thumb|This diagram shows the contradictory relationships between categorical propositions in the [[square of opposition of Aristotelian logic.]]
A logical contradiction occurs when two statements cannot both be true at the same time, as shown in relationships like those mapped in Aristotle's square of opposition. Contradictions matter because they signal when reasoning has gone wrong—if your argument leads to contradictory conclusions, something in your thinking needs to be fixed.
AI-generated from the Wikipedia summary — may contain errors.
thumb|This diagram shows the contradictory relationships between categorical propositions in the [[square of opposition of Aristotelian logic.]]
In traditional logic, a contradiction involves a proposition conflicting either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, The law of noncontradiction states that "It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect."
Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).