Some authors have begun to appeal directly to studies of argumentation in their analyses of mathematical practice. These include researchers from an impressively diverse range of disciplines: not only philosophy of mathematics and argumentation theory, but also psychology, education, and computer science. This introduction provides some background to their work.

Douglas Walton’s multitudinous contributions to the study of argumentation seldom, if ever, directly engage with argumentation in mathematics. Nonetheless, several of the innovations with which he is most closely associated lend themselves to improving our understanding of mathematical arguments. I concentrate on two such innovations: dialogue types (§1) and argumentation schemes (§2). I argue that both devices are much more applicable to mathematical reasoning than may be commonly supposed.

In this paper, we present a survey of the development of the technique of argument diagramming covering not only the fields in which it originated - informal logic, argumentation theory, evidence law and legal reasoning – but also more recent work in applying and developing it in computer science and artificial intelligence. Beginning with a simple example of an everyday argument, we present an analysis of it visualised as an argument diagram constructed using a software tool. In the context of (...) a brief history of the development of diagramming, it is then shown how argument diagrams have been used to analyze and work with argumentation in law, philosophy and artificial intelligence. (shrink)

The paper examines Walton‘s concept of fallacy as it develops throughthree stages of his work: from the early series of papers co-authored withJohn Woods; through a second phase of involvement with thepragma-dialectical perspective; and on to the final phase in which heoffers a distinct pragmatic theory that reaches beyond the perceived limitsof the pragma-dialectical account while still exhibiting a debt to thatperspective and the early investigations with Woods. It is observed how Walton‘s model of fallacy is established in distinction to (...) its competitors,and its various problems and successes are discussed. (shrink)

According to van Eemeren, argumentation theory is a hybrid discipline, because it requires a multidisciplinary, if not interdisciplinary approach, combining descriptive and normative insights. He points out that modern argumentation theorists give substance to the discipline by relying either on a dialectical perspective, concentrating on the reasonableness of argumentation, or on a rhetorical perspective, concentrating on its effectiveness. Both the dialectical and the rhetorical perspective are interpreted in ways related to how they were viewed by Aristotle, but in modern argumentation (...) theory the relationship between the two, captured in Aristotle’s term antistrophos, is lost. According to van Eemeren, this relationship, which he considers crucial to a full-fledged argumentation theory, has been recovered in extended pragma-dialectics with the help of the theoretical notion of ‘strategic manoeuvring.’. (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 van Eemeren, argumentation theory is a hybrid discipline, because it requires a multidisciplinary, if not interdisciplinary approach, combining descriptive and normative insights. He points out that modern argumentation theorists give substance to the discipline by relying either on a dialectical perspective, concentrating on the reasonableness of argumentation, or on a rhetorical perspective, concentrating on its effectiveness. Both the dialectical and the rhetorical perspective are interpreted in ways related to how they were viewed by Aristotle, but in modern argumentation (...) theory the relationship between the two, captured in Aristotle’s term antistrophos, is lost. According to van Eemeren, this relationship, which he considers crucial to a full-fledged argumentation theory, has been recovered in extended pragma-dialectics with the help of the theoretical notion of ‘strategic manoeuvring.’. (shrink)

Rorty claims argument is inherently conservative and philosophical progress comes from "sparkling new ideas," not argument. This assumes an untenable opposition between the generation and the evaluation of ideas, with argument relegated to evaluation. New ideas that contribute to progress arise from critical reflection on problems posed by the tradition, and constrained by the criteria governing evaluation. Thinking directed toward the criticism and evaluation of ideas or products is not algorithmic; it has a generative, creative component. An overall assessment in (...) any complex circumstance requires constructing a new view from the questioning, weighing, rejecting, reconciling, and integrating of numerous divergent points of view. Thus, the process of argumentation can issue in new ideas. (shrink)

The Scientific Revolution spawned not just one methodology, but two. We have emphasized Bacon's inductivism at the expense of Galileo's more abstract, sophisticated method of successive approximation, and so have failed to appreciate Galileo's contribution to the ceteris paribus problem in philosophy of science. My purpose here is to help redress this imbalance. I first briefly review the old unsolved problems, and then point out the Baconian basis of ceteris paribus, as this clause is conventionally understood, and its history from (...) Aristotle to twentieth century Positivism. Then I explore Galileo's method of dealing with unwanted impediments, and the more general problem of 'accidents.' I trace his methodology back to Archimedes and forward through the economic theories of Adam Smith (18th century), J. S. Mill (19th) and Milton Friedman (20th). Finally, I point out ways in which I think Galileo's scientific method sheds light on, and provides a partial solution to, the ceteris paribus problem. (shrink)

Krabbe (2003, in F.H. van Eemeren, J.A. Blair, C.A. Willard and A.F. Snoeck Henkemans (eds.), Proceedings of the Fifth Conference of the International Society for the Study of Argumentation, Sic Sat, Amsterdam, pp. 641–644) defined a metadialogue as a dialogue about one or more dialogues, and a ground-level dialogue as a dialogue that is not a metadialogue. Similarly, I define a meta-argument as an argument about one or more arguments, and a ground-level argument as one which is not a meta-argument. (...) Krabbe (1995, in F.H van Eemeren, R. Grootendorst, J.A. Blair, C.A. Willard and A.F. Snoeck Henkemans (eds.), Proceedings of the Third ISSA Conference on Argumentation, Sic Sat, Amsterdam, pp. 333–344) showed that formal-fallacy criticism (and more generally, fallacy criticism) consists of metadialogues, and that such metadialogues can be profiled in ways that lead to their proper termination or resolution. I reconstruct Krabbe’s metadialogical account into monolectical, meta-argumentative terminology by describing three-types of meta-arguments corresponding to the three ways of proving formal invalidity he studied: the trivial logic-indifferent method; the method of counterexample situation; and the method of formal paraphrase. A fourth type of meta-argument corresponds to what Oliver (1967, Mind 76, 463–478), Govier (1985, Informal Logic 7, 27–33), and Copi (1986) call refutation by logical analogy. A fifth type of meta-argument represents my reconstruction of arguments by parity of reasoning studied by Woods and Hudak (1989, Informal Logic 11, 125–139). Other particular meta-arguments deserving future study are Hume’s critique of the argument from design in the Dialogues Concerning Natural Religion, and Mill’s initial argument in The Subjection of Women about the importance of established custom and general feeling vis-à-vis argumentation. (shrink)

This volume reflects the development and theoretical foundation of a new paradigm for critical thinking based on inquiry. The field of critical thinking, as manifested in the Informal Logic movement, developed primarily as a response to the inadequacies of formalism to represent actual argumentative practice and to provide useful argumentative skills to students. Because of this, the primary focus of the field has been on informal arguments rather than formal reasoning. Yet the formalist history of the field is still evident (...) in its emphasis, with respect to both theory and pedagogy, on the structure and evaluation of individual, de-contextualized arguments. It is our view that such a view of critical thinking is excessively narrow and limited, failing to provide an understanding of argumentation as largely a matter of comparative evaluation of a variety of contending positions and arguments with the goal of reaching a reasoned judgment on an issue. As a consequence, traditional critical thinking instruction is problematic in failing to provide the reasoning skills that students need in order to accomplish this goal. Instead, the goal of critical thinking instruction has been seen largely as a defensive one: of learning to not fall prey to invalid, inadequate, or fallacious arguments. (shrink)

The paper critically investigates the pragma-dialectics of van Eemeren and Grootendorst, particularly the treatment of fallacies. While the pragma-dialectieians claim that dialectics combines the logical and rhetorical approaches to argumentation, it is argued here that the perspective relies heavily on rhetorical features that have been suppressed in the account and that overlooking these features leads to significant problems in the pragma-dialectical perspective. In light of these problems, the author advocates turning attention to a rhetorical account which subsumes the logical and (...) dialectical. (shrink)

In this paper, a solution to the problem of analyzing burden of proof in argumentation is developed by building on the pioneering work of Erik C. W. Krabbe on metadialogues. Three classic cases of burden of proof disputes are analyzed, showing how metadialogue theory can solve the problems they pose. The solution is based on five dialectical requirements: (1) global burden of proof needs to be set at the confrontation stage of a dialogue, (2) there need to be special mechanisms (...) for resolving disputes about burden of proof at all four stages of the dialogue, (3) they are especially significant during the argumentation stage, where burden of proof often shifts back and forth at each move, (4) such local shifts need to be partly regulated by the global burden of proof already set, and (5) the connection between burden of proof and the speech act of making a presumption in a dialogue needs to be clarified. (shrink)

A critical examination of the dialectical approach, focusing on a comparison ofthe illative and the dialectical definitions of argument. I distinguish a moderate, a strong and a hyper dialectical conception of argument. I critique Goldman's argument for the moderate conception and Johnson's argument for the strong conception, and argue that the moderate conception is correct.

I begin by formulating the problem of the nature of fallacy in terms of the logic of the negative evaluation of argument, that is, in terms of a theory of logical criticism; here I discuss several features of my approach and several advantages vis-à-vis other approaches; a main feature of my approach is the concern to avoid both formalist and empiricist excesses. I then define six types of fallaciousness, labeled formal, explanatory, presuppositional, positive, semantical, and persuasive; they all involve arguments (...) whose conclusion may be said not to follow from the premises, that is, they involve the logical evaluation of relationships among propositions. I also provide a set of data consisting of four historical cases or nine specific instances of fallacious arguments; these all pertain to the Copernican controversy about the earth's motion in the seventeenth century. I end with a discussion of further problems and inquiries that deserve attention. (shrink)

It is a feature of scientific inquiry that it proceeds alongside a multitude of non-scientific interests. This statement is as true of the scientific inquiries of previous centuries, many of which brought scientists into conflict with institutionalised religious thinking, as it is true of the scientific inquiries of today, which are conducted increasingly within commercial and political contexts. However, while the fact of the coexistence of scientific and non-scientific interests has changed little over time, what has changed with time is (...) the effect of this coexistence on scientific inquiry itself. While scientists may no longer construct their theories with various religious dictates in mind, growing commercial and political interests in science have served to distort the interpretation of science. Using the U.K.’s recent crisis with bovine spongiform encephalopathy (BSE) as my context, I examine two ways in which this distortion has occurred – the interpretation of the science of BSE by politicians and by commercial parties for the purposes of justifying policy decisions and informing the public of risk, respectively. Fallacious reasoning, I contend, is the manifestation of this distortion in these contexts. In demonstration of this claim, I examine how politicians and commercial parties alike have employed two fallacies in their assessments of the science of BSE. These fallacies extend in novel ways the set of so-called traditional informal fallacies. The interpretation of science, I conclude, is a rich context in which to conduct a study of fallacious reasoning; moreover, such a study can contribute in significant ways, I argue, to the public understanding of science. (shrink)