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.

Arguing that our attachment to Aristotelian modes of discourse makes a revision of their conceptual foundations long overdue, the author proposes the consideration of unacknowledged factors that play a central role in argument itself. These are in particular the subjective imprint and the dynamics of argumentation. Their inclusion in a four-dimensional framework and the focus on thesis validity allow for a more realistic view of our discourse practice. Exhaustive analyses of fascinating historical and contemporary arguments are provided. These range from (...) Columbus’s advocacy of the Western Passage to India, over the trial of King Louis XVI during the French Revolution, to today’s highly charged controversies surrounding euthanasia and embryo research. Excavating foundational issues such as the purpose of argument itself and the contested role of argument as a generator of knowledge, the book culminates in a discussion of the relationship between rationality and reasonableness and criticizes the restrictions of ‘rational’ argument relying on fixed logical, economic or cultural criteria that in reality are mutable. Here, a true, open argument requires the infusion of Paul Lorenzen’s principle of ‘transsubjectivity’, which recognizes but transcends the partiality of the individual and which can be seen in the pragmatic and expanding consensus that humanity can control itself to safeguard the future of a fragile, damaged world. (shrink)

According to the argument scheme approach, to evaluate a given scheme-saturating instance completely does entail asking all critical questions relevant to it. Although this is a central task for argumentation theorists, the field currently lacks a method for providing a complete argument evaluation. Approaching this task at the meta-level, we combine a logical with a substantive approach to the argument schemes by starting from Toulmin’s schema: ‘data, warrant, so claim’. For the yet more general schema: ‘premise; if premise, then conclusion; (...) so conclusion’, we forward a meta-level CQ-list that is arguably both complete and applicable. This list should inform ongoing theoretical efforts at generating appropriate object-level CQs for specific argument schemes. (shrink)

Whether abduction is treated as an argument or as an inference, the mainstream view presupposes a tight connection between abduction and inference to the best explanation. This paper critically evaluates this link and supports a narrower view on abduction. Our main thesis is that merely the hypothesis-generative aspect, but not the evaluative aspect, is properly abductive in the sense introduced by C. S. Peirce. We show why equating abduction with IBE unnecessarily complicates argument evaluation by levelling the status of abduction (...) as a third reasoning mode. We also propose a scheme for abductive argument along with critical questions, and suggest retaining abduction alongside IBE as related but distinct categories. (shrink)

The Toulmin model has been proved useful in law and argumentation theory. This model describes the basic process in justifying a claim, which comprises six elements, i.e., claim (C), data (D), warrant (W), backing (B), qualifier (Q), and rebuttal (R). Specifically, in justifying a claim, one must put forward ‘data’ and a ‘warrant’, whereas the latter is authorized by ‘backing’. The force of the ‘claim’ being justified is represented by the ‘qualifier’, and the condition under which the claim cannot be (...) justified is represented as the ‘rebuttal’. To further improve the model, (Goodnight, Informal Logic 15:41–52, 1993) points out that the selection of a backing needs justification, which he calls legitimation justification. However, how such justification is constituted has not yet been clarified. To identify legitimation justification, we separate it into two parts. One justifies a backing’s eligibility (legitimation justification 1 ; LJ 1 ); the other justifies its superiority over other eligible backings (legitimation justification 2 ; LJ 2 ). In this paper, we focus on LJ 1 and apply it to the legal justification (of judgements) in hard cases for illustration purposes. We submit that LJ 1 refers to the justification of the legal interpretation of a norm by its backing, which can be further separated into several orderable subjustifications. Taking the subjustification of a norm’s existence as an example, we show how it would be influenced by different positions in the philosophy of law. Taking the position of the theory of natural law, such subjustification is presented and evaluated. This paper aims not only to inform ongoing theoretical efforts to apply the Toulmin model in the legal field, but it also seeks to clarify the process in the justification of legal judgments in hard cases. It also offers background information for the possible construction of related AI systems. In our future work, LJ 2 and other subjustifications of LJ 1 will be discussed. (shrink)

This paper describes an approach to legal logic based on the formal analysis of argumentation schemes. Argumentation schemes a notion borrowed from the .eld of argumentation theory - are a kind of generalized rules of inference, in the sense that they express that given certain premises a particular conclusion can be drawn. However, argumentation schemes need not concern strict, abstract, necessarily valid patterns of reasoning, but can be defeasible, concrete and contingently valid, i.e., valid in certain contexts or under certain (...) circumstances. A method is presented to analyze argumentation schemes and it is shown how argumentation schemes can be embedded in a formal model of dialectical argumentation. (shrink)

David Hitchcock and Bart Verheij (eds): Arguing on the Toulmin Model. New Essays in Argument Analysis and Evaluation Content Type Journal Article Pages 1-13 DOI 10.1007/s10503-011-9214-y Authors Lester C. van der Pluijm, University of Amsterdam, Amsterdam, The Netherlands Jacky C. Visser, University of Amsterdam, Amsterdam, The Netherlands Journal Argumentation Online ISSN 1572-8374 Print ISSN 0920-427X.

To illustrate the development of argumentation theory, the paper traces the journey of the pragma-dialectical theory as it widened its scope, step by step, from an abstract model of critical discussion to the complexities of actual argumentative discourse. It describes how, having contextualized, empiricalized and formalized their approach, pragma-dialecticians are now putting the theory’s analytical instruments to good use in identifying prototypical argumentative patterns in specific communicative activity types in the various communicative domains. This means that they can now start (...) answering the crucial question about the typical characteristics of their discourse asked by interested lawyers, politicians, academics and other practitioners of argumentation. (shrink)

Arguments figure prominently in our practices of reason-giving. For example, we use them to advance reasons for their conclusions in order to justify believing something, to explain why we believe something, and to persuade others to believe something. Intuitively, using arguments in these ways requires a certain degree of self-reflection. In this paper, I ask: what cognitive requirements are there for using an argument to advance reasons for its conclusion? Towards a partial response, the paper’s central thesis is that in (...) order to so use an argument one must believe the associated inference claim to the effect that the premises collectively are reasons that support the conclusion. I then argue against making it a further cognitive requirement that one be aware of one’s justification for believing such an inference claim. This thesis provides a rationale for the typical informal-logic textbook characterization of argument and motivates a constraint on adequate accounts of what are referred to as inference claims in the informal logic and argumentation literatures. (shrink)

Some solo verbal reasoning serves the function of arriving at a correct answer to a question from information at the reasoner’s disposal. Such reasoning is good if and only if its grounds are justified and adequate, its warrant is justified, and the reasoner is justified in assuming that no defeaters apply. I distinguish seven sources of justified grounds and state the conditions under which each source is trustworthy. Adequate grounds include all good relevant information practically obtainable by the reasoner. The (...) claim must follow from the grounds in accordance with a justified general warrant. If this warrant is not universal, the reasoner must be justified in assuming that no exception-making circumstances hold in the particular case to which it is applied. (shrink)

Various argumentation analysis tools permit the analyst to represent functional components of an argument (e.g., data, claim, warrant, backing), how arguments are composed of subarguments and defenses against potential counterarguments, and argumentation schemes. In order to facilitate a study of argument presentation in a biomedical corpus, we have developed a hybrid scheme that enables an analyst to encode argumentation analysis within the framework of Rhetorical Structure Theory (RST), which can be used to represent the discourse structure of a text. This (...) paper describes the hybrid representation scheme and illustrates its use for investigation of contexts that license omission of elements of an argument. The analyses given in the paper involve reconstruction of enthymemes. Defeasible argumentation schemes serve as a constraint on reconstruction. In addition, the examples illustrate several other types of contextual constraints on reconstruction of enthymemes. (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)

Although contemporary dialectical logic recognizes an important role for the opponent in argumentation, it remains loyal to the idea that arguments are supportive. In this paper, it is argued that because of this dialectical logic does not take seriously its own dialogical perspective. Without acknowledging a substantial role for rebutting factors in argumentation, the role of the opponent remains secondary. Toulmin’s understanding of the rebuttal suggests a way to incorporate such a substantial role of the opponent.