Mathematical Wit and Mathematical Cognition

Topics in Cognitive Science 5 (2):231-250 (2013)

Authors
Andrew Aberdein
Florida Institute of Technology
Abstract
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 to creative mathematics. The components of the joke are explicated by argumentation schemes devised for application to topic-neutral reasoning. These in turn are classified under seven headings: retroduction, citation, intuition, meta-argument, closure, generalization, and definition. Finally, the wider significance of this account for the cognitive science of mathematics is discussed
Keywords Humor  Citation  Mathematical reasoning  Intuition  Generalization  Mathematical practice  Argumentation schemes  Retroduction
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DOI 10.1111/tops.12020
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References found in this work BETA

Argumentation Schemes.Douglas Walton, Chris Reed & Fabrizio Macagno - 2008 - Cambridge University Press.
Fallacies.C. L. Hamblin - 1970 - Vale Press.
What is Mathematics, Really?Reuben Hersh - 1997 - Oxford University Press.
Mathematics and Plausible Reasoning.George Pólya - 1954 - Princeton: Princeton University Press.

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