Teaching Religious Doubt with Toulmin's Model of Reasoning

Abstract. Teaching students to doubt, that is, to “test,” theological arguments as one might test any other kind of knowledge is challenging in that the warrant for such testing is not immediately clear. Stephen Toulmin, Richard Rieke, and Allan Janik's model of reasoning provides a conceptual framework that demonstrates the logical relationships between a claim, its grounds, warrants, and backing for warrants. Against such a model, the instructor and students may study religious claims, both biblical and theological, with the aim of analyzing the ways such claims find support or a lack of support depending upon the particular ways that claims and evidence have competing warrants. Several pedagogical benefits ensue. First, students see that the validity for theological claims rests as much upon warrants as it does upon grounding. Second, searching for ancient warrants privileges historical‐critical investigation. Third, competing warrants for contradictory theological claims summon pedagogical metaphors of process and development.     

Diagrams as sketches

This article puts forward the notion of ??evolving diagram?? as an important case of mathematical diagram. An evolving diagram combines, through a dynamic graphical enrichment, the representation of an object and the representation of a piece of reasoning based on the representation of that object. Evolving diagrams can be illustrated in particular with category-theoretic diagrams (hereafter ??diagrams*??) in the context of ??sketch theory,?? a branch of modern category theory. It is argued that sketch theory provides a diagrammatic* theory of diagrams*, that it helps to overcome the rivalry between set theory and category theory as a general semantical framework, and that it suggests a more flexible understanding of the opposition between formal proofs and diagrammatic reasoning. Thus, the aim of the paper is twofold. First, it claims that diagrams* provide a clear example of evolving diagrams, and shed light on them as a general phenomenon. Second, in return, it uses sketches, understood as evolving diagrams, to show how diagrams* in general should be re-evaluated positively.     

Cochrane Review as a “Warranting Device” for Reasoning About Health

Contemporary reasoning about health is infused with the work products of experts, and expert reasoning about health itself is an active site for invention and design. Building on Toulmin’s largely undeveloped ideas on field-dependence, we argue that expert fields can develop new inference rules that, together with the backing they require, become accepted ways of drawing and defending conclusions. The new inference rules themselves function as warrants, and we introduce the term “warranting device” to refer to an assembly of the rule plus whatever material, procedural, and institutional resources are required to assure its dependability. We present a case study on the Cochrane Review, a new method for synthesizing evidence across large numbers of scientific studies. After reviewing the evolution and current structure of the device, we discuss the distinctive kinds of critical questions that may be raised around Cochrane Reviews, both within the expert field and beyond. Although Toulmin’s theory of field-dependence is often criticized for its relativism, we find that, as a matter of practical fact, field-specific warrants do not enjoy immunity from external critique. On the contrary, they can be opened to evaluation and critique from any interested perspective.     

The ‘Medical Body’ As Philosophy's Arena

Medicine, as Byron Good argues, reconstitutes thehuman body of our daily experience as a medical body,unfamiliar outside medicine. This reconstitution can be seen intwo ways: (i) as a salutary reminder of the extent to which thereality even of the human body is constructed; and (ii) as anarena for what Stephen Toulmin distinguishes as theintersection of natural science and history, in which many ofphilosophy's traditional (and traditionally abstract) questionsare given concrete and urgent form.This paper begins by examining a number of dualities between themedical body and the body familiar in daily experience. Toulmin's epistemological analysis of clinical medicine ascombining both universal and existential knowledge is thenconsidered. Their expression, in terms of attention,respectively, to natural science and to personal history, isexplored through the epistemological contrasts between themedical body and the familiar body, noting the traditionalphilosophical questions which they in turn illustrate.     

Scientific Discovery With Law-Encoding Diagrams

This article introduces the concept of law-encoding diagrams (LEDs) and presents the argument that they have had a role in scientific discovery that has not been previously recognized. An LED is a representation that correctly encodes the underlying relations of a law, or a system of simultaneous laws, in the structure of a diagram by the means of geometric, topological, and spatial constraints, such that the instantiation of a particular diagram represents a single instance of the phenomena or a particular case of the law(s). Examples of LEDs in the history of science are discussed, and the benefits of using LEDs in discovery are considered. LEDs are distinguished from other forms of diagrammatic representation. Previous work on the computational modeling of diagrammatic law induction is reinterpreted in terms of the search for diagrammatic constraints of LEDs. A general characterization of the role of LEDs in discovery is considered, and a framework for classifying processes of discovery based on LEDs is proposed.     

Electrifying diagrams for learning: principles for complex representational systems

Six characteristics of effective representational systems for conceptual learning in complex domains have been identified. Such representations should: (1) integrate levels of abstraction; (2) combine globally homogeneous with locally heterogeneous representation of concepts; (3) integrate alternative perspectives of the domain; (4) support malleable manipulation of expressions; (5) possess compact procedures; and (6) have uniform procedures. The characteristics were discovered by analysing and evaluating a novel diagrammatic representation that has been invented to support students' comprehension of electricity—AVOW diagrams (Amps, Volts, Ohms, Watts). A task analysis is presented that demonstrates that problem solving using a conventional algebraic approach demands more effort than AVOW diagrams. In an experiment comparing two groups of learners using the alternative approaches, the group using AVOW diagrams learned more than the group using equations and were better able to solve complex transfer problems and questions involving multiple constraints. Analysis of verbal protocols and work scratchings showed that the AVOW diagram group, in contrast to the equations group, acquired a coherently organised network of concepts, learnt effective problem solving procedures, and experienced more positive learning events. The six principles of effective representations were proposed on the basis of these findings. AVOW diagrams are Law Encoding Diagrams, a general class of representations that have been shown to support learning in other scientific domains.     

Do details bug you? Effects of perceptual richness in learning about biological change

People often have difficulty in understanding processes of biological change, and they typically reject drastic life cycle changes such as metamorphosis, except for animals with which they are familiar. Even after a lesson about metamorphosis, people often do not generalize to animals not seen during the lesson. This might be partially due to the perceptual richness of the diagrams typically used during lessons on metamorphosis, which serves to emphasize the individual animal rather than a class of animals. In two studies, we examined whether the perceptual richness of a diagram influences adults' learning and transfer of knowledge about metamorphosis. One study was conducted in a laboratory setting, and the other was online. In both studies, adults who saw the bland diagram during the lesson accurately transferred more than adults who saw the rich diagram during the lesson.     

Evaluating Arguments Based on Toulmin’s Scheme

Toulmin’s scheme for the layout of arguments (1958, The Uses of Argument, Cambridge University Press, Cambridge) represents an influential tool for the analysis of arguments. The scheme enriches the traditional premises-conclusion model of arguments by distinguishing additional elements, like warrant, backing and rebuttal. The present paper contains a formal elaboration of Toulmin’s scheme, and extends it with a treatment of the formal evaluation of Toulmin-style arguments, which Toulmin did not discuss at all. Arguments are evaluated in terms of a so-called dialectical interpretation of their assumptions. In such an interpretation, an argument’s assumptions can be evaluated as defeated, e.g., when there is a defeating reason against the assumption. The present work builds on recent research on defeasible argumentation (cf. e.g. the work of Pollock, Reiter, Loui, Vreeswijk, Prakken, Hage and Dung). More specifically, the author’s work on the dialectical logic DEFLOG and the argumentation tool ARGUMED serve as starting points.     

Medial frontal cortex function: An introduction and overview

The growing attention being given to medial frontal cortex (MFC) in cognitive neuroscience studies has fostered a number of theoretical and paradigmatic perspectives that diverge in important ways. This has led to a great deal of research fractionation, with investigators studying domains and issues in MFC function that sometimes bear (at least at the surface) little relation to the questions addressed by others studying the same brain region. The present issue of Cognitive, Affective, & Behavioral Neuroscience presents articles inspired by a conference bringing together views from across this diversity of research, highlighting both the richness and vibrancy of the field and the challenges to be faced in terms of integration, synthesis, and precision among the theoretical accounts. The present article presents a brief introduction, overview, and road map to the field and to the special issue devoted to MFC function.     

The effect of emergent features on judgments of quantity in configural and separable displays

Two experiments investigated effects of emergent features on perceptual judgments of comparative magnitude in three diagrammatic representations: kiviat charts, bar graphs, and line graphs. Experiment 1 required participants to compare individual values; whereas in Experiment 2 participants had to integrate several values to produce a global comparison. In Experiment 1, emergent features of the diagrams resulted in significant distortions of magnitude judgments, each related to a common geometric illusion. Emergent features are also widely believed to underlie the general superiority of configural displays, such as kiviat charts, for tasks requiring the integration of information. Experiment 2 tested the extent of this benefit using diagrams with a wide range of values. Contrary to the results of previous studies, the configural display produced the poorest performance compared to the more separable displays. Moreover, the pattern of responses suggests that kiviat users switched from an integration strategy to a sequential one depending on the shape of the diagram. The experiments demonstrate the powerful interaction between emergent visual properties and cognition and reveal limits to the benefits of configural displays for integration tasks.     

Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization

Proof-theoretical notions and techniques, developed on the basis of sentential/symbolic representations of formal proofs, are applied to Euler diagrams. A translation of an Euler diagrammatic system into a natural deduction system is given, and the soundness and faithfulness of the translation are proved. Some consequences of the translation are discussed in view of the notion of free ride, which is mainly discussed in the literature of cognitive science as an account of inferential efficacy of diagrams. The translation enables us to formalize and analyze free ride in terms of proof theory. The notion of normal form of Euler diagrammatic proofs is investigated, and a normalization theorem is proved. Some consequences of the theorem are further discussed: in particular, an analysis of the structure of normal diagrammatic proofs; a diagrammatic counterpart of the usual subformula property; and a characterization of diagrammatic proofs compared with natural deduction proofs.     

Task‐Related Factors that Influence the Spontaneous Use of Diagrams in Math Word Problems

Diagrams are effective tools for problem solving. However, previous findings indicate that students generally do not use diagrams spontaneously. This study examined task‐related factors that may influence the spontaneity of diagram use. Experiment 1 compared two possible explanations: the first, that the length‐relatedness of the story context of the problem (i.e. whether it involves the measurement of length) determines the likelihood of diagram use; and the second, that the cognitive cost of transforming the situation described in the word problem to an abstract diagrammatic representation is the more important factor. Four math word problems, differing in their story context and structure, were administered to eighth‐grade Japanese students (n = 125) to solve. The results provide support for the cognitive transformation cost explanation. The results of experiment 2, in which the problems were administered to students in both Japan (n = 291) and New Zealand (n = 323), confirm this finding. Copyright © 2011 John Wiley & Sons, Ltd.     

The Family Diagram and Genogram: Comparisons and Contrasts

The family diagram and its derivative the genogram are widely used in marriage and family therapy, other mental health disciplines, and family medicine. After a brief history of the origins of the family diagram and genogram, several different areas are compared in order to help distinguish differences between family diagrams and genograms. The results of these evaluations illustrate some similarities in format and symbols due to a common history, but distinct differences in purpose, theoretical basis, rationale for data collection, and interpretation guidelines. Divergent theoretical perspectives explain the differences between family diagrams and genograms. The family diagram is intertwined with Bowen family systems theory, while the genogram emphasizes how the nuclear family interacts within multiple contextual levels. The family diagram and genogram are not synonymous; rather, they are distinctly different methods of family assessment.     

An Eye‐Tracking Study of Exploitations of Spatial Constraints in Diagrammatic Reasoning

Semantic studies on diagrammatic notations (Barwise & Etchemendy, 1990 ; Shimojima, 1995 ; Stenning & Lemon, 2001 ) have revealed that the “non‐deductive,” “emergent,” or “perceptual” effects of diagrams (Chandrasekaran, Kurup, Banerjee, Josephson, & Winkler, 2004 ; Kulpa, 2003 ; Larkin & Simon, 1987 ; Lindsay, 1988 ) are all rooted in the exploitation of spatial constraints on graphical structures. Thus, theoretically, this process is a key factor in inference with diagrams, explaining the frequently observed reduction of inferential load. The purpose of this study was to examine the empirical basis for this theoretical suggestion, focusing on the reality of the constraint‐exploitation strategy in actual practices of diagrammatic reasoning. Eye movements were recorded while participants used simple position diagrams to solve three‐ or four‐term transitive inference problems. Our experiments revealed that the participants could exploit spatial constraints on graphical structures even when (a) they were not in the position of actually manipulating diagrams, (b) the semantic rule for the provided diagrams did not match their preferences, and (c) the constraint‐exploitation strategy invited a partly adverse effect. These findings indicate that the hypothesized process is in fact robust, with the potential to broadly account for the inferential advantage of diagrams.     

The Entangling of Problems,Solutions and Markets: On Building a Market for Privacy

An increasing number of public problems have been subject to market-based interventions as solutions. However, the relationship between problems and solutions in market-based interventions is complex. On occasions solutions are reformulated as understanding of the nature of the problem are advanced. Alternatively, problems are reconfigured to fit a standard solution. Or solutions are said to generate numerous new problems. The complex entangling of problems, solutions and markets can be explored by focusing on the field of online privacy. The complexities of this field can be analysed through three science and technology studies (STS) treatments of problems and solutions. First, issue-problematisation can be used to understand the ways in which a problem is assembled and comes to form the focus for discussion as an issue. Second, a paradigm-exemplar approach can assess the extent to which a particular coupling of problem and solution becomes an exemplar for others to draw on. Third, ontological constitution provides a focal point for analysing the ways in which the very nature of entities involved in problems, solutions and markets can be considered. There is analytic utility in each of these approaches in engaging with online privacy regulation and the emerging role of start-ups in introducing new privacy products to an emerging market place. However, these STS approaches leave us with questions regarding the relationship between market solutions and publics, the co-ordination of entities in market solutions and the normative questions that arise from entangling markets, problems and solutions.     

TURNING STONES INTO BREAD: DEVELOPING SYNERGISTIC SCIENCE/RELIGION APPROACHES TO THE WORLD FOOD CRISIS

The Institute on Religion in an Age of Science (IRAS) has a long history of delivering conferences addressing topics of interest in the field of science and religion. The following papers from the 2013 summer conference on “The Scientific, Spiritual, and Moral Challenges in Solving the World Food Crisis” are, in keeping with the eclectic nature of these conferences, very different in content and approach. Such differences underline the challenges of synergistically combining scientific and religious insights to increase understanding of global problems and their possible solutions. This in turn reflects deeper questions about the purpose and nature of the science/religion dialogue. These papers suggest various ways in which the two perspectives can be combined in the pursuit of building better understandings of food‐related issues, as well as highlighting difficulties and limitations which need to be addressed if the fruits of such dialogue are to make a wider impact. As such they serve as useful pointers for how this type of science/religion interaction might be further developed and deployed.     

Comprehension as affected by structure of problem representation

A problem-like branching system describing what prizes (A through F) were awarded for particular outcomes of a tournament of games among three teams was presented to 200 subjects as either a verbal list with “go to” structure (Jump), a shortened verbal list (Short-Jump), nested verbal paragraphs with “if ... then..., else” structure (Nest), a matrix table (Example), or as diagrammatic representations of each of these. In tests of comprehension, the overall performance increased from lowest to highest as follows: Jump < Short-Jump ? Nest < Example, and this order was particularly strong for performance on complex questions relative to less complex questions. Jump and Short-Jump performance was relatively higher with diagrams and Example was lower with diagrams. Implications for a theory of problem representation and for development of computer programming languages were discussed.     

Premissary relevance

Premissary relevance is a property of arguments understood as speech act complexes. It is explicable in terms of the idea of a premise's lending support to a conclusion. Premissary relevance is a function of premises belonging to a set which authoritatively warrants an inference to a conclusion. An authoritative inference warrant will have associated with it a conditional proposition which is true— that is to say, which can be justified. The study of the Aristotelian doctrine of topoi or argument schemes may contribute to the task of identifying authoritative warrants.     

Counterexample Search in Diagram-Based Geometric Reasoning

Topological relations such as inside, outside, or intersection are ubiquitous to our spatial thinking. Here, we examined how people reason deductively with topological relations between points, lines, and circles in geometric diagrams. We hypothesized in particular that a counterexample search generally underlies this type of reasoning. We first verified that educated adults without specific math training were able to produce correct diagrammatic representations contained in the premisses of an inference. Our first experiment then revealed that subjects who correctly judged an inference as invalid almost always produced a counterexample to support their answer. Noticeably, even if the counterexample always bore a certain level of similarity to the initial diagram, we observed that an object was more likely to be varied between the two drawings if it was present in the conclusion of the inference. Experiments 2 and 3 then directly probed counterexample search. While participants were asked to evaluate a conclusion on the basis of a given diagram and some premisses, we modulated the difficulty of reaching a counterexample from the diagram. Our results indicate that both decreasing the counterexample density and increasing the counterexample distance impaired reasoning performance. Taken together, our results suggest that a search procedure for counterexamples, which proceeds object-wise, could underlie diagram-based geometric reasoning. Transposing points, lines, and circles to our spatial environment, the present study may ultimately provide insights on how humans reason about topological relations between positions, paths, and regions.     

Reflective Sociocultural Psychology: Lost and Found in Collaboration with Funding Agencies and ICT Experts

This paper deals with emerging kinds of collaboration between researchers, funding agencies and ICT (Information and Communications Technology) experts. The goal of this paper is to analyze the challenges and opportunities for researchers presented by such collaborations. The analysis is based on a sociocultural approach, and leads to the following conclusions: (a) the main challenges to collaboration arise from the fact that partners’ communities have different goals and use different sets of mediation tools, (b) there are different ways for researchers to cope with more powerful partners such as major funding agencies (refusing collaboration, pseudo collaboration, asymmetric collaboration, and real partnership), (c) appropriation of mediation tools developed by partners could be useful for researchers, (d) collaboration with partners could be a source of new theoretically interesting phenomenon, and (e) communication with partners who are not familiar with our routine discourses might help us to improve our own understanding.