Peirce on mathematical reasoning and discovery

Ahti Veikko Pietarinen

doi:10.1007/978-3-031-03945-4_51

Peirce on mathematical reasoning and discovery

Ahti Veikko Pietarinen^*

^*Corresponding author for this work

Academy of Chinese, History, Religion and Philosophy

Research output: Chapter in book/report/conference proceeding › Chapter › peer-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 language	English
Title of host publication	Handbook of Cognitive Mathematics
Editors	Marcel Danesi
Publisher	Springer Cham
Pages	1313-1344
Number of pages	32
Edition	1st
ISBN (Electronic)	9783031039454
ISBN (Print)	9783031039447
DOIs	https://doi.org/10.1007/978-3-031-03945-4_51
Publication status	Published - 1 Nov 2022

User-Defined Keywords

Abduction
Abstraction
Cognitive mathematics
Deduction
Generalization
Induction
Mathematical discovery
Peirce

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10.1007/978-3-031-03945-4_51

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Peirce on mathematical reasoning and discovery

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