Show Summary Details

Page of

PRINTED FROM OXFORD HANDBOOKS ONLINE (www.oxfordhandbooks.com). © Oxford University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a title in Oxford Handbooks Online for personal use (for details see Privacy Policy and Legal Notice).

date: 21 February 2020

Abstract and Keywords

To an unappreciated degree, the history of Western philosophy is the history of attempts to understand why mathematics is applicable to Nature, despite apparently good reasons to believe that it should not be. A cursory look at the great books of philosophy bears this out. Plato's Republic invokes the theory of “participation” to explain why, for instance, geometry is applicable to ballistics and the practice of war, despite the Theory of Forms, which places mathematical entities in a different (higher) realm of being than that of empirical Nature. This argument is part of Plato's general claim that theoretical learning, in the end, is more useful than “practical” pursuits. John Stuart Mill's account of the applicability of mathematics to nature is unique: it is the only one of the major Western philosophies which denies the major premise upon which all other accounts are based. Mill simply asserts that mathematics itself is empirical, so there is no problem to begin with.

Keywords: Western philosophy, theory of participation, Plato, empirical nature, mathematical entity, applicability of mathematics

Access to the complete content on Oxford Handbooks Online requires a subscription or purchase. Public users are able to search the site and view the abstracts and keywords for each book and chapter without a subscription.

Please subscribe or login to access full text content.

If you have purchased a print title that contains an access token, please see the token for information about how to register your code.

For questions on access or troubleshooting, please check our FAQs, and if you can''t find the answer there, please contact us.