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706Leonard 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.
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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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25Commentary on: Michel Dufour's "Argument and explanation in 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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725The philosophy of alternative logicsIn Leila Haaparanta (ed.), The development of modern logic, Oxford University Press. pp. 613-723. 2011.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
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211Rationale of the Mathematical JokeIn 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.
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35Is 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.
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599Logic for dogsIn 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
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24Edouard Morot-Sir, The Imagination of Reference II: Perceiving, Indicating, Naming (review)Philosophy in Review 16 (4): 270-271. 1996.
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700Five theories of reasoning: Interconnections and applications to mathematicsLogic 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
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1The companions and Socrates: Is Inara a hetaera?In Rhonda V. Wilcox & Tanya Cochran (eds.), Investigating Firefly and Serenity: Science Fiction on the Frontier, I. B. Tauris. pp. 63-75. 2008.
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279Observations on Sick MathematicsIn 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
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63Fallacies in MathematicsProceedings 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.
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61The parallel structure of mathematical reasoningIn 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
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489Raising the tone: Definition, bullshit, and the definition of bullshitIn 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.
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 |