TY - CHAP
T1 - Rethinking ampliative reasoning
AU - Grosholz, Emily Rolfe
N1 - Publisher Copyright:
© Springer International Publishing AG 2016.
PY - 2016
Y1 - 2016
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.
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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 -