•  20
    Douglas Walton, One-Sided Arguments: A Dialectical Analysis of Bias (review)
    Philosophy in Review 21 (2): 152-154. 2001.
  •  159
    Virtue in argument
    Argumentation 24 (2): 165-179. 2010.
    Virtue theories have become influential in ethics and epistemology. This paper argues for a similar approach to argumentation. Several potential obstacles to virtue theories in general, and to this new application in particular, are considered and rejected. A first attempt is made at a survey of argumentational virtues, and finally it is argued that the dialectical nature of argumentation makes it particularly suited for virtue theoretic analysis.
  •  35
    The Argument of Mathematics (edited book)
    Springer. 2013.
    Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, ra…Read more
  •  100
    Mathematical Wit and Mathematical Cognition
    Topics in Cognitive Science 5 (2): 231-250. 2013.
    The published works of scientists often conceal the cognitive processes that led to their results. Scholars of mathematical practice must therefore seek out less obvious sources. This article analyzes a widely circulated mathematical joke, comprising a list of spurious proof types. An account is proposed in terms of argumentation schemes: stereotypical patterns of reasoning, which may be accompanied by critical questions itemizing possible lines of defeat. It is argued that humor is associated w…Read more
  •  37
    Classical recapture
    In V. Fano, M. Stanzione & G. Tarozzi (eds.), Prospettive Della Logica E Della Filosofia Della Scienza, Rubettino. pp. 11-18. 2001.
  •  267
    The philosophy of alternative logics
    In Leila Haaparanta (ed.), The Development of Modern Logic, Oxford University Press. pp. 613-723. 2009.
    This chapter focuses on alternative logics. It discusses a hierarchy of logical reform. It presents case studies that illustrate particular aspects of the logical revisionism discussed in the chapter. The first case study is of intuitionistic logic. The second case study turns to quantum logic, a system proposed on empirical grounds as a resolution of the antinomies of quantum mechanics. The third case study is concerned with systems of relevance logic, which have been the subject of an especial…Read more
  •  74
    Rationale of the Mathematical Joke
    In Alison Pease, Markus Guhe & Alan Smaill (eds.), Proceedings of AISB 2010 Symposium on Mathematical Practice and Cognition, Aisb. pp. 1-6. 2010.
    A widely circulated list of spurious proof types may help to clarify our understanding of informal mathematical reasoning. An account in terms of argumentation schemes is proposed.
  •  24
    Is formal logic a failure? It may be, if we accept the context-independent limits imposed by Russell, Frege, and others. In response to difficulties arising from such limitations I present a Toulmin-esque social recontextualization of formal logic. The results of my project provide a positive view of formal logic as a success while simultaneously reaffirming the social and contextual concerns of argumentation theorists, critical thinking scholars, and rhetoricians.
  •  125
    Logic for dogs
    In Steven D. Hales (ed.), What Philosophy Can Tell You About Your Dog, Open Court. pp. 167-181. 2008.
    Imagine a dog tracing a scent to a crossroads, sniffing all but one of the exits, and then proceeding down the last without further examination. According to Sextus Empiricus, Chrysippus argued that the dog effectively employs disjunctive syllogism, concluding that since the quarry left no trace on the other paths, it must have taken the last. The story has been retold many times, with at least four different morals: (1) dogs use logic, so they are as clever as humans; (2) dogs use logic, so usi…Read more
  •  655
    Five theories of reasoning: Interconnections and applications to mathematics
    with Alison Pease
    Logic and Logical Philosophy 20 (1-2): 7-57. 2011.
    The last century has seen many disciplines place a greater priority on understanding how people reason in a particular domain, and several illuminating theories of informal logic and argumentation have been developed. Perhaps owing to their diverse backgrounds, there are several connections and overlapping ideas between the theories, which appear to have been overlooked. We focus on Peirce’s development of abductive reasoning [39], Toulmin’s argumentation layout [52], Lakatos’s theory of reasoni…Read more
  •  103
    Observations on Sick Mathematics
    In Bart van Kerkhove, Jean Paul van Bendegem & Jonas de Vuyst (eds.), Philosophical Perspectives on Mathematical Practice, College Publications. pp. 269--300. 2010.
    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 speci…Read more
  •  46
    Fallacies in Mathematics
    Proceedings of the British Society for Research Into Learning Mathematics 27 (3): 1-6. 2007.
    This paper considers the application to mathematical fallacies of techniques drawn from informal logic, specifically the use of ”argument schemes’. One such scheme, for Appeal to Expert Opinion, is considered in some detail.
  •  38
    The parallel structure of mathematical reasoning
    In Alison Pease & Brendan Larvor (eds.), Proceedings of the Symposium on Mathematical Practice and Cognition Ii: A Symposium at the Aisb/Iacap World Congress 2012, Society For the Study of Artificial Intelligence and the Simulation of Behaviour. pp. 7--14. 2012.
    This paper proposes an account of mathematical reasoning as parallel in structure: the arguments which mathematicians use to persuade each other of their results comprise the argumentational structure; the inferential structure is composed of derivations which offer a formal counterpart to these arguments. Some conflicts about the foundations of mathematics correspond to disagreements over which steps should be admissible in the inferential structure. Similarly, disagreements over the admissibil…Read more
  •  137
    Raising the tone: Definition, bullshit, and the definition of bullshit
    In G. Reisch & G. Hardcastle (eds.), Bullshit and Philosophy, Open Court. pp. 151-169. 2006.
    Bullshit is not the only sort of deceptive talk. Spurious definitions are another important variety of bad reasoning. This paper will describe some of these problematic tactics, and show how Harry Frankfurt’s treatment of bullshit may be extended to analyze their underlying causes. Finally, I will deploy this new account of definition to assess whether Frankfurt’s definition of bullshit is itself legitimate.
  •  114
    What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, and ‘beautiful’? By applying empirical methods developed by social psychologists, we demonstrate that mathematicians' appraisals of proofs vary on four dimensions: aesthetics, intricacy, utility, and precision. We pay particular attention to mathematical beauty and show that, contrary to the classical view, beauty and simplicity are almost entirely unrelated in mathematics.
  •  141
    Mathematics and argumentation
    Foundations of Science 14 (1-2): 1-8. 2009.
    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.
  •  55
    If good argument is virtuous, then fallacies are vicious. Yet fallacies cannot just be identified with vices, since vices are dispositional properties of agents whereas fallacies are types of argument. Rather, if the normativity of good argumentation is explicable in terms of virtues, we should expect the wrongness of fallacies to be explicable in terms of vices. This approach is defended through case studies of several fallacies, with particular emphasis on the ad hominem.
  •  51
    Is it possible to distinguish communities of arguers by tracking the argumentation schemes they employ? There are many ways of relating schemes to communities, but not all are productive. Attention must be paid not only to the admissibility of schemes within a community of argumentational practice, but also to their comparative frequency. Two examples are discussed: informal mathematics, a convenient source of well-documented argumentational practice, and anthropological evidence of nonstandard …Read more
  •  45
    This book explores the results of applying empirical methods to the philosophy of logic and mathematics. Much of the work that has earned experimental philosophy a prominent place in twenty-first century philosophy is concerned with ethics or epistemology. But, as this book shows, empirical methods are just as much at home in logic and the philosophy of mathematics. Chapters demonstrate and discuss the applicability of a wide range of empirical methods including experiments, surveys, interviews…Read more
  •  24
    Ralph Johnson argues that mathematical proofs lack a dialectical tier, and thereby do not qualify as arguments. This paper argues that, despite this disavowal, Johnson’s account provides a compelling model of mathematical proof. The illative core of mathematical arguments is held to strict standards of rigour. However, compliance with these standards is itself a matter of argument, and susceptible to challenge. Hence much actual mathematical practice takes place in the dialectical tier.
  • Proofs and rebuttals: Applying Stephen Toulmin's layout of arguments to mathematical proof
    In Marta Bílková & Ondřej Tomala (eds.), The Logica Yearbook 2005, Filosofia. pp. 11-23. 2006.
    This paper explores some of the benefits informal logic may have for the analysis of mathematical inference. It shows how Stephen Toulmin’s pioneering treatment of defeasible argumentation may be extended to cover the more complex structure of mathematical proof. Several common proof techniques are represented, including induction, proof by cases, and proof by contradiction. Affinities between the resulting system and Imre Lakatos’s discussion of mathematical proof are then explored.
  •  125
    The Vices of Argument
    Topoi 35 (2): 413-422. 2016.
    What should a virtue theory of argumentation say about fallacious reasoning? If good arguments are virtuous, then fallacies are vicious. Yet fallacies cannot just be identified with vices, since vices are dispositional properties of agents whereas fallacies are types of argument. Rather, if the normativity of good argumentation is explicable in terms of virtues, we should expect the wrongness of bad argumentation to be explicable in terms of vices. This approach is defended through analysis of s…Read more
  •  43
    Several authors have recently begun to apply virtue theory to argumentation. Critics of this programme have suggested that no such theory can avoid committing an ad hominem fallacy. This criticism is shown to trade unsuccessfully on an ambiguity in the definition of ad hominem. The ambiguity is resolved and a virtue-theoretic account of ad hominem reasoning is defended