Abduction and the explanation of anomalies: the case of proof by contradiction

Abstract Some difficulties with proof by contradiction seem to be overcome when students spontaneously produce indirect argumentation. In this paper, we explore this issue and discuss some differences between indirect argumentation and proof by contradiction. We will highlight how an abductive process, involved in generating some indirect argumentation, can have an important role in explaining the absurd proposition, in filling the gap between the final contradiction and the statement to be proved and in the treatment of impossible mathematical objects.