In philosophy, an antinomy (/ænˈtɪnəmi/; Ancient Greek: antí 'against' + nómos 'law') is a real or apparent contradiction between two conclusions, both of which seem justified. It is a term used in logic and epistemology, particularly in the philosophy of Immanuel Kant.

Antinomy is a common form of argument in the dialogues of Plato. Kant credited Zeno of Elea (see Zeno's paradoxes) as the inventor of the antinomic mode of argumentation, which he described as a "skeptical method" of "watching, or rather provoking, a conflict of assertions, not for the purpose of deciding in favor of one or the other side, but of investigating whether the object of the controversy is not perhaps a deceptive appearance which each vainly tries to grasp, and in regard to which, even if there were no opposition to overcome, neither can arrive at any result".

The antinomic procedure was further developed by Fichte, Schelling and Hegel. Hegel said that Kant was in error when he limited the antinomies to cosmological ideas, claiming that the world itself contains contradiction. Schopenhauer said that the antitheses in Kant's antinomies were justified, but claimed the theses (cosmological propositions) to be sophisms.

Antinomies can be found in Plato, in substance though not by this name (cf. Phaedo 102; Rep. 523 ff., Parm. 135 E). Modern usage dates back to a 17th-century legal term, which acquired philosophical significance in Immanuel Kant's Critique of Pure Reason (CPR). In the Transcendental Dialectic, Kant defines an antinomy as a "conflict of laws" (CPR A407/B434).

Kant's use of the term was derived from jurisprudence, where it refers to a conflict between laws, and from biblical exegesis, where it refers to conflict between passages of scripture.

In modern logic, the term "antinomy" is not used consistently and is sometimes not clearly distinguished from the term paradox. In the German language, however, it is customary to reserve the term "antinomy" for contradictions that can be rigorously proven within the framework of a formal system and which thus indicate an error in the conception of the rules of inference or the axioms of that system (e.g. the antinomies of naive set theory, the best known being Russell's paradox). In contrast, a paradox (Ancient Greek παρά para "beside, apart" and δόξα doxa "expectation, opinion", παράδοξον paradoxon "contrary to expectation, contrary to common opinion") is usually used to describe a well-founded statement that contradicts conventional wisdom, but which does not cause any real logical difficulties. Many scientific insights can appear paradoxical in this harmless sense (e.g., the twin paradox in Einstein's theory of relativity or the so-called paradoxes of material implication in formal logic; see relevance logic). In English, the term antinomy is not particularly widespread and its application is mostly limited to Kantian antinomies.

In modern logic, a "contradiction" is simply understood as the conjunction of a statement and its negation, i.e. a statement of the form ${\displaystyle A\land \lnot A}$ (read: "A and not-A"). This broad term is neutral with regard to the question of provability or justifiability, and includes, for example, contradictions that are derived within a proof by contradiction specifically for the purpose of negating one of the assumptions involved in the derivation. Therefore, not all contradiction is philosophically problematic.

Separately from this usage, the word "contradiction" is also used in Hegelian dialectics, where it includes social conflict, antagonisms and such.