counterexample: meaning, definition, pronunciation and examples
C2 (Proficient)Formal, Academic, Technical, Legal, Philosophical, Scientific
Quick answer
What does “counterexample” mean?
A specific example or case that disproves a general statement, proposition, or theory.
Audio
Pronunciation
Definition
Meaning and Definition
A specific example or case that disproves a general statement, proposition, or theory.
An instance, fact, or argument that contradicts or challenges a widely held belief, a proposed rule, or a logical claim, thereby requiring the original statement to be modified or abandoned.
Dialectal Variation
British vs American Usage
Differences
No significant difference in meaning or usage. The hyphenated form 'counter-example' is slightly more common in UK publications, while 'counterexample' (closed) is standard in US academic writing.
Connotations
Identical connotations of logical proof and falsification in both dialects.
Frequency
Higher frequency in academic texts globally; slightly higher incidence in American mathematical literature.
Grammar
How to Use “counterexample” in a Sentence
NOUN + to + NOUN PHRASE (a counterexample to the conjecture)VERB + as + COUNTEREXAMPLE (cite as a counterexample)PREP + COUNTEREXAMPLE (by counterexample)Vocabulary
Collocations
Examples
Examples of “counterexample” in a Sentence
noun
British English
- The mathematician sought a single counter-example to overturn the lemma.
- This historical case is often used as a counter-example to simplistic theories of progress.
American English
- Her research provided a decisive counterexample to the prevailing model.
- The attorney presented a counterexample that undermined the prosecution's generalization.
Usage
Meaning in Context
Business
Rare. Might be used in strategic analysis: 'The success of their lean startup is a counterexample to the belief that heavy initial funding is necessary.'
Academic
Common in mathematics, logic, philosophy, and sciences: 'The student constructed a clever counterexample to the proposed theorem.'
Everyday
Very rare. Would sound overly formal: 'My uncle, a healthy lifelong smoker, is often cited as a counterexample to the dire warnings.'
Technical
Core term in formal logic, mathematics, and computer science: 'The algorithm's failure on this specific input serves as a counterexample to its claimed universality.'
Vocabulary
Synonyms of “counterexample”
Strong
Weak
Vocabulary
Antonyms of “counterexample”
Watch out
Common Mistakes When Using “counterexample”
- Using it to mean simply a 'different example' or an 'alternative'.
- Using it for a mere exception that doesn't definitively disprove a rule (e.g., 'He's a counterexample to all accountants being boring' – this is weak, not logical falsification).
- Misspelling as 'counter example' (open) in formal writing.
FAQ
Frequently Asked Questions
Both 'counterexample' (closed, preferred in American English) and 'counter-example' (hyphenated, slightly more common in British English) are accepted. Consistency within a document is key.
Yes, especially in logic and philosophy. A hypothetical, but logically possible, scenario can serve as a counterexample to a claim of necessity or universal validity.
An 'exception' is a case that does not follow a rule but may not invalidate it (the rule may account for exceptions). A 'counterexample' definitively falsifies a universal claim ('all', 'every', 'never'), requiring the claim to be rejected or substantially revised.
Yes, but it retains its formal, logical sense. It's used in philosophy, law, economics, and rigorous argumentation in any field where universal claims are made and tested.
A specific example or case that disproves a general statement, proposition, or theory.
Counterexample is usually formal, academic, technical, legal, philosophical, scientific in register.
Counterexample: in British English it is pronounced /ˌkaʊntərɪɡˈzɑːmpl̩/, and in American English it is pronounced /ˈkaʊn.tɚ.ɪɡˌzæm.pəl/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think: A COUNTER argument in the form of an EXAMPLE. It COUNTERs a claim with a specific EXAMPLE.
Conceptual Metaphor
KNOWLEDGE AS STRUCTURE (a counterexample is a crack or flaw in a logical edifice); ARGUMENT AS WAR (a counterexample is a targeted strike against a universal claim).
Practice
Quiz
In which context is the word 'counterexample' most precisely and appropriately used?