For how can we make out by experience, whether the world is from eternity or had a beginning, whether matter is infinitely divisible or consists of simple parts? Such concept cannot be given in any experience, be it ever so extensive, and consequently the falsehood either of the positive or the negative proposition cannot be discovered by this touchstone. The only possible way in which reason could have revealed unintentionally its secret Dialectics, falsely announced as Dogmatics, would be when it were made to ground an assertion upon a universally admitted principle, and to deduce the exact contrary with the greatest accuracy of inference from another which is equally granted. This is actually here the case with regard to four natural ideas of reason, whence four assertions on the one side, and as many counter-assertions on the other arise, each consistently following from universally-acknowledged principles. Thus they reveal by the use of these principles the dialectical illusion of pure reason which would otherwise forever remain concealed. This is therefore a decisive experiment, which must necessarily expose any error lying hidden in the assumptions of reason. 32 Contradictory propositions cannot both be false, except the concept, which is the subject of both, is self- contradictory; for example, the propositions, "a square circle is round, and a square circle is not round," are both false. For, as to the former it is false, that the circle is round, because it is quadrangular; and it is likewise false, that it is not round, that is, angular, because it is a circle. For the logical criterion of the impossibility of a concept consists in this, that if we presuppose it, two contradictory propositions both become false; consequently, as no middle between them is conceivable, nothing at all is thought by that concept. Sect. 52. c. The first two antinomies, which I call mathematical, because they are concerned with the addition or division of the homogeneous, are founded on such a self- contradictory concept; and hence I explain how it happens, that both the Thesis and Antithesis of the two are false. When I speak of objects in time and in space, it is not of things in themselves, of which I know nothing, but of things in appearance, that is, of experience, as the particular way of cognising objects which is afforded to man. I must not say of what I think in time or in space, that in itself, and independent of these my thoughts, it exists in space and in time; for in that case I should contradict myself; because space and time, together with the appearances in them, are nothing existing in themselves and outside of my representations, but are themselves only modes of representation, and it is palpably contradictory to say, that a mere mode of representation exists without our representation.
Objects of the senses therefore exist only in experience; whereas to give them a self-subsisting existence apart from experience or before it, is merely to represent to ourselves that experience actually exists apart from experience or before it. Now if I inquire after the quantity of the world, as to space and time, it is equally impossible, as regards all my notions, to declare it infinite or to declare it finite. For neither assertion can be contained in experience, because experience either of an infinite space, or of an infinite time elapsed, or again, of the boundary of the world by a void space, or by an antecedent void time, is impossible; these are mere ideas. This quantity of the world, which is determined in either way, should therefore exist in the world itself apart from all experience. This contradicts the notion of a world of sense, which is merely a complex of the appearances whose existence and connection occur only in our representations, that is, in experience, since this latter is not an object in itself, but a mere mode of representation. Hence it follows, that as the concept of an absolutely existing world of sense is self-contradictory, the solution of the problem concerning its quantity, whether attempted affirmatively or negatively, is always false. The same holds good of the second antinomy, which relates to the division of phenomena. For these are mere representations, and the parts exist merely in their representation, consequently in the division, or in a possible experience where they are given, and the division reaches only as far as this latter reaches. To assume that an appearance, e.g., that of body, contains in itself before all experience all the parts, which any possible experience can ever reach, is to impute to a mere appearance, which can exist only in experience, an existence previous to experience. In other words, it would mean that mere representations exist before they can be found in our faculty of representation. Such an assertion is self-contradictory, as also every solution of our misunderstood problem, whether we maintain, that bodies in themselves consist of an infinite number of parts, or of a finite number of simple parts. Sect. 53. In the first (the mathematical) class of antinomies the falsehood of the assumption consists in representing in one concept something self-contradictory as if it were compatible (i.e., an appearance as an object in itself).
