Philosophy of mathematics and philosophy of history

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The arguments in this book depend more on the study of history than on the study of logic; logic plays a role, but it is subordinate or subsidiary. Philosophers are now used to the idea that history is central to philosophy of science, but its pertinence to the philosophy of mathematics seems to need renewed defense. Thus I rehearse the helpful argument of the philosopher of history, W. B. Gallie, who shows that there can be no Ideal Chronicle, which in turn helps me to contest Philip Kitcher’s early and influential position in The Nature of Mathematical Knowledge, where he invokes the history of mathematics but in a manner that finally leaves mathematics once again ahistorical. Thus I turn to the French philosopher of mathematics Jean Cavaillès whose sense of history was more refined, make some remarks about reference, and take up briefly Wiles’ strategy in his celebrated proof of Fermat’s Last Theorem, in order to carry out a thought experiment involving the ‘Math Genie’ that shows that proofs are embedded in history, like all human actions.

Original languageEnglish (US)
Title of host publicationStudies in Applied Philosophy, Epistemology and Rational Ethics
PublisherSpringer International Publishing
Pages21-38
Number of pages18
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

History
Philosophy of History
Philosophy of Mathematics
Mathematics
Logic
Philosopher
Philosophers of History
Subsidiaries
Contests
Fermat
Thought Experiments
History of Mathematics
Ideal
French philosopher
Philosophy of Science
Human Action
Chronicles
Pertinence

All Science Journal Classification (ASJC) codes

  • Philosophy

Cite this

Grosholz, E. R. (2016). Philosophy of mathematics and philosophy of history. In Studies in Applied Philosophy, Epistemology and Rational Ethics (pp. 21-38). (Studies in Applied Philosophy, Epistemology and Rational Ethics; Vol. 30). Springer International Publishing. https://doi.org/10.1007/978-3-319-46690-3_2
Grosholz, Emily Rolfe. / Philosophy of mathematics and philosophy of history. Studies in Applied Philosophy, Epistemology and Rational Ethics. Springer International Publishing, 2016. pp. 21-38 (Studies in Applied Philosophy, Epistemology and Rational Ethics).
@inbook{d79e43df3c664908a78dcfa176336d7f,
title = "Philosophy of mathematics and philosophy of history",
abstract = "The arguments in this book depend more on the study of history than on the study of logic; logic plays a role, but it is subordinate or subsidiary. Philosophers are now used to the idea that history is central to philosophy of science, but its pertinence to the philosophy of mathematics seems to need renewed defense. Thus I rehearse the helpful argument of the philosopher of history, W. B. Gallie, who shows that there can be no Ideal Chronicle, which in turn helps me to contest Philip Kitcher’s early and influential position in The Nature of Mathematical Knowledge, where he invokes the history of mathematics but in a manner that finally leaves mathematics once again ahistorical. Thus I turn to the French philosopher of mathematics Jean Cavaill{\`e}s whose sense of history was more refined, make some remarks about reference, and take up briefly Wiles’ strategy in his celebrated proof of Fermat’s Last Theorem, in order to carry out a thought experiment involving the ‘Math Genie’ that shows that proofs are embedded in history, like all human actions.",
author = "Grosholz, {Emily Rolfe}",
year = "2016",
month = "1",
day = "1",
doi = "10.1007/978-3-319-46690-3_2",
language = "English (US)",
series = "Studies in Applied Philosophy, Epistemology and Rational Ethics",
publisher = "Springer International Publishing",
pages = "21--38",
booktitle = "Studies in Applied Philosophy, Epistemology and Rational Ethics",

}

Grosholz, ER 2016, Philosophy of mathematics and philosophy of history. in Studies in Applied Philosophy, Epistemology and Rational Ethics. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol. 30, Springer International Publishing, pp. 21-38. https://doi.org/10.1007/978-3-319-46690-3_2

Philosophy of mathematics and philosophy of history. / Grosholz, Emily Rolfe.

Studies in Applied Philosophy, Epistemology and Rational Ethics. Springer International Publishing, 2016. p. 21-38 (Studies in Applied Philosophy, Epistemology and Rational Ethics; Vol. 30).

Research output: Chapter in Book/Report/Conference proceedingChapter

TY - CHAP

T1 - Philosophy of mathematics and philosophy of history

AU - Grosholz, Emily Rolfe

PY - 2016/1/1

Y1 - 2016/1/1

N2 - The arguments in this book depend more on the study of history than on the study of logic; logic plays a role, but it is subordinate or subsidiary. Philosophers are now used to the idea that history is central to philosophy of science, but its pertinence to the philosophy of mathematics seems to need renewed defense. Thus I rehearse the helpful argument of the philosopher of history, W. B. Gallie, who shows that there can be no Ideal Chronicle, which in turn helps me to contest Philip Kitcher’s early and influential position in The Nature of Mathematical Knowledge, where he invokes the history of mathematics but in a manner that finally leaves mathematics once again ahistorical. Thus I turn to the French philosopher of mathematics Jean Cavaillès whose sense of history was more refined, make some remarks about reference, and take up briefly Wiles’ strategy in his celebrated proof of Fermat’s Last Theorem, in order to carry out a thought experiment involving the ‘Math Genie’ that shows that proofs are embedded in history, like all human actions.

AB - The arguments in this book depend more on the study of history than on the study of logic; logic plays a role, but it is subordinate or subsidiary. Philosophers are now used to the idea that history is central to philosophy of science, but its pertinence to the philosophy of mathematics seems to need renewed defense. Thus I rehearse the helpful argument of the philosopher of history, W. B. Gallie, who shows that there can be no Ideal Chronicle, which in turn helps me to contest Philip Kitcher’s early and influential position in The Nature of Mathematical Knowledge, where he invokes the history of mathematics but in a manner that finally leaves mathematics once again ahistorical. Thus I turn to the French philosopher of mathematics Jean Cavaillès whose sense of history was more refined, make some remarks about reference, and take up briefly Wiles’ strategy in his celebrated proof of Fermat’s Last Theorem, in order to carry out a thought experiment involving the ‘Math Genie’ that shows that proofs are embedded in history, like all human actions.

UR - http://www.scopus.com/inward/record.url?scp=85019697554&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019697554&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-46690-3_2

DO - 10.1007/978-3-319-46690-3_2

M3 - Chapter

AN - SCOPUS:85019697554

T3 - Studies in Applied Philosophy, Epistemology and Rational Ethics

SP - 21

EP - 38

BT - Studies in Applied Philosophy, Epistemology and Rational Ethics

PB - Springer International Publishing

ER -

Grosholz ER. Philosophy of mathematics and philosophy of history. In Studies in Applied Philosophy, Epistemology and Rational Ethics. Springer International Publishing. 2016. p. 21-38. (Studies in Applied Philosophy, Epistemology and Rational Ethics). https://doi.org/10.1007/978-3-319-46690-3_2