it stands, it is nothing more than an indication of the present condition of the problem, without any other positive contribution than the suggestion regarding the Clarke-Leibniz dispute. I hope at no distant day to publish studies on the history of Kant's development which will explain from the Reflexionen the transformation in Kant's views between 1768 and 1770. According to my results, the material before us in the Reflexionen can only be explained by supposing that Hume furnished the impulse and tendency for this transformation, while the antinomies conditioned the particular solution of the problem. A bibliography of special literature, especially of that which is concerned with Eberhard's controversies and with the dispute between Trendelenburg and Fischer, form the concluding part of the work.
I must still pause a few moments to consider Kant's attitude towards the problems of pure and applied mathematics. Vaihinger gives the following exposition (p. 333) of Kant's views on these points, as they appear in the first edition (R Va) in the section on space. "1) Kant proves first of all as his first double proposition that space is an a priori and a perceptive idea [Vorstellung]. 2) There results, as an interpolated inference from this proposition, the explanation of the propositions of pure mathematics as necessary [third space argument], and synthetic [conclusion of the fourth space argument]. 3) Then the second double proposition is propounded and proven [?], viz., that space does not belong to things-in-themselves, but is the form of the phenomena of the external sense. 4) The explanation of the validity of the application of pure mathematics to objects of experience follows from this second proposition" [in "Inferences from the above Notions," b, end of the first section = R Vb, p. 42]. In the third division of § 7, the problems of pure and applied mathematics are, according to Vaihinger, confused with each other, while in the last two divisions of No. I, in § 8, they are professedly treated separately. The treatment in the Prolegomena, §§ 6-13, is confused from the point where a transition must have been made in "Conclusions from the Transcendental Æsthetic," and in § 3 of the second edition (Transcendental Explanation). § 3, the first two sections of which deal with pure mathematics, and the third which deals with applied mathematics—by treating of applied mathematics before reaching the "conclusions," and consequently before its possibility has yet been proven, interrupts, according to Vaihinger, in a very provoking manner, the thought of R Va, which is by no means clear but which can still be followed.
