kontradiktion

Kontradiktion, in logic and philosophy, refers to a situation in which a proposition and its negation are both true, or when a set of statements entails both a statement and its negation. In classical logic, this is ruled out by the law of non-contradiction, which states that a proposition cannot be true and false at the same time. A common formal indication of contradiction is the conjunction P and not P.

In formal systems, a contradiction can be detected when assumptions lead to the derivation of both a statement and its negation, potentially triggering the principle of explosion in classical logic: from a contradiction, any proposition follows. This property makes consistency a central concern in mathematics, computer science, and formal epistemology. To address contradictions without collapsing into triviality, logicians have developed non-classical logics, such as paraconsistent logics, which tolerate some contradictions without implying that all propositions are true. Dialetheism is a related position that holds that some contradictions can be true.

Historically, the idea dates to Aristotle, who framed the law of non-contradiction as a fundamental principle of rational thought. In mathematical proof, contradictions typically signal an error in reasoning or an inconsistency among axioms. In software verification and knowledge representation, detecting contradictions is essential for maintaining coherent models and avoiding invalid inferences. The term kontradiktion is also used in broader or rhetorical senses to describe claims that oppose each other within a discourse, though this usage is less technical than its logical meaning.

Kontradiktion thus denotes both a technical concept in formal logic and a broader notion of incompatibility between statements, with important implications for reasoning, proof, and consistency.