Counterexample
A case that breaks or narrows a claim
A counterexample is a case that violates the prediction of a claim, forcing either rejection or narrowing of scope. It is a specific kind of attack: not an argument that the claim is wrong in general, but evidence that it fails in a particular instance.
Counterexamples are epistemically powerful because they are concrete. A single well-documented counterexample can outweigh many confirming instances, especially if the claim was stated as universal. This is why rebuttal-first search and counterexample-first search prioritize finding them early.
In a Dialectical Graph, counterexamples are nodes
connected to claims via an attacks edge. They carry their own
evidence spans, scope, and source, so
the attack can itself be scrutinized.