Principles à priori are so called, not merely because they contain in themselves the grounds of other judgements, but also because they themselves are not grounded in higher and more general cognitions. This peculiarity, however, does not raise them altogether above the need of a proof. For although there could be found no higher cognition, and therefore no objective proof, and although such a principle rather serves as the foundation for all cognition of the object, this by no means hinders us from drawing a proof from the subjective sources of the possibility of the cognition of an object. Such a proof is necessary, moreover, because without it the principle might be liable to the imputation of being a mere gratuitous assertion. In the second place, we shall limit our investigations to those principles which relate to the categories. For as to the principles of transcendental æsthetic, according to which space and time are the conditions of the possibility of things as phenomena, as also the restriction of these principles, namely, that they cannot be applied to objects as things in themselves—these, of course, do not fall within the scope of our present inquiry. In like manner, the principles of mathematical science form no part of this system, because they are all drawn from intuition, and not from the pure conception of the understanding. The possibility of these principles, however, will necessarily be considered here, inasmuch as they are synthetical judgements à priori, not indeed for the purpose of proving their accuracy and apodeictic certainty, which is unnecessary, but merely to render conceivable and deduce the possibility of such evident à priori cognitions. But we shall have also to speak of the principle of analytical judgements, in opposition to synthetical judgements, which is the proper subject of our inquiries, because this very opposition will free the theory of the latter from all ambiguity, and place it clearly before our eyes in its true nature. SYSTEM OF THE PRINCIPLES OF THE PURE UNDERSTANDING Section I. Of the Supreme Principle of all Analytical Judgements Whatever may be the content of our cognition, and in whatever manner our cognition may be related to its object, the universal, although only negative conditions of all our judgements is that they do not contradict themselves; otherwise these judgements are in themselves (even without respect to the object) nothing. But although there may exist no contradiction in our judgement, it may nevertheless connect conceptions in such a manner that they do not correspond to the object, or without any grounds either à priori or à posteriori for arriving at such a judgement, and thus, without being self-contradictory, a judgement may nevertheless be either false or groundless.