## 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 |
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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 | |

Publication status | Published - 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