If by intelligible objects we understand things which can be thought by means of the pure categories, without the need of the schemata of sensibility, such objects are impossible. For the condition of the objective use of all our conceptions of understanding is the mode of our sensuous intuition, whereby objects are given; and, if we make abstraction of the latter, the former can have no relation to an object. And even if we should suppose a different kind of intuition from our own, still our functions of thought would have no use or signification in respect thereof. But if we understand by the term, objects of a non-sensuous intuition, in respect of which our categories are not valid, and of which we can accordingly have no knowledge (neither intuition nor conception), in this merely negative sense noumena must be admitted. For this is no more than saying that our mode of intuition is not applicable to all things, but only to objects of our senses, that consequently its objective validity is limited, and that room is therefore left for another kind of intuition, and thus also for things that may be objects of it. But in this sense the conception of a noumenon is problematical, that is to say, it is the notion of a thing of which we can neither say that it is possible, nor that it is impossible, inasmuch as we do not know of any mode of intuition besides the sensuous, or of any other sort of conceptions than the categories—a mode of intuition and a kind of conception neither of which is applicable to a non-sensuous object. We are on this account incompetent to extend the sphere of our objects of thought beyond the conditions of our sensibility, and to assume the existence of objects of pure thought, that is, of noumena, inasmuch as these have no true positive signification. For it must be confessed of the categories that they are not of themselves sufficient for the cognition of things in themselves and, without the data of sensibility, are mere subjective forms of the unity of the understanding. Thought is certainly not a product of the senses, and in so far is not limited by them, but it does not therefore follow that it may be employed purely and without the intervention of sensibility, for it would then be without reference to an object. And we cannot call a noumenon an object of pure thought; for the representation thereof is but the problematical conception of an object for a perfectly different intuition and a perfectly different understanding from ours, both of which are consequently themselves problematical. The conception of a noumenon is therefore not the conception of an object, but merely a problematical conception inseparably connected with the limitation of our sensibility. That is to say, this conception contains the answer to the question: “Are there objects quite unconnected with, and independent of, our intuition?”—a question to which only an indeterminate answer can be given. That answer is: “Inasmuch as