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

All Science Journal Classification (ASJC) codes

  • Philosophy

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  • 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