Peirce on mathematical reasoning and discovery

Ahti Veikko Pietarinen*

*Corresponding author for this work

    Research output: Chapter in book/report/conference proceedingChapterpeer-review

    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.

    Original languageEnglish
    Title of host publicationHandbook of Cognitive Mathematics
    EditorsMarcel Danesi
    PublisherSpringer Cham
    Pages1313-1344
    Number of pages32
    Edition1st
    ISBN (Electronic)9783031039454
    ISBN (Print)9783031039447
    DOIs
    Publication statusPublished - 1 Nov 2022

    Scopus Subject Areas

    • Mathematics(all)
    • Social Sciences(all)
    • Medicine(all)
    • Neuroscience(all)

    User-Defined Keywords

    • Abduction
    • Abstraction
    • Cognitive mathematics
    • Deduction
    • Generalization
    • Induction
    • Mathematical discovery
    • Peirce

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