Mathematical Wit and Mathematical Cognition

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

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Andrew Aberdein
Florida Institute of Technology

Citations of this work

The Argument of Mathematics.Andrew Aberdein & Ian J. Dove (eds.) - 2013 - Dordrecht, Netherland: Springer.
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.

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References found in this work

Argumentation schemes.Douglas Walton, Chris Reed & Fabrizio Macagno - 2008 - New York: Cambridge University Press. Edited by Chris Reed & Fabrizio Macagno.
Fallacies.Charles Leonard Hamblin - 1970 - Newport News, Va.: Vale Press.
Argumentation Schemes.Douglas Walton, Christopher Reed & Fabrizio Macagno - 2008 - Cambridge and New York: Cambridge University Press. Edited by Chris Reed & Fabrizio Macagno.
Fallacies.C. L. Hamblin - 1970 - Revue Philosophique de la France Et de l'Etranger 160:492-492.

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