Geometry, nevertheless, advances steadily and securely in the province of pure a priori cognitions, without needing to ask from philosophy any certificate as to the pure and legitimate origin of its fundamental conception of space.But the use of the conception in this science extends only to the external world of sense, the pure form of the intuition of which is space; and in this world, therefore, all geometrical cognition, because it is founded upon a priori intuition, possesses immediate evidence, and the objects of this cognition are given a priori (as regards their form) in intuition by and through the cognition itself.With the pure conceptions of understanding, on the contrary, commences the absolute necessity of seeking a transcendental deduction, not only of these conceptions themselves, but likewise of space, because, inasmuch as they make affirmations concerning objects not by means of the predicates of intuition and sensibility, but of pure thought a priori, they apply to objects without any of the conditions of sensibility.Besides, not being founded on experience, they are not presented with any object in a priori intuition upon which, antecedently to experience, they might base their synthesis.Hence results, not only doubt as to the objective validity and proper limits of their use, but that even our conception of space is rendered equivocal; inasmuch as we are very ready with the aid of the categories, to carry the use of this conception beyond the conditions of sensuous intuition- and, for this reason, we have already found a transcendental deduction of it needful.The reader, then, must be quite convinced of the absolute necessity of a transcendental deduction, before taking a single step in the field of pure reason; because otherwise he goes to work blindly, and after he has wondered about in all directions, returns to the state of utter ignorance from which he started.He ought, moreover, clearly to recognize beforehand the unavoidable difficulties in his undertaking, so that he may not afterwards complain of the obscurity in which the subject itself is deeply involved, or become too soon impatient of the obstacles in his path; because we have a choice of only two things- either at once to give up all pretensions to knowledge beyond the limits of possible experience, or to bring this critical investigation to completion.
We have been able, with very little trouble, to make it comprehensible how the conceptions of space and time, although a priori cognitions, must necessarily apply to external objects, and render a synthetical cognition of these possible, independently of all experience.For inasmuch as only by means of such pure form of sensibility an object can appear to us, that is, be an object of empirical intuition, space and time are pure intuitions, which contain a priori the condition of the possibility of objects as phenomena, and an a priori synthesis in these intuitions possesses objective validity.
On the other hand, the categories of the understanding do not represent the conditions under which objects are given to us in intuition; objects can consequently appear to us without necessarily connecting themselves with these, and consequently without any necessity binding on the understanding to contain a priori the conditions of these objects.Thus we find ourselves involved in a difficulty which did not present itself in the sphere of sensibility, that is to say, we cannot discover how the subjective conditions of thought can have objective validity, in other words, can become conditions of the possibility of all cognition of objects;for phenomena may certainly be given to us in intuition without any help from the functions of the understanding.Let us take, for example, the conception of cause, which indicates a peculiar kind of synthesis, namely, that with something, A, something entirely different, B, is connected according to a law.It is not a priori manifest why phenomena should contain anything of this kind (we are of course debarred from appealing for proof to experience, for the objective validity of this conception must be demonstrated a priori), and it hence remains doubtful a priori, whether such a conception be not quite void and without any corresponding object among phenomena.For that objects of sensuous intuition must correspond to the formal conditions of sensibility existing a priori in the mind is quite evident, from the fact that without these they could not be objects for us; but that they must also correspond to the conditions which understanding requires for the synthetical unity of thought is an assertion, the grounds for which are not so easily to be discovered.For phenomena might be so constituted as not to correspond to the conditions of the unity of thought; and all things might lie in such confusion that, for example, nothing could be met with in the sphere of phenomena to suggest a law of synthesis, and so correspond to the conception of cause and effect; so that this conception would be quite void, null, and without significance.Phenomena would nevertheless continue to present objects to our intuition; for mere intuition does not in any respect stand in need of the functions of thought.
