Dutilh Novaes (2020) defines deductive dialogues as Prover-Skeptic games. The key distinction between the Prover-Skeptic and Prover-Refuter frameworks is that the Skeptic does not “lose” after being convinced by the Prover’s argument, unlike the Refuter that actively tries to disprove the argument. (This framework is also more aligned with the Hegelian-dialectical perspective that the ultimate goal of the dialogue, or game, is to arrive at true belief. See also: Inquiry is the struggle to go from doubt to belief, after Peirce.)
The requirements for a Skeptic to be persuaded by a proof depend on context, but include, minimally:
- Accepting premises. If the Skeptic admits conditional persuasion, then they must believe that the premises are important enough to establish a proof about.
- Not having counterexamples.
- Being convinced by each step of the argument. (See also: the requirement that deductive arguments have stepwise perspicuity.)