"On the other hand, the categories of the understanding do not represent the conditions under which objects are given in perception; consequently, objects can certainly appear to us without their necessarily being related to functions of the understanding, and therefore without the understanding containing _a priori_ the conditions of these objects. Hence a difficulty appears here, which we did not meet in the field of sensibility, viz. how _subjective conditions of thought_ can have _objective validity_, i. e. can furnish conditions of the possibility of all knowledge of objects; for phenomena can certainly be given us in perception without the functions of the understanding. Let us take, for example, the conception of cause, which indicates a peculiar kind of synthesis in which on A something entirely different B is placed[6] according to a law. It is not _a priori_ clear why phenomena should contain something of this kind ... and it is consequently doubtful _a priori_, whether such a conception is not wholly empty, and without any corresponding object among phenomena. For that objects of sensuous perception must conform to the formal conditions of the sensibility which lie _a priori_ in the mind is clear, since otherwise they would not be objects for us; but that they must also conform to the conditions which the understanding requires for the synthetical unity of thought is a conclusion the cogency of which it is not so easy to see. For phenomena might quite well be so constituted that the understanding did not find them in conformity with the conditions of its unity, and everything might lie in such confusion that, e. g. in the succession of phenomena, nothing might present itself which would offer a rule of synthesis, and so correspond to the conception of cause and effect, so that this conception would be quite empty, null, and meaningless. Phenomena would none the less present objects to our perception, for perception does not in any way require the functions of thinking."[7]
This passage, if read in connexion with that immediately preceding it,[8] may be paraphrased as follows: 'The argument of the _Aesthetic_ assumes the validity of mathematical judgements, which as such relate to space and time, and thence it deduces the phenomenal character of space and time, and of what is contained therein. At the same time the possibility of questioning the validity of the law of causality, and of similar principles, may lead us to question even the validity of mathematical judgements. In the case of mathematical judgements, however, in consequence of their relation to perception, an answer is readily forthcoming. We need only reverse the original argument and appeal directly to the phenomenal character of space and time and of what is contained in them. Objects in space and time, being appearances, must conform to the laws according to which we have appearances; and since space and time are only ways in which we perceive, or have appearances, mathematical laws, which constitute the general nature of space and time, are the laws according to which we have appearances. Mathematical laws, then, constitute the general structure of appearances, and, as such, enter into the very being of objects in space and time. But the case is otherwise with the conceptions and principles underlying natural science. For the law of causality, for instance, is a law not of our perceiving but of our thinking nature, and consequently it is not presupposed in the presentation to us of objects in space and time. Objects in space and time, being appearances, need conform only to the laws of our perceiving nature. We have therefore to explain the possibility of saying that a law of our thinking nature must be valid for objects which, as conditioned merely by our perceiving nature, are independent of the laws of our thinking; for phenomena might be so constituted as not to correspond to the necessities of our thought.'