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  1. Design Thinking in Argumentation Theory and Practice.Sally Jackson - 2015 - Argumentation 29 (3):243-263.
    This essay proposes a design perspective on argumentation, intended as complementary to empirical and critical scholarship. In any substantive domain, design can provide insights that differ from those provided by scientific or humanistic perspectives. For argumentation, the key advantage of a design perspective is the recognition that humanity’s natural capacity for reason and reasonableness can be extended through inventions that improve on unaided human intellect. Historically, these inventions have fallen into three broad classes: logical systems, scientific methods, and disputation frameworks. (...)
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  • Comments on 'Strategic Maneuvering in Mathematical Proofs'.Sally Jackson - 2008 - Argumentation 22 (3):469-472.
    “Black box argument” is a metaphor for modular components of argumentative discussion that are, within a particular discussion, not open to expansion. In public policy debate such as the controversy over abstinence-only sex education, scientific conclusions enter the discourse as black boxes consisting of a result returned from an external and largely impenetrable process. In one way of looking at black box arguments, there is nothing fundamentally new for the argumentation theorist: A black box argument is very like any other (...)
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  • Proofs, Mathematical Practice and Argumentation.Begoña Carrascal - 2015 - Argumentation 29 (3):305-324.
    In argumentation studies, almost all theoretical proposals are applied, in general, to the analysis and evaluation of argumentative products, but little attention has been paid to the creative process of arguing. Mathematics can be used as a clear example to illustrate some significant theoretical differences between mathematical practice and the products of it, to differentiate the distinct components of the arguments, and to emphasize the need to address the different types of argumentative discourse and argumentative situation in the practice. I (...)
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  • 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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  • Mathematics and argumentation.Andrew Aberdein - 2009 - 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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  • 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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  • Non-deductive Logic in Mathematics: The Probability of Conjectures.James Franklin - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Springer. pp. 11--29.
    Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...)
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