What does a strong counterexample achieve in an argument?

A strong counterexample effectively undermines the argument's validity by demonstrating that the conclusion does not necessarily follow from the premises. When a counterexample is presented, it illustrates a specific situation in which the argument fails to hold true, thereby exposing flaws or weaknesses in the reasoning. This directly impacts the argument by showing that even if the premises are true, the conclusion may still be false or not universally applicable. Therefore, the presence of a strong counterexample is crucial as it challenges the logical connection the argument tries to establish, making it an essential tool in evaluating the soundness of an argument.