Antinomic is a word which means contradictory or showing opposing truths. Some synonyms for antinomic are paradoxical, conflicting, contrary, counterintuitive, incompatible, and incongruous. Paradoxical refers to a situation where the truth contradicts logic or intuition. Conflicting and contrary connote a situation when two or more ideas or opinions don't match up. Counterintuitive refers to something that is surprising or goes against common sense. Incompatible refers to two things that cannot coexist or are not suited for one another. Finally, incongruous denotes a situation when two or more elements are unexpectedly out of place when put together.