What does counterexample mean?
A counterexample is a specific example that disproves a general claim, proposition, or theory. If someone asserts that 'all members of a group have property X,' a single demonstrated instance lacking property X is enough to refute the claim entirely. The term is most at home in mathematics, logic, and philosophy, where constructing counterexamples is a core method for testing conjectures and sharpening definitions — a beautiful counterexample can end decades of debate about whether a proposed theorem holds. Beyond technical fields, the word also appears in everyday intellectual discussion, describing any exception that undermines a sweeping generalization. Counterexamples are prized for their economy of persuasion: while countless confirming instances can never conclusively prove a universal statement, one genuine counterexample destroys it outright. This asymmetry makes the concept foundational to scientific reasoning and critical thinking alike, embodying the principle that falsification requires only a single well-chosen case.
nounAn example that disproves a proposition, general claim, or theory; in mathematics and logic, a specific case showing that a statement asserted as universally true is false.
- A specific instance that disproves a universal claim, proposition, or theory.
- (Mathematics/logic) A case demonstrating that a conjectured theorem or statement is false.
"The mathematician demolished the conjecture with a single elegant counterexample."
"Her data provided a striking counterexample to the widely accepted model of consumer behavior."
"To disprove the assertion that all swans are white, a single black swan serves as a decisive counterexample."
Standard regular plural; common in mathematical literature when multiple disproving cases are discussed.
"The paper catalogued several counterexamples to the proposed classification scheme."
In mathematics, a single counterexample can destroy a conjecture that thousands of verified cases seemed to confirm — one exception beats infinite agreement.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of counterexample
Counterexample is formed from the prefix 'counter-,' from Latin 'contra' meaning against or opposite, combined with 'example,' from Latin 'exemplum,' meaning a sample or pattern. The compound emerged in English scholarly writing, particularly within logic and mathematics, where the practice of refuting claims by citing disconfirming instances became formalized. It shares its Latin roots with words such as exemplary and exemplify, and its prefix with words like counterpart and contradict.
How counterexample is actually used
Counterexample is chiefly used in academic and technical registers — mathematics, logic, philosophy, and science — though it appears in general intellectual discourse. It carries no strong connotation beyond precision: offering a counterexample is generally seen as rigorous rather than hostile. The word is countable and typically appears with the indefinite article ('a counterexample').
Easily confused with counterexample
An example illustrates or supports a claim, whereas a counterexample is a specific instance that disproves it.