The Informal Logic of Mathematical Proof

Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is that a more nuanced understanding of mathematical proof and discovery may be achieved by paying attention to the aspects of mathematical argumentation which can be captured by informal, rather than formal, logic. Two accounts of argumentation are considered: the pioneering work of Stephen Toulmin [The uses of argument, Cambridge University Press, 1958] and the more recent studies of Douglas Walton, [e.g. The new dialectic: Conversational contexts of argument, University of Toronto Press, 1998]. The focus of both of these approaches has largely been restricted to natural language argumentation. However, Walton's method in particular provides a fruitful analysis of mathematical proof. He offers a contextual account of argumentational strategies, distinguishing a variety of different types of dialogue in which arguments may occur. This analysis represents many different fallacious or otherwise illicit arguments as the deployment of strategies which are sometimes admissible in contexts in which they are inadmissible. I argue that mathematical proofs are deployed in a greater variety of types of dialogue than has commonly been assumed. I proceed to show that many of the important philosophical and pedagogical problems of mathematical proof arise from a failure to make explicit the type of dialogue in which the proof is introduced.Comment: 14 pages, 1 figure, 3 tables. Forthcoming in Perspectives on Mathematical Practices: Proceedings of the Brussels PMP2002 Conference (Logic, Epistemology and the Unity of the Sciences Series), J. P. Van Bendegem & B. Van Kerkhove, edd. (Dordrecht: Kluwer, 2004

In memoriam Douglas N. Walton: the influence of Doug Walton on AI and law

Doug Walton, who died in January 2020, was a prolific author whose work in informal logic and argumentation had a profound influence on Artificial Intelligence, including Artificial Intelligence and Law. He was also very interested in interdisciplinary work, and a frequent and generous collaborator. In this paper seven leading researchers in AI and Law, all past programme chairs of the International Conference on AI and Law who have worked with him, describe his influence on their work

Emotion, Relevance and Consolation Arguments

There is a kind of argument offered to console people who are sorry or depressed, to the effect that they should not feel so badly because others are even worse off. In such arguments, B tries to console A for A’s suffering on the grounds that some other person or persons, C, have suffered equally bad things or even worse. Here, A and B may be the same person: people sometimes seek to console themselves. The point is to diminish A’s grief on the grounds that he or she is not alone in feeling it. If a person is grieving from having lost a job, well, there are others who have had the similar experiences or worse; they may have lost several jobs or never had a decent job in the first place. If she has been diagnosed with an illness requiring unpleasant lifestyle restrictions well, many other people are ill and many have worse diseases – terminal illnesses characterized by severe physical pain, for instance. I have often played the role of A in this scenario and that of B, and who knows, perhaps I have, without knowing it, played the role of C as well. Many in the audience could probably report the same thing, since Consolation Arguments of this type are rather common. A recent item circulated on the Internet and forwarded to me by David Hitchcock included the following, among others

Arendtiška Antigonės interpretacija: teisumu grįsta tironija

The aim of this article is to investigate the tyrannical similarity between Antigone and Creon through Hannah Arendt’s political philosophy. As Arendt claimed, tyranny firstly signals the end of the political through which men can share their natality. The very meaning of tyranny is the domination by absoluteness that ends deliberation among mortal beings. Antigone only focuses on the divine law, which is seen as absolute righteousness that precedes the law of the city, and so, she tends to ignore any other option on rightfulness. This article aims to show that not only Creon but also Antigone can be regarded as a tyrant, since Antigone tends to sublime her dedication to an infallible justice, causing her to deny any other claim on justice.Šio straipsnio tikslas – remiantis Hannah Arendt politine filosofija išnagrinėti Antigonės ir Kreonto panašumą tironiškumo požiūriu. Kaip teigia Arendt, tironija pirmiausia signalizuoja politiškumo, kuris įgalina žmones dalintis savo gimstamumu, pabaigą. Pati tironijos prasmė yra absoliutumo įsiviešpatavimas, užbaigiantis bet kokius mirtingų būtybių svarstymus. Antigonė žvelgia vien į dieviškąjį įstatymą ir laiko jį absoliučiu teisumu, kuris esąs pranašesnis už miesto teisę, todėl ji linkusi ignoruoti bet kokio kito teisumo galimybę. Šiuo straipsniu siekiama parodyti, kad tironu galima laikyti ne tik Kreontą, bet ir Antigonę, nes Antigonė aukština savo pasišventimą neklystamam teisingumui, taigi ji neigia bet kokį kitą teisingumo pagrindą

Argumentation and disagreement:a pluralistic approach

In our everyday life and in the public sphere, we often find disagreements that the parties cannot resolve nor even overcome. We might call them persistent disagreements. The main question of this thesis is: “What can the parties do to overcome disagreements reasonably, especially when disagreements are persistent?” I argue that the most reasonable way to deal with disagreement is by using argumentation, whereby I approach argumentation pluralistically. This pluralistic approach implies an expansion of traditional approaches to argumentation like pragma-dialectics or informal logic. According to this pluralistic approach, rational persuasion need not be the only goal of argumentation, because it rarely succeeds, especially in the case of persistent disagreement. Therefore, a pluralistic approach to argumentation implies: a) that the parties might overcome their disagreements by reasonable means different from persuasion - among these means we can consider deliberation, negotiation and settlement; b) that if those means revolve around presenting reasons, they should be considered under the concept argumentation; c) that sometimes persuasion is necessary, but that even then, if the setting of the dialogue is sub-optimal, as in the persistent case, we need a general or nonspecific normative approach to evaluate the contributions of the parties; d) that when fallacies are presented, the proper response to them will depend on certain circumstances of the dialogue, considering the goal of overcoming disagreements reasonably; e) that for overcoming disagreements the parties may need to shift between different dialogue types, and that those shifts have special conditions of their own

Developing University Students’ Argumentative Discourse: An Ill-Structured Issue Pertaining To Black African Immigrants And African Americans

The overarching goal of this three-article five-chapter dissertation was to develop university students’ argument-counterargument integration abilities in persuasive essay writing on an ill-structured issue pertaining to black African immigrants and African Americans. Article One consisted of using phenomenography as a research approach to identify the qualitatively different ways university students perceive black African immigrants and African Americans. The university participants had 24 perceptions in which 10 pertained to black African immigrants and 14 to African Americans. The perceptions were grouped into six descriptive categories. The variations in perceptions were then used as statements for argumentation. The study implies that university students’ perceptions can be translated into arguments or claims to teach argumentation. Article Two is a mixed methods study that examined the effectiveness of criteria instruction and collaborative reasoning on university students’ argumentation abilities. The study consisted of 23 participants in the experimental group and 17 in the control. The following data were collected over the course of 10 weeks: participants\u27 pre-tests, mid-tests, post-tests, and final term papers; audio recordings of the collaborative reasoning group discussions; and observation notes. Analyses were done using a rubric, statistical tests, and dialogue types. The Mann-Whitney U test indicated that while there was no significant statistical difference between the experimental group and control group at the start of study (pre-test), there was a significant statistical difference between the groups on the mid-test, post-test, and final term paper. The findings indicate that the experimental group exhibited better argument-counterargument integration on the writing assessments as a result of learning the criteria instruction and participating in collaborative reasoning. A qualitative analysis revealed that mixed dialogue transpired in each collaborative reasoning group. The study implies that criteria instruction and collaborative reasoning can be used to develop university students’ argumentative discourse. Article Three is a case study that documented two first-year university students’ experiences in the learning of argument-counterargument integration in persuasive essay writing. Learning the criteria instruction for argumentation and participating in collaborative reasoning groups helped the case study university students (one) construct arguments using key elements specified in modified TAP, (two) discuss and explore the ill-structured issue with other university students, and (three) acquire information to develop their arguments and counterarguments. The study implies that educators meet with university students independently and recurrently to monitor students’ learning since paper analyzing is not enough to comprehend students’ knowledge and understanding of argumentation

Coding Christianity: Negotiating Religious Dialogue in Online Participatory Spaces

This dissertation examines rhetorical conditions and internet-mediated communication strategies that open and close dialogue between individuals with diverse and conflicting worldviews. The author illustrates this tension through sacred-secular interactions in college composition classrooms and online environments, positing that navigating conflict between these discourses—namely those espoused by religiously committed students and public university instructors—often requires stepping outside of adversarial communication frameworks. This project makes a case for models of civic engagement that use more deliberative rhetorical approaches prioritizing empathy over defensiveness and understanding before persuasion. To develop these non-adversarial communication approaches for the composition classroom, the author looks to participatory media for insights and studies the negotiation strategies of Christian and atheist YouTube users who leverage the affordances of the video medium, internet logics, and invitational rhetorical strategies to engage ideological differences in their respective online communities. Through mixed methods research involving in-depth interviews with five YouTube vloggers, netnographic study of over 3,000 videos, and statistical analysis of 76,000+ user comments, Coding Christianity finds that perspective-taking in conflict-ridden environments can happen between netizens when content creators opt out of “flame wars” and, instead, explicitly model critical openness and charitable listening to perceived “others.” The author ultimately suggests that sacred-secular tension in both academic and digital environments be used, not diffused, to negotiate conflicting values and engage in rigorous, civil dialogues