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Andrew Aberdein
Florida Institute of Technology
  1. Intellectual Humility and Argumentation.Andrew Aberdein - forthcoming - In Mark Alfano, Michael Lynch & Alessandra Tanesini (eds.), The Routledge Handbook of the Philosophy of Humility. Routledge.
    In this chapter I argue that intellectual humility is related to argumentation in several distinct but mutually supporting ways. I begin by drawing connections between humility and two topics of long-standing importance to the evaluation of informal arguments: the ad verecundiam fallacy and the principle of charity. I then explore the more explicit role that humility plays in recent work on critical thinking dispositions, deliberative virtues, and virtue theories of argumentation.
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  2. Virtue in Argument.Andrew Aberdein - 2010 - 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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  3.  69
    Arrogance and Deep Disagreement.Andrew Aberdein - forthcoming - In Alessandra Tanesini & Michael Lynch (eds.), Polarisation, Arrogance, and Dogmatism: Philosophical Perspectives. London: Routledge. pp. 39-52.
    I intend to bring recent work applying virtue theory to the study of argument to bear on a much older problem, that of disagreements that resist rational resolution, sometimes termed "deep disagreements". Just as some virtue epistemologists have lately shifted focus onto epistemic vices, I shall argue that a renewed focus on the vices of argument can help to illuminate deep disagreements. In particular, I address the role of arrogance, both as a factor in the diagnosis of deep disagreements and (...)
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  4.  82
    Courageous Arguments and Deep Disagreements.Andrew Aberdein - forthcoming - Topoi:1-8.
    Deep disagreements are characteristically resistant to rational resolution. This paper explores the contribution a virtue theoretic approach to argumentation can make towards settling the practical matter of what to do when confronted with apparent deep disagreement, with particular attention to the virtue of courage.
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  5. Eudaimonistic Argumentation.Andrew Aberdein - 2020 - In Bart Garssen & Frans van Eemeren (eds.), From Argument Schemes to Argumentative Relations in the Wild: A Variety of Contributions to Argumentation Theory. Cham: Springer Verlag. pp. 97–106.
    Virtue theories have lately enjoyed a modest vogue in the study of argumentation, echoing the success of more far-reaching programmes in ethics and epistemology. Virtue theories of argumentation (VTA) comprise several conceptually distinct projects, including the provision of normative foundations for argument evaluation and a renewed focus on the character of good arguers. Perhaps the boldest of these is the pursuit of the fully satisfying argument, the argument that contributes to human flourishing. This project has an independently developed epistemic analogue: (...)
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  6.  95
    Beauty Is Not Simplicity: An Analysis of Mathematicians' Proof Appraisals.Matthew Inglis & Andrew Aberdein - 2015 - Philosophia Mathematica 23 (1):87-109.
    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.
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  7.  37
    In Defence of Virtue: The Legitimacy of Agent-Based Argument Appraisal.Andrew Aberdein - 2014 - 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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  8.  68
    The Vices of Argument.Andrew Aberdein - 2016 - Topoi 35 (2):413-422.
    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 several fallacies, with particular emphasis (...)
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  9.  80
    Introduction.Andrew Aberdein & Matthew Inglis - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. Bloomsbury Academic. pp. 1-13.
    There has been little overt discussion of the experimental philosophy of logic or mathematics. So it may be tempting to assume that application of the methods of experimental philosophy to these areas is impractical or unavailing. This assumption is undercut by three trends in recent research: a renewed interest in historical antecedents of experimental philosophy in philosophical logic; a “practice turn” in the philosophies of mathematics and logic; and philosophical interest in a substantial body of work in adjacent disciplines, such (...)
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  10. Evidence, Proofs, and Derivations.Andrew Aberdein - 2019 - ZDM 51 (5):825-834.
    The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation schemes, in particular, (...)
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  11.  19
    Explanation in Mathematical Conversations: An Empirical Investigation.Alison Pease, Andrew Aberdein & Ursula Martin - 2019 - Philosophical Transactions of the Royal Society A 377.
    Analysis of online mathematics forums can help reveal how explanation is used by mathematicians; we contend that this use of explanation may help to provide an informal conceptualization of simplicity. We extracted six conjectures from recent philosophical work on the occurrence and characteristics of explanation in mathematics. We then tested these conjectures against a corpus derived from online mathematical discussions. To this end, we employed two techniques, one based on indicator terms, the other on a random sample of comments lacking (...)
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  12.  87
    Introduction: Virtues and Arguments.Andrew Aberdein & Daniel H. Cohen - 2016 - Topoi 35 (2):339-343.
    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 (...)
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  13. Five Theories of Reasoning: Interconnections and Applications to Mathematics.Alison Pease & Andrew Aberdein - 2011 - 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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  14. The Philosophy of Alternative Logics.Andrew Aberdein & Stephen Read - 2009 - In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press. pp. 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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  15.  6
    Are Aesthetic Judgements Purely Aesthetic? Testing the Social Conformity Account.Matthew Inglis & Andrew Aberdein - forthcoming - ZDM.
    Many of the methods commonly used to research mathematical practice, such as analyses of historical episodes or individual cases, are particularly well-suited to generating causal hypotheses, but less well-suited to testing causal hypotheses. In this paper we reflect on the contribution that the so-called hypothetico-deductive method, with a particular focus on experimental studies, can make to our understanding of mathematical practice. By way of illustration, we report an experiment that investigated how mathematicians attribute aesthetic properties to mathematical proofs. We demonstrate (...)
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  16.  55
    The Informal Logic of Mathematical Proof.Andrew Aberdein - 2006 - In Reuben Hersh (ed.), 18 Unconventional Essays About the Nature of Mathematics. Springer Verlag. pp. 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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  17. The Uses of Argument in Mathematics.Andrew Aberdein - 2005 - 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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  18.  50
    Arguments with Losers.Andrew Aberdein - 2016 - Florida Philosophical Review 16 (1):1-11.
  19.  91
    Mathematics and Argumentation.Andrew Aberdein - 2008 - 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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  20.  52
    Observations on Sick Mathematics.Andrew Aberdein - 2010 - In Bart van Kerkhove, Jean Paul van Bendegem & Jonas de Vuyst (eds.), Philosophical Perspectives on Mathematical Practice. College Publications. pp. 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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  21.  51
    Managing Informal Mathematical Knowledge: Techniques From Informal Logic.Andrew Aberdein - 2006 - 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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  22.  28
    Advances in Experimental Philosophy of Logic and Mathematics.Andrew Aberdein & Matthew Inglis (eds.) - 2019 - London: Bloomsbury Academic.
    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, and data-mining. Distinct themes emerge (...)
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  23.  86
    Mathematical Wit and Mathematical Cognition.Andrew Aberdein - 2013 - 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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  24.  29
    Virtuous Norms for Visual Arguers.Andrew Aberdein - 2018 - Argumentation 32 (1):1-23.
    This paper proposes that virtue theories of argumentation and theories of visual argumentation can be of mutual assistance. An argument that adoption of a virtue approach provides a basis for rejecting the normative independence of visual argumentation is presented and its premisses analysed. This entails an independently valuable clarification of the contrasting normative presuppositions of the various virtue theories of argumentation. A range of different kinds of visual argument are examined, and it is argued that they may all be successfully (...)
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  25.  39
    Persuasive Definition.Andrew Aberdein - 1997 - 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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  26.  45
    Fallacy and Argumentational Vice.Andrew Aberdein - 2013 - 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.
    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.
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  27. The Parallel Structure of Mathematical Reasoning.Andrew Aberdein - 2012 - 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.
    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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  28.  12
    Diversity in Proof Appraisal.Matthew Inglis & Andrew Aberdein - 2016 - In Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 2012--2014. Basel, Switzerland: pp. 163-179.
    We investigated whether mathematicians typically agree about the qualities of mathematical proofs. Between-mathematician consensus in proof appraisals is an implicit assumption of many arguments made by philosophers of mathematics, but to our knowledge the issue has not previously been empirically investigated. We asked a group of mathematicians to assess a specific proof on four dimensions, using the framework identified by Inglis and Aberdein (2015). We found widespread disagreement between our participants about the aesthetics, intricacy, precision and utility of the proof, (...)
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  29.  76
    Logic for Dogs.Andrew Aberdein - 2008 - In Steven D. Hales (ed.), What Philosophy Can Tell You About Your Dog. Open Court. pp. 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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  30.  46
    Fallacies in Mathematics.Andrew Aberdein - 2007 - 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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  31. Strange Bedfellows: The Interpenetration of Philosophy and Pornography.Andrew Aberdein - 2010 - In Dave Monroe (ed.), Porn: How to Think with Kink. Wiley-Blackwell. pp. 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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  32.  98
    Leonard Nelson: A Theory of Philosophical Fallacies: Translated by Fernando Leal and David Carus Springer, Cham, Switzerland, 2016, Vi + 211 Pp. [REVIEW]Andrew Aberdein - 2017 - Argumentation 31 (2):455-461.
  33.  19
    The Dialectical Tier of Mathematical Proof.Andrew Aberdein - 2011 - 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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  34.  59
    Raising the Tone: Definition, Bullshit, and the Definition of Bullshit.Andrew Aberdein - 2006 - In G. Reisch & G. Hardcastle (eds.), Bullshit and Philosophy. Open Court. pp. 151-169.
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  35.  12
    Redefining Revolutions.Andrew Aberdein - 2018 - In Moti Mizrahi (ed.), The Kuhnian image of science: Time for a decisive transformation? London: Rowman & Littlefield. pp. 133–154.
    In their account of theory change in logic, Aberdein and Read distinguish 'glorious' from 'inglorious' revolutions--only the former preserves all 'the key components of a theory' [1]. A widespread view, expressed in these terms, is that empirical science characteristically exhibits inglorious revolutions but that revolutions in mathematics are at most glorious [2]. Here are three possible responses: 0. Accept that empirical science and mathematics are methodologically discontinuous; 1. Argue that mathematics can exhibit inglorious revolutions; 2. Deny that inglorious revolutions are (...)
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  36.  13
    Commentary On: Michel Dufour's "Argument and Explanation in Mathematics".Andrew Aberdein - 2013 - 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.
  37.  46
    Rationale of the Mathematical Joke.Andrew Aberdein - 2010 - In Alison Pease, Markus Guhe & Alan Smaill (eds.), Proceedings of AISB 2010 Symposium on Mathematical Practice and Cognition. AISB. pp. 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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  38.  35
    Classical Recapture.Andrew Aberdein - 2001 - In V. Fano, M. Stanzione & G. Tarozzi (eds.), Prospettive Della Logica E Della Filosofia Della Scienza. Rubettino. pp. 11-18.
  39.  15
    Commentary on Menashe Schwed, "A Wittgensteinian Approach to Rationality in Argumentation".Andrew Aberdein - 2009 - In Juho Ritola (ed.), Argument cultures: Proceedings of OSSA 2009. OSSA.
  40.  40
    Individual Members 2008.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 - Bulletin of Symbolic Logic 14 (4).
  41.  21
    Francine F. Abeles; Mark E. Fuller . Modern Logic, 1850–1950, East and West. Xiii + 258 Pp., Figs. Basel: Springer, 2016. $69.99. [REVIEW]Andrew Aberdein - 2017 - Isis 108 (3):719-720.
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  42.  25
    Mohan Ganesalingam. The Language of Mathematics: A Linguistic and Philosophical Investigation. FoLLI Publications on Logic, Language and Information. [REVIEW]Andrew Aberdein - 2017 - Philosophia Mathematica 25 (1):143–147.
  43.  34
    Individual Members 2005.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 - Bulletin of Symbolic Logic 11 (4).
  44. Individual Members 2010.Martın Abadi, Yoshihiro Abe, Andreas Abel, Francine F. Abeles, Andrew Aberdein, J. David Abernethy, Kuanysh Abeshev, Nate Ackerman, Winfred P. Adams & Miloš Adzic - 2010 - Bulletin of Symbolic Logic 16 (4).
  45.  32
    Individual Members 2006.Martın Abadi, Yoshihiro Abe, Francine F. Abeles, Andrew Aberdein, Nathanael Ackerman, Bryant Adams, Klaus T. Aehlig, Fritz Aeschbach, Henry Louis Africk & Bahareh Afshari - 2006 - Bulletin of Symbolic Logic 12 (4):625-681.
  46.  48
    Argumentation Schemes and Communities of Argumentational Practice.Andrew Aberdein - 2009 - 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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  47.  25
    Commentary On: Begoña Carrascal's "The Practice of Arguing and the Arguments: Examples From Mathematics".Andrew Aberdein - 2013 - 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.
  48.  23
    The Formal Failure and Social Success of Logic.William Brooke & Andrew Aberdein - 2011 - 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.
    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.
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  49.  25
    Individual Members 2003.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 - Bulletin of Symbolic Logic 9 (4).
  50.  21
    Edouard Morot-Sir, The Imagination of Reference II: Perceiving, Indicating, Naming. [REVIEW]Andrew Aberdein - 1996 - Philosophy in Review 16 (4):270-271.
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