about these objects agree with the latter, when this agreement has not been in any way assisted by experience? In mathematics such procedure is legitimate, because its objects only _are_ quantities for us, and can only be represented as quantities, in so far as we can generate their representation by repeating a unit a number of times. Hence the concepts of quantity can be self-producing, and their principles can therefore be determined _a priori_. But when we ask how the understanding can form to itself completely _a priori_ concepts of things in their _qualitative_ determination, with which these things must of necessity agree, or formulate in regard to their possibility principles which are independent of experience, but with which experience must exactly conform,--we raise a question, that of the origin of the agreement of our faculty of understanding with the things in themselves, over which obscurity still hangs.”[808] The section before us represents the same general standpoint as that given in the above letter. Here, too, it is the validity of the _a priori_ concepts in reference to _things in themselves_ that is under consideration. The implication of Kant’s argument is that the categories, being neither determinable nor discoverable by means of experience, will only apply to appearances if they determine, or rather reveal, the actual non-experienced nature of things in themselves. These pure concepts, it is implied, owing to their combined _a priori_ and intellectual characteristics, make this inherent claim. Either they are altogether empty and illusory, or such unlimited validity must be granted to them. Kant, that is to say, still holds, as in the _Dissertation_, that sense-representations reveal things as they _appear_, intellectual representations things as they _are_. “We have either to surrender completely all claims to judgments of pure reason, in the most esteemed of all fields, that which extends beyond the limits of all possible experience, or we must bring this Critical investigation to perfection.”[809] The pure concepts, unlike space, “apply to objects generally, apart from the conditions of sensibility.”[810] But here also, as in the letter to Herz, the strange and problematic character of such knowledge is clearly recognised.