The Informal Logic of Mathematical Proof

Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is that a more nuanced understanding of mathematical proof and discovery may be achieved by paying attention to the aspects of mathematical argumentation which can be captured by informal, rather than formal, logic. Two accounts of argumentation are considered: the pioneering work of Stephen Toulmin [The uses of argument, Cambridge University Press, 1958] and the more recent studies of Douglas Walton, [e.g. The new dialectic: Conversational contexts of argument, University of Toronto Press, 1998]. The focus of both of these approaches has largely been restricted to natural language argumentation. However, Walton's method in particular provides a fruitful analysis of mathematical proof. He offers a contextual account of argumentational strategies, distinguishing a variety of different types of dialogue in which arguments may occur. This analysis represents many different fallacious or otherwise illicit arguments as the deployment of strategies which are sometimes admissible in contexts in which they are inadmissible. I argue that mathematical proofs are deployed in a greater variety of types of dialogue than has commonly been assumed. I proceed to show that many of the important philosophical and pedagogical problems of mathematical proof arise from a failure to make explicit the type of dialogue in which the proof is introduced.Comment: 14 pages, 1 figure, 3 tables. Forthcoming in Perspectives on Mathematical Practices: Proceedings of the Brussels PMP2002 Conference (Logic, Epistemology and the Unity of the Sciences Series), J. P. Van Bendegem & B. Van Kerkhove, edd. (Dordrecht: Kluwer, 2004

Arguing and negotiating in the presence of social influences

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Love and Friendship in the Lysis and the Symposium: Human and Divine

The paper claims that we cannot understand properly Platonic conception of love and friendship unless we read the Lysis in the light of the Symposium and vice verse. Dealing with the crucial question of what made Plato write two different dialogues on the same topic, it advocates an alternative intertextual reading that does not deny progress of Plato’s thinking. Though the Symposium offers, in comparison to the Lysis, a more developed philosophical theory of love, Plato still has good reasons to articulate the dilemmas presented in the Lysis. Combining the contrast in dialogue endings with the similarity in structure and in argumentation, Plato makes clear that, between the Lysis and the Symposium, there is progress and constancy at the same time: while the Symposium gives a philosophical account of what we can call “divine love”, it accepts and even emphasizes the insight of the Lysis that philosophical love can imply lack of what we usually consider worth loving. Plato in the Symposium does not discard “human love” and does not conceal possible troubles of philosophical, i.e. divine love. Therefore, the critique of Plato as being champion of impersonal or “ideal” love is unpersuasive

Strategic Argumentation is NP-Complete

In this paper we study the complexity of strategic argumentation for dialogue games. A dialogue game is a 2-player game where the parties play arguments. We show how to model dialogue games in a skeptical, non-monotonic formalism, and we show that the problem of deciding what move (set of rules) to play at each turn is an NP-complete problem

Proceedings ICPW'07: 2nd International Conference on the Pragmatic Web, 22-23 Oct. 2007, Tilburg: NL

Proceedings ICPW'07: 2nd International Conference on the Pragmatic Web, 22-23 Oct. 2007, Tilburg: N

Empirical Evaluation of Abstract Argumentation: Supporting the Need for Bipolar and Probabilistic Approaches

In dialogical argumentation it is often assumed that the involved parties always correctly identify the intended statements posited by each other, realize all of the associated relations, conform to the three acceptability states (accepted, rejected, undecided), adjust their views when new and correct information comes in, and that a framework handling only attack relations is sufficient to represent their opinions. Although it is natural to make these assumptions as a starting point for further research, removing them or even acknowledging that such removal should happen is more challenging for some of these concepts than for others. Probabilistic argumentation is one of the approaches that can be harnessed for more accurate user modelling. The epistemic approach allows us to represent how much a given argument is believed by a given person, offering us the possibility to express more than just three agreement states. It is equipped with a wide range of postulates, including those that do not make any restrictions concerning how initial arguments should be viewed, thus potentially being more adequate for handling beliefs of the people that have not fully disclosed their opinions in comparison to Dung's semantics. The constellation approach can be used to represent the views of different people concerning the structure of the framework we are dealing with, including cases in which not all relations are acknowledged or when they are seen differently than intended. Finally, bipolar argumentation frameworks can be used to express both positive and negative relations between arguments. In this paper we describe the results of an experiment in which participants judged dialogues in terms of agreement and structure. We compare our findings with the aforementioned assumptions as well as with the constellation and epistemic approaches to probabilistic argumentation and bipolar argumentation

Uses of the argumentation in the negotiation

In the recent literature on conflict resolution tends to underline negotiation model based on the argument or dialogue. Exchange between different styles of argument some trends have emerged in the rhetoric applied to the law, especially in procedural law. During the last decade researchers have recognized the value of the argument to understand various problems of jurisprudence in cases of conflict and strife. This paper proposes a complementary design to the analysis of the negotiation process based on debate and dialogue. It advocates a theory of argumentation in negotiation processes for instances where rational agents use strategies unpredictable with incomplete information.Persuasion, argumentation, negotiation, conflicts and science social.