ANTINOMY, literally the mutual incompatibility, real or apparent, of two laws. The term acquired a special significance in the philosophy of Kant, who used it to describe the contradic tory results of applying to the universe of pure thought the cate gories or criteria proper to the universe of sensible perception (phenomena). These antinomies are four—two mathematical, two dynamical—connected with (I) the limitation of the universe in respect of space and time, (2) the theory that the whole con sists of indivisible atoms (whereas, in fact, none such exist), (3) the problem of freedom in relation to universal causality, (4) the existence of a universal being—about each of which pure reason contradicts the empirical, as thesis and antithesis. Kant claimed to solve these contradictions by saying that in no case is the con tradiction real, however seriously it has been intended by the opposing partisans, or must appear to the mind without critical enlightenment. It is wrong, therefore, to impute to Kant, as is often done, the view that human reason is, on ultimate subjects, at war with itself, in the sense of being impelled by equally strong arguments towards alternatives contradictory of each other. The difficulty arises from a confusion between the spheres of phe nomena and noumena. In fact no rational cosmology is possible.