(Cross-posted at M-Phi)

Some months ago I wrote two posts on the concept of indirect proofs: one presenting a dialogical conception of these proofs, and the other analyzing the concept of ‘proofs through the impossible’ in the *Prior Analytics*. Since then I gave a few talks on this material, receiving useful feedback from audiences in Groningen and Paris. Moreover, this week we hosted the conference ‘Dialectic and Aristotle’s Logic’ in Groningen, and after various talks and discussions I have come to formulate some new ideas on the topic of reductio proofs and their dialectical/dialogical underpinnings. So for those of you who enjoyed the previous posts, here are some further thoughts and tentative answers to lingering questions.

Recall that the dialogical conception I presented in previous posts was meant to address the awkwardness of the first speech act in a reductio proof, namely that of supposing precisely that which you intend to refute by showing that it entails an absurdity. From studies in the literature on math education, it is known that this first step can be very confusing to students learning the technique of reductio proofs. On the dialogical conception, however, no such awkwardness arises, as there is a division of roles between the agent who supposes the initial thesis to be refuted, and the agent who in fact derives an absurdity from the thesis.

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