The paper describes four dialogue systems, developed in the tradition of Charles Hamblin. The first system provides an answer for Achilles in Lewis Carroll's parable, the second an analysis of the fallacy of begging the question, the third a non-psychologistic account of conversational implicature, and the fourth an analysis of equivocation and of objections to it. Each avoids combinatorial explosions, and is intended for real-time operation.

In this paper a dialogical account of begging the question is applied to various contexts which are not obviously dialogues: - reading prose, working through a deductive system, presenting a legal case, and thinking to oneself. The account is then compared with that in chapter eight of D. Walton'sBegging the Question (New York; Greenwood, 1991).

This paper discusses some of the ways in which circular definitions and circular explanations entail or fail to entail infinite regresses. And since not all infinite regresses are vicious, a few criteria of viciousness are examined in order to determine when the entailment of a regress refutes a circular definition or a circular explanation.