The solution distinguishes the first two antinomies, as the mathematical, from the second two, as the dynamical antinomies; in the former, since it is a question of the composition and division of quanta, the conditions may be homogeneous with the conditioned, in the latter, heterogeneous.  In the former, thesis and antithesis are alike false, since both start from the inadmissible assumption that the universe (the complete series of phenomena) is given, while in fact it is only required of us (is an Idea).  The world does not exist in itself, but only in the empirical regress of phenomenal conditions, in which we never can reach infinity and never the limitation of the world by an empty space or an antecedent empty time, for infinite space, like empty space (and the same holds in regard to time), is not perceivable.  Consequently the quantity of the world is neither finite nor infinite.  The question of the quantity of the world is unanswerable, because the concept of a sense-world existing by itself (before the regress) is self-contradictory.  Similarly the problem whether the composite consists of simple elements is insoluble, because the assumption that the phenomenon of body is a thing in itself, which, antecedent to all experience, contains all the parts that can be reached in experience—­in other words, that representations exist outside of the representative faculty—­is absurd.  Matter is infinitely divisible, no doubt, yet it does not consist of infinitely numerous parts, and just as little of a definite number of simple parts, but the parts exist merely in the representation of them, in the division (decomposition), and this goes as far as possible experience extends.  The case is different with the dynamical antinomies, where thesis and antithesis can both be true, in so far as the former is referred to things in themselves and the latter to phenomena.  The contradiction vanishes if we take that which the thesis asserts and the antithesis denies in different senses.  The fact that in the world of phenomena the causal nexus proceeds without interruption and without end, so that there is no room in it either for an absolutely necessary Being or for freedom, does not conflict with this other, that beyond the world of sense there may exist an omnipotent, omniscient cause of the world, and an intelligible freedom as the ground of our empirically necessary actions.  “May exist,” since for the critical philosopher, who has learned that every extension of knowledge beyond the limits of experience is impossible, the question can concern only the conceivability of the world-ground and of freedom.  This possibility is amply sufficient to give a support for faith, as, on the other hand, it is indispensable in order to satisfy at once the demands of the understanding and of reason, especially to satisfy their practical interests.  For if it were not possible to resolve the apparent contradiction, and to show its members capable of reconciliation,