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367Mohan 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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471Virtue 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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391Mathematical 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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682Leonard 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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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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709The 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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208Rationale 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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573Logic 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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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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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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271Observations 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
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 |