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, 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. (shrink)

Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of mathematical reasoning closely resemble patterns of reasoning in nonmathematical domains. Hence the tools developed to understand informal reasoning, collectively known as argumentation theory, are also applicable to much mathematical argumentation. This chapter investigates some of the details of that application. Consideration is given to the many contrasting meanings (...) of the word “argument”; to some of the specific argumentation-theoretic tools that have been applied to mathematics, notably Toulmin layouts and argumentation schemes; to some of the different ways that argumentation is implicated in mathematical practices; and to the social aspects of mathematical argumentation. (shrink)

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 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)

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)

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)

According to a dialectical approach to argumentation, a single argument can be seen as a dialogical "Why? Because!" sequence. Does this also apply to multimodal arguments? This paper focuses on multimodal arguments with a predominantly visual character and shows that dialogues are helpful for identifying and reconstructing arguments in multimodal communication. To include nonverbal arguments in dialectical argumentation theory, it is proposed to regard dialogue as mode-fluid. The account of multimodal argument as dialogue will be compared with Champagne and Pietarinen’s (...) account of visual argument as movement. (shrink)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...) or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

Argumentation virtue theory is a new field in argumentation studies. As in the case of virtue ethics and virtue epistemology, the study of virtue argumentation draws its inspiration from the works of Aristotle. First, I discuss the specifics of the argumentational virtues and suggest that they have an instrumental nature, modeled on the relation between the Aristotelian intellectual virtue of ‘practical wisdom’ and the moral virtues. Then, inspired by Aristotle’s discussion of akrasia, I suggest that a theory of fallacy in (...) argumentation virtue theory can be built upon the concept of ‘incontinence’. (shrink)

What role, if any, does dialectic play in Aristotle’s epistemology in the Topics? In this paper I argue that it does play a role, but a role that is independent of endoxa. In the first section, I sketch the case for thinking that dialectic plays a distinctively epistemological role—not just a methodological role, or a merely instrumental role in getting episteme. In the second section, I consider three ways it could play that role, on two of which endoxa play at (...) least a co-starring role. But in the third section, I argue that endoxa don’t play that co-starring role, by arguing for a deflationary account of what endoxa are. For that reason, the third view emerges as the most plausible; but the third view is, I’ll suggest, Platonic. (shrink)

Walter Sinnott-Armstrong argues that moral disagreement and widespread moral bias pose a serious problem for moral intuitionism. Seneca’s view that we just recognise the good could be criticised using a similar argument. His approach to argumentation offers a way out, one that may serve as a model for a revisionary intuitionism.