Editing Antinomy (section)

== Terminology ==
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|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.<ref name=":0" />

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 (rule of inference)|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 <math>A \land \lnot A</math> (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.