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Peirce on Mathematical Reasoning and Discovery

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Handbook of Cognitive Mathematics

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Abstract

Topics pertinent to mathematics concern the modes of reasoning in mathematics and their contribution to the discovery of new mathematical ideas, objects, patterns, and structures. Since the late nineteenth century, Charles S. Peirce developed a comprehensive theory of mathematical reasoning and its logical philosophy. It defines concepts such as abstraction and generalization, the three-stage model of reasoning (abduction, deduction, and induction), and diagrammatic reasoning, which are the cornerstones of the theory of mathematical practice that takes mathematical objects to be hypothetical mental creations of mathematical cognition. This chapter is a survey of Peirce’s notions central to reasoning and discovery in mathematics.

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Acknowledgments

This chapter is an output of a research project implemented as part of the Basic Research Program at the National Research University Higher School of Economics (HSE University).

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Base-rate fallacy foiled

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Authors and Affiliations

  1. Tallinn University of Technology, Tallinn, Estonia

    Ahti-Veikko Pietarinen

  2. Research University Higher School of Economics, Moscow, Russia

    Ahti-Veikko Pietarinen

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  1. Ahti-Veikko Pietarinen
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Correspondence to Ahti-Veikko Pietarinen .

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Editors and Affiliations

  1. Anthropology, University of Toronto, Toronto, ON, Canada

    Marcel Danesi

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  1. York University, Toronto, ON, Canada

    Vitaly Kiryushenko

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Pietarinen, AV. (2021). Peirce on Mathematical Reasoning and Discovery. In: Danesi, M. (eds) Handbook of Cognitive Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-44982-7_51-1

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  • DOI: https://doi.org/10.1007/978-3-030-44982-7_51-1

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  • Print ISBN: 978-3-030-44982-7

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