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Profile: Andrew Aberdein (Florida Institute of Technology)
  1. Andrew Aberdein (2014). In Defence of Virtue: The Legitimacy of Agent-Based Argument Appraisal. Informal Logic 34 (1):77-93.
    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.
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  2. Andrew Aberdein (2013). Mathematical Wit and Mathematical Cognition. Topics in Cognitive Science 5 (2):231-250.
    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 with risky forms of inference, which are essential (...)
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  3. Andrew Aberdein & Ian J. Dove (eds.) (2013). The Argument of Mathematics. Springer.
    Bartha, P. (2013). Analogical arguments in mathematics. In A. Aberdein & I.J. Dove (Eds), The Argument of Mathematics (pp. 197—236). Dordrecht: Springer. Bourbaki, N. (1968). Elements of mathematics: Theory of sets. Berlin: Springer.
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  4. Arnfinn Aamodt, Martın Abadi, Areski Nait Abdallah, Yoshihiro Abe, Andreas Abel, Francine F. Abeles, Andrew Aberdein, Kuanysh Abeshev, Nate Ackerman & Juan Pablo Acosta López (2012). Individual Members 2012. Bulletin of Symbolic Logic 18 (4).
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  5. Andrew Aberdein (2012). 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. 7--14.
    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 admissibility of steps in the argumentational structure correspond to different views about mathematical practice. (...)
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  6. Arnfinn Aamodt, Martın Abadi, Yoshihiro Abe, Andreas Abel, Francine F. Abeles, Andrew Aberdein, Kuanysh Abeshev, Nate Ackerman, Martin Adamcik & Winfred P. Adams (2011). Individual Members 2011. Bulletin of Symbolic Logic 17 (4).
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  7. Andrew Aberdein (2011). The Dialectical Tier of Mathematical Proof. In Frank Zenker (ed.), Argumentation: Cognition & Community. Proceedings of the 9th International Conference of the Ontario Society for the Study of Argumentation (OSSA), May 18--21, 2011. OSSA.
    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.
     
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  8. Alison Pease & Andrew Aberdein (2011). Five Theories of Reasoning: Interconnections and Applications to Mathematics. Logic and Logical Philosophy 20 (1-2):7-57.
    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 reasoning in mathematics [23], Pollock’s notions of counterexample [44], and argumentation (...)
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  9. Martın Abadi, Yoshihiro Abe, Andreas Abel, Francine F. Abeles, Andrew Aberdein, J. David Abernethy, Kuanysh Abeshev, Nate Ackerman, Winfred P. Adams & Miloš Adzic (2010). Individual Members 2010. Bulletin of Symbolic Logic 16 (4).
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  10. Andrew Aberdein (2010). Argumentation Schemes and Communities of Argumentational Practice. In Juho Ritola (ed.), Argument Cultures: Proceedings of OSSA 2009. OSSA.
    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 reasoning.
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  11. Andrew Aberdein (2010). Observations on Sick Mathematics. In Bart van Kerkhove, Jean Paul van Bendegem & Jonas de Vuyst (eds.), Philosophical Perspectives on Mathematical Practice. College Publications. 269--300.
    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 specific mathematical fallacies may be characterized in terms of argumentation (...)
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  12. Andrew Aberdein (2010). Rationale of the Mathematical Joke. In Alison Pease, Markus Guhe & Alan Smaill (eds.), Proceedings of AISB 2010 Symposium on Mathematical Practice and Cognition. AISB. 1-6.
    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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  13. Andrew Aberdein (2010). Strange Bedfellows: The Interpenetration of Philosophy and Pornography. In Dave Monroe (ed.), Porn: How to Think with Kink. Wiley-Blackwell. 22-34.
    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 existence poses a problem for philosophical arguments against pornography.
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  14. Andrew Aberdein (2010). Virtue in Argument. Argumentation 24 (2):165-179.
    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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  15. Martın Abadi, Yoshihiro Abe, Andreas Abel, Francine F. Abeles, Andrew Aberdein, J. David Abernethy, Nate Ackerman, Bryant Adams, Winifred P. Adams & Klaus T. Aehlig (2009). Individual Members 2009. Bulletin of Symbolic Logic 15 (4).
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  16. Andrew Aberdein (2009). Mathematics and Argumentation. Foundations of Science 14 (1-2):1-8.
    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.
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  17. Andrew Aberdein & Stephen Read (2009). The Philosophy of Alternative Logics. In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press. 613-723.
    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 especially detailed reform (...)
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  18. Martın Abadi, Yoshihiro Abe, Andreas Abel, Francine F. Abeles, Andrew Aberdein, J. David Abernethy, Bryant Adams, Klaus T. Aehlig, Fritz Aeschbach & Henry Louis Africk (2008). Individual Members 2008. Bulletin of Symbolic Logic 14 (4).
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  19. Andrew Aberdein (2008). Logic for Dogs. In Steven D. Hales (ed.), What Philosophy Can Tell You About Your Dog. Open Court. 167-181.
    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) (...)
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  20. Andrew Aberdein (2008). The 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. 63-75.
  21. Martın Abadi, Yoshihiro Abe, Andreas Abel, Francine F. Abeles, Andrew Aberdein, Nathanael Ackerman, Bryant Adams, Klaus T. Aehlig, Fritz Aeschbach & Henry Louis Africk (2007). Individual Members 2007. Bulletin of Symbolic Logic 13 (4).
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  22. Andrew Aberdein (2007). Fallacies in Mathematics. Proceedings of the British Society for Research Into Learning Mathematics 27 (3):1-6.
    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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  23. Martın Abadi, Yoshihiro Abe, Francine F. Abeles, Andrew Aberdein, Nathanael Ackerman, Bryant Adams, Klaus T. Aehlig, Fritz Aeschbach, Henry Louis Africk & Bahareh Afshari (2006). Individual Members 2006. Bulletin of Symbolic Logic 12 (4).
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  24. Andrew Aberdein (2006). Introduction to the New Edition. In The Elements: Books I-XIII by Euclid. Barnes & Noble.
  25. Andrew Aberdein (2006). Managing Informal Mathematical Knowledge: Techniques From Informal Logic. Lecture Notes in Artificial Intelligence 4108:208--221.
    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 informal mathematical (...)
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  26. Andrew Aberdein (2006). Proofs and Rebuttals: Applying Stephen Toulmin's Layout of Arguments to Mathematical Proof. In Marta Bílková & Ondřej Tomala (eds.), The Logica Yearbook 2005. Filosofia. 11-23.
    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.
     
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  27. Andrew Aberdein (2006). Raising the Tone: Definition, Bullshit, and the Definition of Bullshit. In G. Reisch & G. Hardcastle (eds.), Bullshit and Philosophy. Open Court. 151-169.
     
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  28. Andrew Aberdein (2006). The Elements: Books I-XIII by Euclid. Barnes & Noble.
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  29. Andrew Aberdein (2006). The Informal Logic of Mathematical Proof. In Reuben Hersh (ed.), 18 Unconventional Essays About the Nature of Mathematics. Springer-Verlag. 56-70.
    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 (...)
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  30. Martın Abadi, Areski Nait Abdallah, Yoshihiro Abe, Francine F. Abeles, Andrew Aberdein, Vicente Aboites, Nathanael Ackerman, Bryant Adams, John W. Addison Jr & Sergey Adian (2005). Individual Members 2005. Bulletin of Symbolic Logic 11 (4).
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  31. Andrew Aberdein (2005). The Uses of Argument in Mathematics. Argumentation 19 (3):287-301.
    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 layouts. However, cases of genuine conflict characteristically reflect an underlying (...)
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  32. Martın Abadi, Areski Nait Abdallah, Yoshihiro Abe, Francine F. Abeles, Andrew Aberdein, Vicente Aboites, Nathanael Ackerman, John W. Addison Jr, Klaus T. Aehlig & Fritz Aeschbach (2004). Individual Members 2004. Bulletin of Symbolic Logic 10 (4).
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  33. Martın Abadi, Yoshihiro Abe, Francine F. Abeles, Andrew Aberdein, Vicente Aboites, Nathanael Ackerman, Roger D. Acord, Zofia Adamowicz, John W. Addison Jr & Fritz Aeschbach (2003). Individual Members 2003. Bulletin of Symbolic Logic 9 (4).
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  34. Andrew Aberdein (2003). Balderdash and Chicanery: Science and Beyond. In James South (ed.), Buffy the Vampire Slayer and Philosophy: Fear and Trembling in Sunnydale. Open Court. 79-90.
    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 Vampire Slayer adroitly negotiates the borderlines between these narratives (...)
     
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  35. Andrew Aberdein (2001). Classical Recapture. In V. Fano, M. Stanzione & G. Tarozzi (eds.), Prospettive Della Logica E Della Filosofia Della Scienza. Rubettino. 11-18.
  36. Andrew Aberdein (2001). Douglas Walton, One-Sided Arguments: A Dialectical Analysis of Bias Reviewed By. Philosophy in Review 21 (2):152-154.
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  37. Andrew Aberdein (1998). Persuasive Definition. In H. V. Hansen, C. W. Tindale & A. V. Colman (eds.), Argumentation and Rhetoric. Vale.
    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 alternative.
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  38. Andrew Aberdein (1997). Dale Jacquette, Meinongian Logic: The Semantics of Existence and Nonexistence Reviewed By. Philosophy in Review 17 (3):176-178.
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  39. Andrew Aberdein (1996). Edouard Morot-Sir, The Imagination of Reference II: Perceiving, Indicating, Naming Reviewed By. Philosophy in Review 16 (4):270-271.
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