Peirce on Mathematical Reasoning and Discovery

Ahti-Veikko Pietarinen ()
Additional contact information
Ahti-Veikko Pietarinen: Tallinn University of Technology

Chapter 41 in Handbook of Cognitive Mathematics, 2022, pp 1313-1344 from Springer

Abstract: 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.

Keywords: Peirce; Mathematical discovery; Cognitive mathematics; Abstraction; Generalization; Abduction; Deduction; Induction (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-03945-4_51

Ordering information: This item can be ordered from
http://www.springer.com/9783031039454

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

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().