Meta-cognitive unity in indirect proofs.

In this paper we focus on the cognitive aspects of indirect argumentation and proving processes. Drawing on the Habermas model of rational behaviour in three components (epistemic, teleological, and communicative) and on the notion of cognitive unity as developed by Boero and his collaborators, we distinguish between two levels of argumentation, a ‘ground level’ and a ‘meta-level’. On the base of a case study in early Calculus context (secondary school), we introduce the notion of ‘meta-cognitive unity’, which may give reason of success and difficulties in indirect proving processes. Furthermore, we use Peirce’s account of abduction to shed light into some cognitive processes behind the production of indirect proofs.