This article investigates how Plato thinks we secure necessary motivational conditions for inquiry. After presenting a typology of zetetic breakdowns in the dialogues, I identify norms of inquiry Plato believes all successful inquirers must satisfy. Satisfying these norms requires trust that philosophy will not harm but benefit inquirers overall. This trust cannot be secured by protreptic argument. Instead, it requires divine intervention—an extra-rational foundation for rational inquiry.

It is well known that reductio ad absurdum arguments raise a number of interesting philosophical questions. What does it mean to assert something with the precise goal of then showing it to be false, i.e. because it leads to absurd conclusions? What kind of absurdity do we obtain? Moreover, in the mathematics education literature number of studies have shown that students find it difficult to truly comprehend the idea of reductio proofs, which indicates the cognitive complexity of these constructions. In (...) this paper, I start by discussing four philosophical issues pertaining to reductio arguments. I then briefly present a dialogical conceptualization of deductive arguments, according to which such arguments are best understood as a dialogue between two participants—Prover and Skeptic. Finally, I argue that many of the philosophical and cognitive difficulties surrounding reductio arguments are dispelled or at least further clarified once one adopts a dialogical perspective. (shrink)