The fact that a part of our cognitions is a priori admits of no other explanation than that these constitute the forms of our intellect

The passage

The fact, strictly proved by Kant, that we are conscious of a part of our cognitions a priori admits of no other explanation than that these constitute the forms of our intellect; indeed this is less an explanation than merely the plain expression of the fact itself.

The third sentence of the paragraph, the thesis the rest of it argues: the next sentence opens with »Denn« and the chain that follows, from what a priori means to the intellect's own forms, is formalized as a-schopenhauer-cognitions-a-priori-are-the-intellects-own-forms, whose conclusion is the paragraph's »Demnach« sentence (c-schopenhauer-cognitions-a-priori-and-forms-of-the-intellect-two-expressions-for-one-thing). The statement keeps both halves, the uniqueness of the explanation, »gar keine andere Erklärung ... als«, and the correction, »weniger eine Erklärung, als eben nur der deutliche Ausdruck der Thatsache selbst«; neither is a premise of the argument, which proves the synonymy and not the uniqueness. »Diese« are the a priori cognitions, the part named in the fact. The Schopenhauer sentence that says the same of space in particular is the appendix's »eine a priori gegebene, folglich subjektive Form unsers Intellekts« (c-schopenhauer-causality-sensation-and-space-are-subjective), on which the sharing with Kant is set; this general statement names no form, and the comparison x-thing-in-itself says why no link is set on it.