•  27
    Was Aristotle a virtue argumentation theorist?
    In Joseph Bjelde, David Merry & Christopher Roser (eds.), Essays on Argumentation in Antiquity, Springer. pp. 215-229. 2021.
    Virtue theories of argumentation (VTA) emphasize the roles arguers play in the conduct and evaluation of arguments, and lay particular stress on arguers’ acquired dispositions of character, that is, virtues and vices. The inspiration for VTA lies in virtue epistemology and virtue ethics, the latter being a modern revival of Aristotle’s ethics. Aristotle is also, of course, the father of Western logic and argumentation. This paper asks to what degree Aristotle may thereby be claimed as a forefath…Read more
  •  81
    Until recently, discussion of virtues in the philosophy of mathematics has been fleeting and fragmentary at best. But in the last few years this has begun to change. As virtue theory has grown ever more influential, not just in ethics where virtues may seem most at home, but particularly in epistemology and the philosophy of science, some philosophers have sought to push virtues out into unexpected areas, including mathematics and its philosophy. But there are some mathematicians already there, …Read more
  •  102
    Truth in Fiction: Rethinking its Logic, by John Woods, Springer, 2018 (review)
    Philosophia 49 (2): 873-881. 2021.
    A review of John Woods, Truth in Fiction: Rethinking its Logic. Cham: Springer, 2018.
  •  61
    Douglas Walton’s multitudinous contributions to the study of argumentation seldom, if ever, directly engage with argumentation in mathematics. Nonetheless, several of the innovations with which he is most closely associated lend themselves to improving our understanding of mathematical arguments. I concentrate on two such innovations: dialogue types (§1) and argumentation schemes (§2). I argue that both devices are much more applicable to mathematical reasoning than may be commonly supposed.
  •  104
    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 ou…Read more
  •  77
    Mathematical Monsters
    In Diego Compagna & Stefanie Steinhart (eds.), Monsters, Monstrosities, and the Monstrous in Culture and Society, . pp. 391-412. 2019.
    Monsters lurk within mathematical as well as literary haunts. I propose to trace some pathways between these two monstrous habitats. I start from Jeffrey Jerome Cohen’s influential account of monster culture and explore how well mathematical monsters fit each of his seven theses. The mathematical monsters I discuss are drawn primarily from three distinct but overlapping domains. Firstly, late nineteenth-century mathematicians made numerous unsettling discoveries that threatened their understandi…Read more
  •  12
    Truth in Fiction: Rethinking its Logic, by John Woods, Springer, 2018 (review)
    Philosophia 49 (2): 873-881. 2021.
    A review of John Woods, Truth in Fiction: Rethinking its Logic. Cham: Springer, 2018.
  •  7
    Records of online collaborative mathematical activity provide us with a novel, rich, searchable, accessible and sizeable source of data for empirical investigations into mathematical practice. In this paper we discuss how the resources of crowdsourced mathematics can be used to help formulate and answer questions about mathematical practice, and what their limitations might be. We describe quantitative approaches to studying crowdsourced mathematics, reviewing work from cognitive history (compar…Read more
  •  28
    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 inves…Read more
  •  249
    Arrogance and deep disagreement
    In Alessandra Tanesini & Michael Lynch (eds.), Polarisation, Arrogance, and Dogmatism: Philosophical Perspectives, Routledge. pp. 39-52. 2020.
    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 …Read more
  •  183
    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.
  •  262
    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 flouri…Read more
  •  511
    Intellectual humility and argumentation
    In Mark Alfano, Michael Lynch & Alessandra Tanesini (eds.), The Routledge Handbook of the Philosophy of Humility, Routledge. pp. 325-334. 2020.
    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.
  •  51
    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 t…Read more
  •  191
    Evidence, Proofs, and Derivations
    ZDM 51 (5): 825-834. 2019.
    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,…Read more
  •  33
    Explanation in mathematical conversations: An empirical investigation
    with Alison Pease and Ursula Martin
    Philosophical Transactions of the Royal Society A 377. 2019.
    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, th…Read more
  •  159
    In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics, Bloomsbury Academic. pp. 1-13. 2019.
    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 b…Read more
  •  51
    Virtuous Norms for Visual Arguers
    Argumentation 32 (1): 1-23. 2018.
    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,…Read more
  •  19
    Virtue Argumentation and Bias
    Argumentation, Objectivity and Bias: Proceedings of the 11th International Conference of the Ontario Society for the Study of Argumentation (OSSA), May 18--21, 2016. 2016.
    Is bias an obstacle to a virtue theory of argumentation? Virtue theories seem vulnerable to a situationist challenge, analogous to similar challenges in virtue ethics and epistemology, that behavioural dispositions are too situation-specific for virtues to be psychologically plausible. This paper argues that virtue argumentation may respond to this challenge by combining a defence of the virtue of humility with a demonstration of the role of attitude strength, as exhibited by deep-seated virtues…Read more
  •  12
    Commentary on Patrick Bondy, “Bias in Legitimate Ad Hominem Arguments”
    Argumentation, Objectivity and Bias: Proceedings of the 11th International Conference of the Ontario Society for the Study of Argumentation (OSSA), May 18–21, 2016. 2016.
  •  112
    Arguments with losers
    Florida Philosophical Review 16 (1): 1-11. 2016.
  •  20
    Douglas Walton, One-Sided Arguments: A Dialectical Analysis of Bias (review)
    Philosophy in Review 21 (2): 152-154. 2001.
  •  157
    Virtue in argument
    Argumentation 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.
  •  35
    The 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
  •  99
    Mathematical Wit and Mathematical Cognition
    Topics 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