- A counterexample is an example that refutes a claim about some subject-matter. Switzerland is a counter-example to the claim that all countries with armed citizens are dangerous. Notice that it is not a counterexample to the claim that some countries with armed citizens are dangerous. Much philosophy proceeds by finding counterexamples. For example, the claim that if you have promised someone to be at a place at a time, you must be there, could be countered with the example of a situation in which the person you promised has died in the meantime. In some developments of logic a counterexample set is made by combining the premises of some argument with the negation of the conclusion, and seeing if a contradiction can be derived. If it can, then the original argument was valid.
Philosophy dictionary. Academic. 2011.
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counterexample — [kount′ər eg zam΄pəl] n. an example used to support an argument or claim that is in opposition to another argument or claim … English World dictionary
Counterexample — In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule. For example, consider the proposition all students are lazy . Because this statement makes the claim that a… … Wikipedia
counterexample — noun Date: 1852 an example that refutes or disproves a proposition or theory … New Collegiate Dictionary
counterexample — /kown teuhr ig zam peuhl, zahm /, n. an example that refutes an assertion or claim. [1955 60; COUNTER + EXAMPLE] * * * … Universalium
counterexample — noun An exception to a proposed general rule; a specific instance of the falsity of a universally quantified statement … Wiktionary
counterexample — n. example that refutes a theory or claim; example used to prove that a statement is false … English contemporary dictionary
counterexample — coun·ter·example … English syllables
counterexample — coun•ter•ex•am•ple [[t]ˈkaʊn tər ɪgˌzæm pəl, ˌzɑm [/t]] n. cvb an example that refutes an assertion or claim • Etymology: 1955–60 … From formal English to slang
counterexample — noun refutation by example • Hypernyms: ↑disproof, ↑falsification, ↑refutation * * * ˌ noun Etymology: counter + example : an example that disproves a theorem or proposition ; broadly : an example that is inconsiste … Useful english dictionary
Minimal counterexample — In mathematics, the method of considering a minimal counterexample (or minimal criminal) combines the ideas of inductive proof and proof by contradiction. Abstractly, in trying to prove a proposition P, one assumes that it is false, and that… … Wikipedia