What is antinomy? The Shorter Oxford English Dictionary defines it as ‘a contradiction between conclusions which seem equally logical, reasonable or necessary.’ For our purposes, however, this definition is not quite accurate; the opening words should read ‘an appearance of contradiction.’ For the whole point of an antinomy—in theology, at any rate—is that it is not a real contradiction, though it looks like one. It is an apparent incompatibility between two apparent truths. An antinomy exists when a pair of principles stand side by side, seemingly irreconcilable, yet both undeniable. There are cogent reasons for believing each of them; each rests on clear and solid evidence; but it’s a mystery to you how they can be squared to each other. You see that each must be true on its own, but you do not see how they can both be true together. Let me give an example. Modern physics faces an antinomy, in this sense, in its study of light. There is cogent evidence to show that light consists of waves, and equally cogent evidence to show that it consists of particles. It is not apparent how light can be both waves and particles, but the evidence is there, and so neither view can be ruled out in favor of the other. Neither, however, can be reduced to the other or explained in terms of the other; the two seemingly incompatible positions must be held together, and both must be treated as true. Such a necessity scandalizes our tidy minds, no doubt, but there is no help for it if we are to be loyal to the facts.
It appears, therefore, that an antinomy is not the same thing as a paradox. A paradox is a figure of speech, a play on words. It is a form of statement that seems to unite two opposite ideas, or to deny something by the very terms in which it is asserted.