The purpose of this paper is to show the pervasive, though often implicit, role of arguments in negotiation dialogue. This holds even for negotiations that start from a difference of interest such as mere bargaining through offers and counteroffers. But it certainly holds for negotiations that try to settle a difference of opinion on policy issues. It will be demonstrated how a series of offers and counteroffers in a negotiation dialogue contains a reconstructible series of implicit persuasion dialogues. The paper is a sequel to van Laar and Krabbe (2017), in which we showed that for some differences of opinion it may be reasonable to shift from persuasion dialogue, aimed at a resolution of the difference on the merits, to negotiation dialogue, aimed at compromise, whereas in the present paper we show that such a shift need not amount to the abandonment of argumentation. Our main aim in this paper as well as in the previous one is to contribute to the theory of argumentation within the context of negotiation and compromise formation.

Negotiation is not only used to settle differences of interest but also to settle differences of opinion. Discussants who are unable to resolve their difference about the objective worth of a policy or action proposal may be willing to abandon their attempts to convince the other and search instead for a compromise that would, for each of them, though only a second choice yet be preferable to a lasting conflict. Our questions are: First, when is it sensible to enter into negotiations and when would this be unwarranted or even fallacious? Second, what is the nature of a compromise? What does it mean to settle instead of resolve a difference of opinion, and what might be the dialectical consequences of mistaking a compromise for a substantial resolution? Our main aim is to contribute to the theory of argumentation within the context of negotiation and compromise formation and to show how arguing disputants can shift to negotiation in a dialectically virtuous way.

This paper makes an independent start with formalizing the rules for the argumentation stage of critical discussions (van Eemeren and Grootendorst A systematic theory of argumentation: The pragma-dialectical approach, Cambridge University Press, Cambridge, 2004, Ch. 6). It does not deal with the well-known code of conduct consisting of ten rules (the “ten commandments”) but with the system consisting of fifteen (or seventeen) rules on which the code of conduct is based. The rules of this system are scrutinized and problems they raise are discussed. Then a formal dialectical system is defined that reflects most of the contents of these rules. The aim is to elucidate the way the rules work and to show how a formal approach can be useful to achieve this. It is also shown how the present method can be used to study the nature of circular argumentation. While, generally, the formalization follows closely the original rules for the argumentation stage of critical discussions, there will also be proposed some modifications of the original protocol.

This paper attempts to systematically characterize critical reactions in argumentative discourse, such as objections, critical questions, rebuttals, refutations, counterarguments, and fallacy charges, in order to contribute to the dialogical approach to argumentation. We shall make use of four parameters to characterize distinct types of critical reaction. First, a critical reaction has a focus, for example on the standpoint, or on another part of an argument. Second, critical reactions appeal to some kind of norm, argumentative or other. Third, they each have a particular illocutionary force, which may include that of giving strategic advice to the other. Fourth, a critical reaction occurs at a particular level of dialogue (the ground level or some meta-level). The concepts here developed shall be applied to discussions of critical reactions by Aristotle and by some contemporary authors.

a Norwegian philosopher, who was born in Aker (now part of

This paper explores applications of concepts from argumentation theory to mathematical proofs. Note is taken of the various contexts in which proofs occur and of the various objectives they may serve. Examples of strategic maneuvering are discussed when surveying, in proofs, the four stages of argumentation distinguished by pragma-dialectics. Derailments of strategies (fallacies) are seen to encompass more than logical fallacies and to occur both in alleged proofs that are completely out of bounds and in alleged proofs that are at least mathematical arguments. These considerations lead to a dialectical and rhetorical view of proofs.

Any well-structured argumentative exchange must be preceded by some preparatory stages. In the pragma-dialectical four-stage model of critical discussion, the clarification of issues and positions is relegated to the confrontation stage and the other preparatory matters are dealt within the opening stage. In the opening stage, the parties involved come to agree to discuss their differences and to do so by an argumentative exchange rather than by, say, a sequence of bids and offers. They should also come to agree on the rules of dialogue, on roles, on logical principles, on types of argument, and on the propositions that can be used as basic premises. All in all, a lot of work needs to be done before the first topical argument can be put forward. Especially the opening stage seems prone to further disagreements and protracted discussions, e.g., about the admissibility of particular kinds of argument or particular basic premises. There is also the problem that a successful opening stage threatens to settle matters beforehand and thus put the argumentation stage out of business. The paper suggests some measures that could alleviate the workload of the opening stage, without making the argumentation stage otiose.