Rethinking ampliative reasoning

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish (US)
Title of host publicationStudies in Applied Philosophy, Epistemology and Rational Ethics
PublisherSpringer International Publishing
Pages39-58
Number of pages20
DOIs
StatePublished - Jan 1 2016

Publication series

NameStudies in Applied Philosophy, Epistemology and Rational Ethics
Volume30
ISSN (Print)2192-6255
ISSN (Electronic)2192-6263

Fingerprint

Mathematics
Reviewing
Number Theory
Topology
Educators
Algebra
Philosopher
Geometry

All Science Journal Classification (ASJC) codes

  • Philosophy

Cite this

Grosholz, E. R. (2016). Rethinking ampliative reasoning. In 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
Grosholz, Emily Rolfe. / Rethinking ampliative reasoning. Studies in Applied Philosophy, Epistemology and Rational Ethics. Springer International Publishing, 2016. pp. 39-58 (Studies in Applied Philosophy, Epistemology and Rational Ethics).
@inbook{098153d4faca4ab6862a57b4889639fb,
title = "Rethinking ampliative reasoning",
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.",
author = "Grosholz, {Emily Rolfe}",
year = "2016",
month = "1",
day = "1",
doi = "10.1007/978-3-319-46690-3_3",
language = "English (US)",
series = "Studies in Applied Philosophy, Epistemology and Rational Ethics",
publisher = "Springer International Publishing",
pages = "39--58",
booktitle = "Studies in Applied Philosophy, Epistemology and Rational Ethics",

}

Grosholz, ER 2016, Rethinking ampliative reasoning. in 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.

Studies in Applied Philosophy, Epistemology and Rational Ethics. Springer International Publishing, 2016. p. 39-58 (Studies in Applied Philosophy, Epistemology and Rational Ethics; Vol. 30).

Research output: Chapter in Book/Report/Conference proceedingChapter

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 -

Grosholz ER. Rethinking ampliative reasoning. In Studies in Applied Philosophy, Epistemology and Rational Ethics. Springer International Publishing. 2016. p. 39-58. (Studies in Applied Philosophy, Epistemology and Rational Ethics). https://doi.org/10.1007/978-3-319-46690-3_3