law of contradiction
C2Academic, Formal, Technical
Definition
Meaning
The logical principle stating that a statement and its negation cannot both be true at the same time and in the same sense.
A foundational axiom in classical logic and philosophy that asserts a proposition cannot be both true and false simultaneously, forming a basis for rational discourse and systematic reasoning. In broader contexts, it may refer to the incompatibility of opposing principles.
Linguistics
Semantic Notes
This is a formal, technical term from logic and philosophy. It is often capitalised as 'Law of Contradiction'. It is a principle, not a statute or a legislated law. It is conceptually synonymous with the 'principle of non-contradiction'.
Dialectal Variation
British vs American Usage
Differences
No significant lexical differences. Spelling of related words (e.g., 'principle', 'formalise/formalize') may differ. It is equally common in academic texts in both varieties.
Connotations
Purely academic and formal in both varieties. Carries connotations of rigorous, classical logic.
Frequency
Extremely low frequency in general language but stable, core frequency within academic philosophy, logic, mathematics, and critical thinking courses.
Vocabulary
Collocations
Grammar
Valency Patterns
The law of contradiction states that...According to the law of contradiction, ...This violates the law of contradiction.Vocabulary
Synonyms
Neutral
Weak
Vocabulary
Antonyms
Usage
Context Usage
Business
Virtually never used except in highly abstract strategic or analytical discussions.
Academic
Primary domain. Core term in logic, philosophy, mathematics, and critical thinking. Used in lectures, textbooks, and papers.
Everyday
Extremely rare. Might be used in a simplified form in arguments, e.g., 'That's a contradiction, it can't be both.'
Technical
Essential in formal logic, computer science (boolean logic), legal reasoning, and analytical philosophy.
Examples
By Part of Speech
verb
British English
- The theory seems to contravene the law of contradiction.
- One cannot simultaneously affirm and deny a proposition without contradicting the fundamental law.
American English
- His argument violates the law of contradiction.
- To claim both is to logically contradict yourself.
Examples
By CEFR Level
- A light cannot be on and off at the same time. That's like the law of contradiction.
- In logic, the law of contradiction says you can't have 'A' and 'not A' both be true.
- The defendant's alibi was rejected because his statements were mutually exclusive, violating the basic law of contradiction.
- Proponents of paraconsistent logic seek to develop formal systems that can tolerate violations of the classical law of contradiction without resulting in triviality.
Learning
Memory Aids
Mnemonic
Think: A door cannot be both fully OPEN and fully CLOSED at the exact same moment. This 'law' locks out that impossibility.
Conceptual Metaphor
LOGICAL CONSISTENCY IS STRUCTURAL SOUNDNESS (a building cannot stand if its blueprint says a wall is both present and absent).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Do not translate 'law' as 'закон' in the sense of legislation. 'Закон противоречия' is the established term in Russian logic, but the concept is abstract, not juridical. The Russian phrase might sound overly formal or technical if used outside academic contexts.
Common Mistakes
- Confusing it with the 'law of excluded middle' (which deals with a statement being either true or false). Using it to describe mere disagreement rather than a direct logical contradiction (e.g., 'We have different opinions' is not a violation of this law). Capitalising inconsistently.
Practice
Quiz
Which of the following scenarios directly violates the law of contradiction?
FAQ
Frequently Asked Questions
No. The law of contradiction states 'A and not-A' cannot both be true. The law of excluded middle states that for any proposition 'A', either 'A' is true or 'not-A' is true; there is no third option. They are related but distinct fundamental laws of classical logic.
Aristotle is most famously associated with its explicit formulation in his metaphysical works, particularly in 'Metaphysics' Book IV, where he defends it as the most certain of all principles.
Yes. Some non-classical logics, such as paraconsistent logic and dialetheism, reject the universal applicability of the law of contradiction, allowing for 'true contradictions' in certain contexts to handle paradoxes or inconsistent information.
Implicitly, it underpins all coherent argumentation and fact-checking. When we point out that someone is 'contradicting themselves', we are appealing to this intuitive principle to highlight an error in reasoning.