Mathematics and etiology never penetrate the inner nature of things, since the thing in itself is never reducible to the form of the principle of sufficient reason
Even if mathematics gives exhaustive cognition of the spatial and temporal relations of appearances and etiology gives completely the lawful conditions under which they enter time and space, with their help we never penetrate into the inner nature of things: the thing in itself, which in appearing presents the phenomena, is in its appearance wholly subject to the principle of sufficient reason but itself never reducible to that form, and so is not to be explained etiologically down to the last nor ever fathomed completely.
so dringen wir mit deren Hülfe doch nimmermehr in das innere Wesen der Dinge
with their help we still never penetrate into the inner nature of things
Denn es ist eben das Ding an sich, welches, indem es erscheint, jene Phänomene darstellt, von ihnen selbst gänzlich verschieden, zwar in seiner Erscheinung dem Satz vom Grund, als der Form der Vorstellung, völlig unterworfen, selbst aber nie auf diese Form zurückzuführen, und daher nicht ätiologisch bis auf das Letzte zu erklären, nicht jemals vollständig zu ergründen
For it is precisely the thing in itself which, in appearing, presents those phenomena, wholly different from them itself, in its appearance indeed completely subject to the principle of sufficient reason as the form of the representation, but itself never reducible to this form, and therefore not to be explained etiologically down to the last, never to be fathomed completely
§ 24, second paragraph, the sentences from »Wenn daher auch alle Mathematik«. The first is a concession, »wenn auch ... so dringen wir ... doch nimmermehr«, and the statement keeps it as »even if«; what remains for every explanation to presuppose, the forces of nature, »das Grundlose«, is in the passage and not in the statement. The third sentence, »Denn es ist eben das Ding an sich«, gives the ground, and the statement joins the two by a colon where the text has »Denn«; the step is not formalized. The claim concerns explanation by the sciences, not inference: what § 19 says of the law of causality, that it never leads beyond representation (c-schopenhauer-causality-never-leads-beyond-representation), is a different sentence, and the map links neither to the other. »Qualitates occultae« and »Aetiologie« are Schopenhauer's; »etiology« follows them.