Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. -/- The book begins by first challenging the (...) assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. ​. (shrink)

This paper examines arguments that take counter- considerations into account, and it does so from a dialogical point of view. According to my account, a counterconsideration is part of a critical reaction from a real or imagined opponent, and an arguer may take it into account in his argument in at least six fully responsive ways. Conductive arguments will be characterized as one of these types. In this manner, the paper aims to show how conducive, and related kinds of argument (...) can be understood dialogically. (shrink)

According to pragma-dialectical methodology, a party in an argumentative discussion can be assumed to manoeuvre strategically between dialectical and rhetorical objectives. One confrontational form of strategic manoeuvring occurs when a critic charges an arguer with advancing a standpoint that has socially harmful consequences. In special situations this form of manoeuvring can be dialectically sound, for example when the standpoint is advanced in a way that damages the dialectical process. The boundary between fallacious and dialectically sound applications of this form of (...) manoeuvring is examined by looking for the manoeuvring’s soundness conditions. (shrink)

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. (shrink)

When is an argument to be called one-sided? When is putting forward such an argument fallacious? How can we develop a model for critical discussion, such that a fallaciously one-sided argument corresponds to a violation of a discussion rule? These issues are dealt with within ‘the limits of the dialogue model of argument’ by specifying a type of persuasion dialogue in which an arguer can offer complex arguments to anticipate particular responses by a critic.

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. (shrink)

There is a widely held concern that using war and sport metaphors to describe argument contributes to the breakdown of argumentative processes. The thumbnail version of this worry about such metaphors is that they promote adversarial conceptions of argument that lead interlocutors with those conceptions to behave adversarially in argumentative contexts. These actions are often aggressive, which undermines argument exchange by either excluding many from such exchanges or turning exchanges more into verbal battles. These worries are legitimate as far as (...) they go, and given that well-run argumentation is a good thing, we would be remiss not to consider whether our vocabulary inhibits argument's proper functioning. .. (shrink)

A critic may attack an arguer personally by pointing out that the arguer’s position is pragmatically inconsistent: the arguer does not practice what he preaches. A number of authors hold that such attacks can be part of a good argumentative discussion. However, there is a difficulty in accepting this kind of contribution as potentially legitimate, for the reason that there is nothing wrong for a protagonist to have an inconsistent position, in the sense of committing himself to mutually inconsistent propositions. (...) If so, any such charge seems to be irrelevant. The questions to be answered in this essay are: what, if any, is the dialectical rationale for this type of criticism, and in what situations, if any, is this kind of charge dialectically legitimate? It will be shown that these attacks can be dialectically legitimate, in special circumstances, and that they can be seen as strategic␣manoeuvres where a party attempts to reconcile his dialectical and his rhetorical objectives. (shrink)

The use of ambiguous expressions in argumentative dialogues can lead to misunderstanding and equivocation. Such ambiguities are here called active ambiguities . However, even a normative model of persuasion dialogue ought not to ban active ambiguities altogether, one reason being that it is not always possible to determine beforehand which expressions will prove to be actively ambiguous. Thus, it is proposed that argumentative norms should enable each participant to put forward ambiguity criticisms as well as self-critical ambiguity corrections, inducing them (...) to improve their language if necessary. In order to discourage them from nitpicking and from arriving at excessively high levels of precision, the parties are also provided with devices with which to examine whether the ambiguity corrections or ambiguity criticisms have been appropriate. A formal dialectical system is proposed, in the Hamblin style, that satisfies these and some other philosophical desiderata. (shrink)

How does the analysis and evaluation of argumentation depend on the dialogue type in which the argumentation has been put forward? This paper focuses on argumentative bluff in eristic discussion. Argumentation cannot be presented without conveying the pretence that it is dialectically reasonable, as well as, at least to some degree, rhetorically effective. Within eristic discussion it can be profitable to engage in bluff with respect to such claims. However, it will be argued that such bluffing is dialectically inadmissible, even (...) within an eristic discussion. (shrink)

In this paper, I try to develop an informal model for the analysis and evaluation of argumentative strategies based on active authorities. The explanations necessary to understand the idea of the model and what is modelled are given through the development of the paper. I first give an example of argumentative activities. After that, the main assumption of the model is given. In the third part, the relevant aspects of the argumentative activity are analysed, while the principles of the evaluation (...) are explained in the fourth part. The informal model is presented in the fifth part. In the final remarks, the suggestions for further work are given, as well as a comparison with some related recent works in argumentation theory. (shrink)

The three research questions of this study have been: what exactly is active ambiguity?; how should we assess active ambiguities in an argumentative discussion?; what does an adequate dialectical account of active ambiguity look like? These three questions have been answered by giving a definition of active ambiguity, and by elaborating on the properties of active ambiguity. Based on the survey of possible consequences of active ambiguities, and based on the basic division of labour in a persuasion dialogue, we arrived (...) at a set of requirements that a normative, procedural account of active ambiguity should satisfy. The model for ambiguity dialectic both provides a detailed account of evaluating active ambiguities, as well as a dialectical account of dealing with alleged active ambiguity. The distinction between constitutive and regulative rules for discussion has made it possible to provide a discussion model in which discussants can raise the issue of active ambiguity, and in which they can argue about the correctness of such points of order. This immanent dialectical approach has lead to a fourfold classification of fallacies: by using an actively ambiguous expression a party either violates a regulative, or a constitutive rule for persuasion dialogue, and if this party violates a rule, he or she either commits a fallacy of ambiguity, and possibly also the more complex fallacy of equivocation. This model for ambiguity dialectic has been shown to be useful for the analysis and evaluation of complex debates and discussions. The present study can be extended in various ways:  A model for critical discussion can be enriched so that it accommodates other regulative rules, such as the rule that requires arguments to be valid. By doing so, other points of order and other fallacy criticisms can be studied from the perspective of a critical metadiscussion.  The results concerning active ambiguity can be applied to other modes of reasoning, such as visual argumentation.  The results can be applied to ambiguity at the level of larger stretches of argumentative discourse. That could lead to a fruitful contribution to the theory of argument structures.  There still is a need for dialectical models that concern the use of usage declaratives different from providing a disambiguation, such as the use of definitions, clarifications of unfamiliar expressions, amplifications, etc., and the question would have to be answered how the rules with respect to active ambiguity would relate to those models.  The model can be enriched by inserting a specific ‘linguistic utterance meaning testing machine’. That would be a major step towards implementing the model in a computer program.  The use of descriptive profiles of dialogue could be improved further. In order to analyse the way parties respond to dialectically complex contributions, we are in need of a dialectical theory that provides the parties with specific rights and obligations for putting forward complex contributions and for responding to complex contributions. (shrink)

In this article, I further analyze the notion of the effectiveness of argumentative strategies, introduced in Jovičić, 2001. The most relevant achievements of the theories of reasonable discussion and the theories of persuasion are called to mind with the aim of explaining the mechanism of the argumentative effectiveness. As a result, a procedure for evaluating the effectiveness of argumentative strategies is suggested.