Evidence, Proofs, and Derivations

The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation schemes, in particular, as a methodology for the study of mathematical practice is thereby demonstrated. Argumentation schemes represent an almost untapped resource for mathematics education. Notably, they provide a consistent treatment of rigorous and non-rigorous argumentation, thereby working to exhibit the continuity of reasoning in mathematics with reasoning in other areas. Moreover, since argumentation schemes are a comparatively mature methodology, there is a substantial body of existing work to draw upon, including some increasingly sophisticated software tools. Such tools have significant potential for the analysis and evaluation of mathematical argumentation. The first four sections of the paper address the relationships of evidence to proof, proof to derivation, argument to proof, and argument to evidence, respectively. The final section directly addresses some of the educational implications of an argumentation scheme account of mathematical reasoning

Argumentation schemes for collaborative planning

Postprin

Assessing relevance

This paper advances an approach to relevance grounded on patterns of material inference called argumentation schemes, which can account for the reconstruction and the evaluation of relevance relations. In order to account for relevance in different types of dialogical contexts, pursuing also non-cognitive goals, and measuring the scalar strength of relevance, communicative acts are conceived as dialogue moves, whose coherence with the previous ones or the context is represented as the conclusion of steps of material inferences. Such inferences are described using argumentation schemes and are evaluated by considering 1) their defeasibility, and 2) the acceptability of the implicit premises on which they are based. The assessment of both the relevance of an utterance and the strength thereof depends on the evaluation of three interrelated factors: 1) number of inferential steps required; 2) the types of argumentation schemes involved; and 3) the implicit premises required

Argumentation schemes from Hamblin's dialectical perspective

This paper aims at a normative account of non-deductive argumentation schemes in the spirit of Hamblin's dialectical philosophy. First, three principles are presented that characterize Hamblin's dialectical stance. Second, argumentation schemes, which have hardly been examined in Hamblin's book Fallacies, shall be dealt with by applying these principles, taking an argumentation scheme from authority as the leading example. Third, a formal dialectical system, along the lines indicated by Hamblin, shall be developed that includes norms for using argumentation schemes and norms for responding to arguments that are presented as instantiating acceptable argumentation schemes

Walton’s Argumentation Schemes

The contribution critically discusses Walton\u27s (and Reed’s and Macagno’s) argumentation scheme approach. On the one hand, its enormous richness and closeness to the empirical argumentation material is appreciated, but, on the other, fundamental conceptual weaknesses are revealed. Although the approach more recently has been declared to strive for “true beliefs and correct choices” it has not systematically developed the proposed schemes in a way that these goals are reached. Accordingly, many proposed schemes are fallacious from an epistemological standpoint

On Recognizing Argumentation Schemes in Formal Text Genres

Argumentation mining research should address the challenge of recognition of argumentation schemes in formal text genres such as scientific articles. This paper argues that identification of argumentation schemes differs from identification of other aspects of discourse such as argumentative zones and coherence relations. Argumentation schemes can be defined at a level of abstraction applicable across the natural sciences. There are useful applications of automatic argumentation scheme recognition. However, it is likely that inference-based techniques will be required.(Note: Due to a publishing error, only the abstract of the paper appeared in the published Seminar Report at http://dx.doi.org/10.4230/DagRep.6.4.80

Justification of Argumentation Schemes

Argumentation schemes are forms of argument that capture stereotypical patterns of human reasoning, especially defeasible ones like argument from expert opinion, that have proved troublesome to view deductively or inductively. Much practical work has already been done on argumentation schemes, proving their worth in A1 [19], but more precise investigations are needed to formalize their structures. The problem posed in this paper is what form justification of a given scheme, as having a certain precise structure of inference, should take. It is argued that defeasible argumentation schemes require both a systematic and a pragmatic justification, of a kind that can only be provided by the case study method of collecting key examples of arguments of the types traditionally classified as fallacies, and subjecting them to comparative examination and analysis. By this method, postulated structures for schemes can be formulated as hypotheses to solve three kinds of problems: (1) how to classify such arguments into different types, (2) how to identify their premises and conclusions, and (3) how to formulate the critical questions used to evaluate each type of argument

On argumentation schemes and the natural classification of arguments

We develop conceptions of arguments and of argument types that will, by serving as the basis for developing a natural classification of arguments, benefit work in artificial intelligence. Focusing only on arguments construed as the semantic entities that are the outcome of processes of reasoning, we outline and clarify our view that an argument is a proposition that represents a fact as both conveying some other fact and as doing so wholly. Further, we outline our view that, with respect to arguments that are propositions, (roughly) two arguments are of the same type if and only if they represent the same relation of conveyance and do so in the same way. We then argue for our conceptions of arguments and argument types, and compare them to rival positions. We also illustrate the need for, and some of the strengths of, our approach to classifying arguments through an examination of aspects of two prominent and recent attempts to classify arguments using argumentation schemes, namely those of M. Kienpointner and D. Walton. Finally, we clarify how our conception of arguments and of argument types can assist in developing an exhaustive classification of arguments

An empirical study of argumentation schemes in deliberative dialogue

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