This paper argues that new light may be shed on mathematical reasoning in its non-pathological forms by careful observation of its pathologies. The first section explores the application to mathematics of recent work on fallacy theory, specifically the concept of an ‘argumentation scheme’: a characteristic pattern under which many similar inferential steps may be subsumed. Fallacies may then be understood as argumentation schemes used inappropriately. The next section demonstrates how some specific mathematical fallacies may be characterized in terms of argumentation (...) schemes. The third section considers the phenomenon of correct answers which result from incorrect methods. This turns out to pose some deep questions concerning the nature of mathematical knowledge. In particular, it is argued that a satisfactory epistemology for mathematical practice must address the role of luck. (shrink)

One of the crucial problems of argumentation schemes as illustrated in (Walton, Reed & Macagno 2008) is their practical use for the purpose of analyzing texts and producing arguments. The high number and the lack of a classification criterion make this instrument extremely difficult to apply practically. The purpose of this paper is to analyze the structure of argumentation schemes and outline a possible criterion of classification based on alternative and mutually-exclusive possibilities. Such a criterion is based not on what (...) an argument is, but how it can be understood and interpreted. The schemes are grouped according to an end-means principle, which is strictly bound to the ontological structure of the conclusion and the premises. On this view, a scheme can be selected according to the intended or reconstructed purpose of an argument and the possible strategies that can be used to achieve it. (shrink)

The relationship between teaching and argumentation is becoming a crucial issue in the field of education and, in particular, science education. Teaching has been analyzed as a dialogue aimed at persuading the interlocutors, introducing a conceptual change that needs to be grounded on the audience’s background knowledge. This paper addresses this issue from a perspective of argumentation studies. Our claim is that argumentation schemes, namely abstract patterns of argument, can be an instrument for reconstructing the tacit premises in students’ argumentative (...) reasoning and retrieving the background beliefs that are the basis of their arguments. On this perspective, the process of premise reconstruction is followed by a heuristic reasoning process aimed at discovering the students’ previous intuitions that can explain the premises and concepts that are left unexpressed in their arguments. The theoretical insights advanced in this paper are illustrated through selected examples taken from activities concerning predictive claims on scientific issues. (shrink)

The purpose of this paper is to analyze the structure and the defeasibility conditions of argument from analogy, addressing the issues of determining the nature of the comparison underlying the analogy and the types of inferences justifying the conclusion. In the dialectical tradition, different forms of similarity were distinguished and related to the possible inferences that can be drawn from them. The kinds of similarity can be divided into four categories, depending on whether they represent fundamental semantic features of the (...) terms of the comparison or non-semantic ones, indicating possible characteristics of the referents. Such distinct types of similarity characterize different kinds of analogical arguments, all based on a similar general structure, in which a common genus is abstracted. Depending on the nature of the abstracted common feature, different rules of inference will apply, guaranteeing the attribution of the analogical predicate to the genus and to the primary subject. This analysis of similarity and the relationship thereof with the rules of inference allows a deeper investigation of the defeasibility conditions. (shrink)

This volume presents a selection of papers reflecting key theoretical issues in argumentation theory. Its six sections are devoted to specific themes, including the analysis and evaluation of argumentation, argument schemes and the contextual embedding of argumentation. The section on general perspectives on argumentation discusses the trends of empiricalization, contextualization and formalization, offers descriptions of the analytical and evaluative tools of informal logic, and highlights selected principles that argumentation theorists do and do not agree upon. In turn, the section on (...) linguistic approaches to argumentation focuses on the problem of distinguishing between explanation and argument, while also elaborating on the role of verbal indicators of argument schemes. All essays included in this volume point out notable recent developments in the study of argumentation. (shrink)

A Bibliography of Douglas Walton’s Published Works, 1971-20.