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.