Jump to ContentJump to Main Navigation
Philosophy of MathematicsStructure and Ontology$
Users without a subscription are not able to see the full content.

Stewart Shapiro

Print publication date: 2000

Print ISBN-13: 9780195139303

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0195139305.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. 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 www.oxfordscholarship.com/page/privacy-policy).date: 25 June 2019

Modality, Structure, Ontology

Modality, Structure, Ontology

Chapter:
(p.216) 7 Modality, Structure, Ontology
Source:
Philosophy of Mathematics
Author(s):

Stewart Shapiro (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0195139305.003.0008

There are a number of nominalist, or antiplatonist programmes in the philosophy of mathematics. Typically, defenders of these programmes maintain that mathematics is not about an independently existing realm of mathematical objects, but that, nevertheless, mathematical propositions have objective, nonvacuous truth conditions. This is accomplished with added ideology – typically a modal operator. I show that for the more prominent cases, there are straightforward translations between the set‐theoretic language of the realist and the nominalistic language with the added ideology. Since the translations preserve warranted belief (from each perspective), I contend that an advocate of any of the rival systems cannot claim an epistemological advantage over an advocate of any other. The treatment yields a structuralist illumination of the trade‐off between ontology and ideology.

Keywords:   ideology, modality, modal operator, nominalism, objectivity, ontology, platonism, structure, translation

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 .