### Abstract

I explore my methodological assumptions by showing why I put so much emphasis on analysis and its interplay with reference in my investigation of ampliative reasoning in mathematics and science. Reviewing recent important work by philosophers of mathematics Karine Chemla, Carlo Cellucci and Danielle Macbeth, I defend my approach and choice of case studies. I also turn to the work by two influential mathematics educators, Kieran and David Egan, in order to revisit my arguments about the circle, and to prepare the ground for my case studies in Chap. 4 and Chap. 5, where number theory is developed in relation to geometry, algebra, complex analysis, and topology.

Original language | English (US) |
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Title of host publication | Studies in Applied Philosophy, Epistemology and Rational Ethics |

Publisher | Springer International Publishing |

Pages | 39-58 |

Number of pages | 20 |

DOIs | |

State | Published - Jan 1 2016 |

### Publication series

Name | Studies in Applied Philosophy, Epistemology and Rational Ethics |
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Volume | 30 |

ISSN (Print) | 2192-6255 |

ISSN (Electronic) | 2192-6263 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Philosophy

### Cite this

*Studies in Applied Philosophy, Epistemology and Rational Ethics*(pp. 39-58). (Studies in Applied Philosophy, Epistemology and Rational Ethics; Vol. 30). Springer International Publishing. https://doi.org/10.1007/978-3-319-46690-3_3

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*Studies in Applied Philosophy, Epistemology and Rational Ethics.*Studies in Applied Philosophy, Epistemology and Rational Ethics, vol. 30, Springer International Publishing, pp. 39-58. https://doi.org/10.1007/978-3-319-46690-3_3

**Rethinking ampliative reasoning.** / Grosholz, Emily Rolfe.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Rethinking ampliative reasoning

AU - Grosholz, Emily Rolfe

PY - 2016/1/1

Y1 - 2016/1/1

N2 - I explore my methodological assumptions by showing why I put so much emphasis on analysis and its interplay with reference in my investigation of ampliative reasoning in mathematics and science. Reviewing recent important work by philosophers of mathematics Karine Chemla, Carlo Cellucci and Danielle Macbeth, I defend my approach and choice of case studies. I also turn to the work by two influential mathematics educators, Kieran and David Egan, in order to revisit my arguments about the circle, and to prepare the ground for my case studies in Chap. 4 and Chap. 5, where number theory is developed in relation to geometry, algebra, complex analysis, and topology.

AB - I explore my methodological assumptions by showing why I put so much emphasis on analysis and its interplay with reference in my investigation of ampliative reasoning in mathematics and science. Reviewing recent important work by philosophers of mathematics Karine Chemla, Carlo Cellucci and Danielle Macbeth, I defend my approach and choice of case studies. I also turn to the work by two influential mathematics educators, Kieran and David Egan, in order to revisit my arguments about the circle, and to prepare the ground for my case studies in Chap. 4 and Chap. 5, where number theory is developed in relation to geometry, algebra, complex analysis, and topology.

UR - http://www.scopus.com/inward/record.url?scp=85019699451&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019699451&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-46690-3_3

DO - 10.1007/978-3-319-46690-3_3

M3 - Chapter

AN - SCOPUS:85019699451

T3 - Studies in Applied Philosophy, Epistemology and Rational Ethics

SP - 39

EP - 58

BT - Studies in Applied Philosophy, Epistemology and Rational Ethics

PB - Springer International Publishing

ER -