Jump to ContentJump to Main Navigation
Mathematics as a Science of Patterns$
Users without a subscription are not able to see the full content.

Michael D. Resnik

Print publication date: 1999

Print ISBN-13: 9780198250142

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198250142.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright 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 monograph in OSO for personal use (for details see http://www.oxfordscholarship.com/page/privacy-policy).date: 17 August 2018

Holism: Evidence in Science and Mathematics

Holism: Evidence in Science and Mathematics

Chapter:
(p.112) 7 Holism: Evidence in Science and Mathematics
Source:
Mathematics as a Science of Patterns
Author(s):

Michael D. Resnik (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0198250142.003.0007

I present a theory of justification for mathematical beliefs that is both non‐foundationalist, in that it claims that some mathematics must be justified indirectly in terms of its consequences, and holistic, in that it maintains that no claim of theoretical science can be confirmed or refuted in isolation but only as a part of a system of hypotheses. Our evidence for mathematics is ultimately empirical because the mathematics that is part of theoretical science, is, in principle, revisable in light of experience and confirmed by experience. Following Henry Kyburg, I develop this idea by claiming that in science we use combinations of mathematical and scientific principles to develop models (mini‐theories) that allow us to calculate values that we then compare with the data. ‘Separatists’ objections to holism revolve around the claim that holism fails to respect our intuitions about mathematics, e.g. that mathematics is clearly distinct from science and that mathematical evidence comes from proofs, rather than from experience. My response to these objections is that holism can accommodate these intuitions by appealing to pragmatic rationality that, on the one hand, underwrites the special role of mathematics and bids us to treat it as if it were a priori, and, on the other, justifies, on the grounds of simplicity and success, a local conception of evidence according to which data can confirm specific hypotheses.

Keywords:   confirmation, empirical, evidence, holism, indirect justification, Kyburg, mathematical realism, models, non‐foundationalism, pragmatism, separatists

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .