to numbers, even this distinction of juxtaposition no longer exists. Here, as with conceptions, absolutely nothing but the identitas indiscernibilium remains : for there is but one five and one seven. And in this we may perhaps also find a reason why 7 + 5 = 12 is a synthetical proposition a priori, founded upon intuition, as Kant profoundly discovered, and not an identical one, as it is called by Herder in his "Metakritik". 12 = 12 is an identical proposition.
In Geometry, it is therefore only in dealing with axioms that we appeal to intuition. All the other theorems are demonstrated : that is to say, a reason of knowing is given, the truth of which everyone is bound to acknowledge. The logical truth of the theorem is thus shown, but not its transcendental truth (v. §§ 30 and 32), which, as it lies in the reason of being and not in the reason of knowing, never can become evident excepting by means of intuition. This explains why this sort of geometrical demonstration, while it no doubt conveys the conviction that the theorem which has been demonstrated is true, nevertheless gives no insight as to why that which it asserts is what it is. In other words, we have not found its Reason of Being ; but the desire to find it is usually then thoroughly roused. For proof by indicating the reason of knowledge only effects conviction (convictio), not knowledge (cognitio) : there fore it might perhaps be more correctly called elenchus than demonstratio. This is why, in most cases, therefore, it leaves behind it that disagreeable feeling which is given by all want of insight, when perceived ; and here, the want of knowledge why a thing is as it is, makes itself all the more keenly felt, because of the certainty just attained, that it is as it is. This impression is very much like the feeling we have, when something has been conjured into or out of our pocket, and we cannot conceive how. The reason of knowing which, in such demonstrations as these, is given without the reason of being, resembles
