Peirce on mathematical reasoning and discovery

Ahti Veikko Pietarinen*

*Corresponding author for this work

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


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
Number of pages32
ISBN (Electronic)9783031039454
ISBN (Print)9783031039447
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


Dive into the research topics of 'Peirce on mathematical reasoning and discovery'. Together they form a unique fingerprint.

Cite this