logical contradiction
Sign in to savethumb|This diagram shows the contradictory relationships between categorical propositions in the [[square of opposition of Aristotelian logic.]]
AI overview
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.
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Article
12 sectionsContents
- History
- In formal logic
- Proof by contradiction
- The notion of contradiction in an axiomatic system and a proof of its consistency
- Philosophy
- Pragmatic contradictions
- Dialectical materialism
- Outside formal logic
- See also
- Notes and references
- Bibliography
- External links
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."