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

User-Defined Keywords

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

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