Let it be supposed that a composite thing (as substance) consists of simple parts. Inasmuch as all external relation, consequently all composition of substances, is possible only in space; the space, occupied by that which is composite, must consist of the same number of parts as is contained in the composite. But space does not consist of simple parts, but of spaces. Therefore, every part of the composite must occupy a space. But the absolutely primary parts of what is composite are simple. It follows that what is simple occupies a space. Now, as everything real that occupies a space, contains a manifold the parts of which are external to each other, and is consequently composite- and a real composite, not of accidents (for these cannot exist external to each other apart from substance), but of substances- it follows that the simple must be a substantial composite, which is self-contradictory.
The second proposition of the antithesis- that there exists in the world nothing that is simple- is here equivalent to the following: The existence of the absolutely simple cannot be demonstrated from any experience or perception either external or internal; and the absolutely simple is a mere idea, the objective reality of which cannot be demonstrated in any possible experience; it is consequently, in the exposition of phenomena, without application and object. For, let us take for granted that an object may be found in experience for this transcendental idea; the empirical intuition of such an object must then be recognized to contain absolutely no manifold with its parts external to each other, and connected into unity. Now, as we cannot reason from the non-consciousness of such a manifold to the impossibility of its existence in the intuition of an object, and as the proof of this impossibility is necessary for the establishment and proof of absolute simplicity; it follows that this simplicity cannot be inferred from any perception whatever. As, therefore, an absolutely simple object cannot be given in any experience, and the world of sense must be considered as the sum total of all possible experiences: nothing simple exists in the world.
This second proposition in the antithesis has a more extended aim than the first. The first merely banishes the simple from the intuition of the composite; while the second drives it entirely out of nature. Hence we were unable to demonstrate it from the conception of a given object of external intuition (of the composite), but we were obliged to prove it from the relation of a given object to a possible experience in general.