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The ground of the distinction of all objects in general into Phenomena and Noumena

[1] All concepts, and with them all principles, even such as are possible a priori, relate to empirical intuitions, that is, to the data for a possible experience. Apart from this relation they have no objective validity, and in respect of their representations are a mere play of imagination or of understanding.

[2] Take, for instance, the concepts of mathematics, considering them first of all in their pure intuitions. Space has three dimensions; between two points there can be only one straight line, etc. Although all these principles, and the representation of the object with which this science occupies itself, are generated in the mind completely a priori, they would mean nothing, were we not always able to present their meaning in appearances, that is, in empirical objects. We therefore demand that a bare concept be made sensible, that is, that an object corresponding to it be presented in intuition. Otherwise the concept would, as we say, be without sense, that is, without meaning.

[3] We cannot define [anything] in any real fashion, that is, make the possibility of [an] object understandable, without at once descending to the conditions of sensibility, and so to the form of appearances to which, as their sole objects, they must consequently be limited.

[4] If I omit from the concept of cause the time in which something follows upon something else in conformity with a rule... [we would] be unable to distinguish cause and effect from one another.

[5] There is something strange and even absurd in the assertion that there should be a concept which possesses a meaning and yet is not capable of any explanation. But the categories have this peculiar feature, that only in virtue of the general condition of sensibility can they possess a determinate meaning and relation to any object... But they cannot themselves be defined.

[6] Accordingly the Transcendental Analytic leads to this important conclusion... the understanding can never transcend those limits of sensibility within which alone objects can be given to us. Its principles are merely rules for the exposition of appearances.

[7] Thought is the act which relates given intuition to an object... Thus the categories, apart from the condition of sensible intuition... have no relation to any determinate object, cannot therefore define any object, and so do not in themselves have the validity of objective concepts.

[8] It therefore follows that the pure category does not suffice for a synthetic a priori principle, that the principles of pure understanding are only of empirical, never of transcendental employment, and that outside the field of possible experience there can be no synthetic a priori principles.

[9] Since, then, as pure categories merely, they are not to be employed empirically, and cannot be employed transcendentally, they cannot, when separated from all sensibility, be employed in any manner whatsoever... They are the pure form of the employment of understanding in respect of objects in general, that is, of thought; but since they are merely its form, through them alone no object can be thought or determined.

[10] Appearances, so far as they are thought as objects according to the unity of the categories, are called phenomena. But if I postulate things which are mere objects of understanding [but] not to one that is sensible... such things would be entitled noumena (intelligibilia).

[11] But we are here subject to an illusion from which it is difficult to escape. The categories are not, as regards their origin, grounded in sensibility... As a matter of fact they are nothing but forms of thought.

[12] Now we must bear in mind that the concept of appearances... justifies the division of objects into phenomena and noumena, and so of the world into a world of the senses and a world of the understanding... [and that these are] in themselves generically distinct from one another. For if the senses represent to us something merely as it appears, this something must also in itself be a thing, and an object of a non-sensible intuition, that is, of the understanding.

[13] Appearances are nothing but representations... [The] transcendental object cannot be separated from the sense data, for nothing is then left through which it might be thought. Consequently it is not in itself an object of knowledge, but only the representation of appearances... At the same time the understanding is well aware that in viewing things in this manner... it cannot make any use of the categories. For the categories have meaning only in relation to the unity of intuition in space and time... In cases where this unity of time is not to be found, and therefore in the case of the noumenon, all employment, and indeed the whole meaning of the categories, entirely vanishes; for we have then no means of determining whether things in harmony with the categories are even possible.

[14] The categories represent no special object... but only serve to determine the transcendental object.

[15] 'Noumenon' must be understood as being such only in a negative sense. If I remove from empirical knowledge all thought (through categories), no knowledge of any object remains... There thus results the concept of a noumenon. It is not of anything, but signifies only the thought of something in general.

[16] But in order that a noumenon may signify a true object... [we must]surely have ground for assuming another kind of intuition... [We cannot argue that] sensible intuition is the only possible intuition, but only that it is so for us. But neither have we been able to prove that another kind of intuition is possible... If the objective reality of a concept cannot be in any way known... I entitle that concept problematic. The concept of a noumenon - that is, of a thing which is not to be thought as object of the senses but as a thing in itself, solely through a pure understanding - is not in any way contradictory. For we cannot assert of sensibility that it is the sole possible kind of intuition... [However], it is still an open question whether [in] the notion of a noumenon... any object whatsoever is left.

[17] I cannot think [of the noumenon] through any category; for a category is valid [only] for empirical intuition... We are unable to comprehend how such noumena can be possible, and the domain that lies out beyond the sphere of appearances is for us empty. That is to say, we have an understanding which problematically extends further, but we have no intuition, indeed not even the concept of a possible intuition, through which objects outside the field of sensibility can be given, and through which the understanding can be employed assertorically beyond that field. The concept of a noumenon is thus a merely limiting concept, the function of which is to curb the pretensions of sensibility; and it is therefore only of negative employment. At the same time it is no arbitrary invention; it is bound up with the limitation of sensibility, though it cannot affirm anything positive beyond the field of sensibility.

[18] What our understanding acquires through this concept of a noumenon, is a negative extension; that is to say, understanding is not limited through sensibility; on the contrary, it itself limits sensibility by applying the term noumena to things in themselves (things not regarded as appearances). But in so doing it at the same time sets limits to itself, recognising that it cannot know these noumena through any of the categories, and that it must therefore think them only under the title of an unknown something.

[19] Such objects of pure understanding will always remain unknown to us; we can never even know whether such a transcendental or exceptional knowledge is possible under any conditions - at least not if it is to be the same kind of knowledge as that which stands under our ordinary categories.

[20] [All this does is to show the] limitation of empirical principles, without itself containing or revealing any other object of knowledge beyond the sphere of those principles.