noun
antinomy; self-contradiction; mutually exclusive alternatives
Originally a philosophical term (Kantian antinomy), now also used more broadly for any situation where two principles or options contradict each other and cannot both be satisfied.
自由と平等は時に二律背反の関係にある。
Freedom and equality are sometimes in an antinomic relationship.
この問題は二律背反に陥っている。
This problem has fallen into a self-contradiction.