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193The Uses of Argument in MathematicsArgumentation 19 (3): 287-301. 2005.Stephen Toulmin once observed that ”it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate’ [Toulmin et al., 1979, An Introduction to Reasoning, Macmillan, London, p. 89]. Might the application of Toulmin’s layout of arguments to mathematics remedy this oversight? Toulmin’s critics fault the layout as requiring so much abstraction as to permit incompatible reconstructions. Mathematical proofs may indeed be represented by fundamentally distinct l…Read more
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492Strange bedfellows: The interpenetration of philosophy and pornographyIn Dave Monroe (ed.), Porn: How to Think with Kink, Wiley-blackwell. pp. 22-34. 2010.This paper explores some surprising historical connections between philosophy and pornography (including pornography written by or about philosophers, and works that are both philosophical and pornographic). Examples discussed include Diderot's Les Bijoux Indiscrets, Argens's Therésè Philosophe, Aretino's Ragionamenti, Andeli's Lai d'Aristote, and the Gor novels of John Norman. It observes that these works frequently dramatize a tension between reason and emotion, and argues that their existen…Read more
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464Managing Informal Mathematical Knowledge: Techniques from Informal LogicLecture Notes in Artificial Intelligence 4108 208--221. 2006.Much work in MKM depends on the application of formal logic to mathematics. However, much mathematical knowledge is informal. Luckily, formal logic only represents one tradition in logic, specifically the modeling of inference in terms of logical form. Many inferences cannot be captured in this manner. The study of such inferences is still within the domain of logic, and is sometimes called informal logic. This paper explores some of the benefits informal logic may have for the management of inf…Read more
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Balderdash and chicanery: Science and beyondIn James B. South (ed.), Buffy the Vampire Slayer and Philosophy: Fear and Trembling in Sunnydale, Open Court. pp. 79-90. 2003.The status and limits of science are the focus of urgent public debate. This paper contributes a philosophical analysis of representations of science and the supernatural in popular culture. It explores and critiques a threefold taxonomy of supernatural narratives: (1) reduction of the supernatural to contemporary science; (2) reduction to a `future science' methodologically continuous with contemporary science; (3) the supernatural as irreducible. The means by which the TV series Buffy the Va…Read more
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134Introduction: Virtues and ArgumentsTopoi 35 (2): 339-343. 2016.It has been a decade since the phrase virtue argumentation was introduced, and while it would be an exaggeration to say that it burst onto the scene, it would be just as much of an understatement to say that it has gone unnoticed. Trying to strike the virtuous mean between the extremes of hyperbole and litotes, then, we can fairly characterize it as a way of thinking about arguments and argumentation that has steadily attracted more and more attention from argumentation theorists. We hope it is …Read more
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39Commentary on: Begoña Carrascal's "The practice of arguing and the arguments: Examples from mathematics"In Dima Mohammed & Marcin Lewinski (eds.), Virtues of argumentation: Proceedings of the 10th International Conference of the Ontario Society for the Study of Argumentation (OSSA), May 22–25, 2013, Ossa. 2014.N/A.
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83The informal logic of mathematical proofIn Reuben Hersh (ed.), 18 Unconventional Essays on the Nature of Mathematics, Springer. pp. 56-70. 2006.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: th…Read more
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112Persuasive definitionIn H. V. Hansen, C. W. Tindale & A. V. Colman (eds.), Argumentation and Rhetoric, Vale. 1998.Charles Stevenson introduced the term 'persuasive definition’ to describe a suspect form of moral argument 'which gives a new conceptual meaning to a familiar word without substantially changing its emotive meaning’. However, as Stevenson acknowledges, such a move can be employed legitimately. If persuasive definition is to be a useful notion, we shall need a criterion for identifying specifically illegitimate usage. I criticize a recent proposed criterion from Keith Burgess-Jackson and offer an…Read more
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400Mohan Ganesalingam. The Language of Mathematics: A Linguistic and Philosophical Investigation. FoLLI Publications on Logic, Language and Information (review)Philosophia Mathematica 25 (1). 2017.
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23Douglas Walton, One-Sided Arguments: A Dialectical Analysis of Bias (review)Philosophy in Review 21 (2): 152-154. 2001.
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507Virtue in argumentArgumentation 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.
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79The 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
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431Mathematical Wit and Mathematical CognitionTopics 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
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50Classical recaptureIn V. Fano, M. Stanzione & G. Tarozzi (eds.), Prospettive Della Logica E Della Filosofia Della Scienza, Rubettino. pp. 11-18. 2001.
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740Leonard Nelson: A Theory of Philosophical Fallacies: Translated by Fernando Leal and David Carus Springer, Cham, Switzerland, 2016, vi + 211 pp (review)Argumentation 31 (2): 455-461. 2017.
University of St. Andrews
PhD, 2001
Melbourne, Florida, United States of America
Areas of Specialization
Logic and Philosophy of Logic |
Philosophy of Mathematics |
Disagreement |
Epistemic Virtues |