a.—Thesis: Space is not a property of things in themselves,[462] nor a relation of them to one another. Proof: The properties of things in themselves can never be intuited prior to their existence, i.e. a priori. Space, as already proved, is intuited in this manner. In other words, the apriority of space is by itself sufficient proof of its subjectivity.
This argument has been the subject of a prolonged controversy between Trendelenburg and Kuno Fischer.[463] Trendelenburg was able to prove his main point, namely, that the above argument is quite inconclusive. Kant recognises only two alternatives, either space as objective is known a posteriori, or being an a priori representation it is subjective in origin. There exists a third alternative, namely, that though our intuition of space is subjective in origin, space is itself an inherent property of things in themselves. The central thesis of the rationalist philosophy of the Enlightenment was, indeed, that the independently real can be known by a priori thinking. Even granting the validity of Kant’s later conclusion, first drawn in the next paragraph, that space is the subjective form of all external intuition, that would only prove that it does not belong to appearances, prior to our apprehension of them; nothing is thereby proved in regard to the character of things in themselves. We anticipate by a priori reasoning only the nature of appearances, never the constitution of things in themselves. Therefore space, even though a priori, may belong to the independently real. The above argument cannot prove the given thesis.
Vaihinger contends[464] that the reason why Kant does not even attempt to argue in support of the principle, that the a priori must be purely subjective, is that he accepts it as self-evident. This explanation does not, however, seem satisfactory. But Vaihinger supplies the data for modification of his own assertion. It was, it would seem, the existence of the antinomies which first and chiefly led Kant to assert the subjectivity of space and time.[465] For as he then believed that a satisfactory solution of the antinomies is possible only on the assumption of the subjectivity of space and time, he regarded their subjectivity as being conclusively established, and accordingly failed to examine with sufficient care the validity of his additional proof from their apriority. This would seem to be confirmed by the fact that when later,[466] in reply to criticisms of the arguments of the first edition, he so far modified his position as to offer reasons in support of the above general principle, even then he nowhere discussed the principle in reference to the forms of sense. All his discussions concern only the possible independent reality of the forms of thought.[467] To the very last Kant would seem to have regarded the above argument as an independent, and by itself a sufficient, proof of the subjectivity of space.
The refutation of Trendelenburg’s argument which is offered by Caird[468] is inconclusive. Caird assumes the chief point at issue, first by ignoring the possibility that space may be known a priori in reference to appearances and yet at the same time be transcendently real; and secondly by ignoring the fact that to deny spatial properties to things in themselves is as great a violation of Critical principles as to assert them. One point, however, in Caird’s reply to Trendelenburg calls for special consideration, viz. Caird’s contention that Kant did actually take account of the third alternative, rejecting it as involving the “absurd” hypothesis of a pre-established harmony.[469] Undoubtedly Kant did so. But the contention has no relevancy to the point before us. The doctrine of pre-established harmony is a metaphysical theory which presupposes the possibility of gaining knowledge of things in themselves. For that reason alone Kant was bound to reject it. A metaphysical proof of the validity of metaphysical judgments is, from the Critical point of view, a contradiction in terms. As the validity of all speculations is in doubt, a proof which is speculative cannot meet our difficulties. And also, as Kant himself further points out, the pre-established harmony, even if granted, can afford no solution of the Critical problem how a priori judgments can be passed upon the independently real. The judgments, thus guaranteed, could only possess de facto validity; we could never be assured of their necessity.[470] It is chiefly in these two inabilities that Kant locates the “absurdity” of a theory of pre-established harmony. The refutation of that theory does not, therefore, amount to a disproof of the possibility which we are here considering.
Conclusion b.—The next paragraph maintains two theses: (a) that space is the form of all outer intuition; (b) that this fact explains what is otherwise entirely inexplicable and paradoxical, namely, that we can make a priori judgments which yet apply to the objects experienced. The first thesis, that the pure intuition of space is only conceivable as the form of appearances of outer sense, is propounded in the opening sentence without argument and even without citation of grounds. The statement thus suddenly made is not anticipated save by the opening sentences of the section on space.[471] It is an essentially new doctrine. Hitherto Kant has spoken of space only as an a priori intuition. The further assertion that as such it must necessarily be conceived as the form of outer sense (i.e. not only as a formal intuition but also as a form of intuition), calls for the most definite and explicit proof. None, however, is given. It is really a conclusion from points all too briefly cited by Kant in the general Introduction, namely, from his distinction between the matter and the form of sense. The assertions there made, in a somewhat casual manner, are here, without notification to the reader, employed as premisses to ground the above assertion. His thesis is not, therefore, as by its face value it would seem to profess to be, an inference from the points established in the preceding expositions. It interprets these conclusions in the light of points considered in the Introduction; and thereby arrives at a new and all-important interpretation of the nature of the a priori intuition of space.
The second thesis employs the first to explain how prior to all experience we can determine the relations of objects. Since (a) space is merely the form of outer sense, and (b) accordingly exists in the mind prior to all empirical intuition, all appearances must exist in space, and we can predetermine them from the pure intuition of space that is given to us a priori. Space, when thus viewed as the a priori form of outer sense, renders comprehensible the validity of applied mathematics.
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.