ANTINOMY (Gr. ἀντί, against, νόμος, law), 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 contradictory results of applying to the universe of pure thought the categories or criteria proper to the universe of sensible perception (phenomena). These antinomies are four—two mathematical, two dynamical—connected with (1) the limitation of the universe in respect of space and time, (2) the theory that the whole consists 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 contradiction real, however really 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 phenomena and noumena. In fact no rational cosmology is possible.
See John Watson, Selections from Kant (trans. Glasgow, 1897), pp. 155 foll.; W. Windelband, History of Philosophy (Eng. trans. 1893); H. Sidgwick, Philos. of Kant, lectures x. and xi. (Lond., 1905); F. Paulsen, I. Kant (Eng. trans. 1902), pp. 216 foll.