One can, indeed, adduce many examples of such fallacies and inaccuracies in Kant; nevertheless, such an accusation will only be justifiable when all other explanations have failed. In this case, the difficulty may, however, be removed, or at least much lessened, if we assume that Kant was neither able nor did he wish to distinguish the problems of pure and applied mathematics. The following considerations led to this conclusion: 1) In the first division of No. b (R Vb, p. 42) no new proposition is advanced, much less proven, but we have only the psychological explanation that space can only be thought as an a priori perception if one regards it as the form of perception. The assertion had already been made—though without proof—in § 1, that pure perception [reine Anschauung] and the form of sensibility [Anschauung] are identical. If the first two space arguments prove that space is an a priori necessary idea, then 'a priori' signifies not only 'before all experience,' and 'independent of all experience,' but also 'valid for all experience, and consequently for the objects of experience.' The conclusion of the first division of b contains nothing, therefore, which had not been already said in the third space argument of R Va.
2) It is impossible to understand this latter argument as referring only to pure mathematics as Vaihinger does. Its arrangement would in that case be the very worst conceivable. It would have been necessary to combine it in one division with the last proposition of the fourth space argument in R Va. And the proof that space is a perceptive magnitude must necessarily have preceded this division. The apodictic character of which the third argument treats is equivalent to objective validity; its opposite is the comparative universality of experience which has been gained by induction from individual cases, and which has reference to individual objects.
3) The same is true in § 3. Here also the discussion of the third division furnishes no new problem, but only repeats in a brief résumé the explanation already given, and adds to it the psychological explanation appearing first in No. b of 'conclusions' (also taken again from § 1), and also insists on the equivalence of pure perception with the form of perception. The first two divisions of § 3 deal just as much with applied mathematics as the third does. The distinctions which Vaihinger brings to light deal only with artificial refinements of the text, and he here seems to forsake for the sake of a favorite hypothesis the sound exegetical principles which had elsewhere guided him. This hypothesis is shown to be
