Jump to ContentJump to Main Navigation
The Oxford Handbook of Philosophy of Mathematics and Logic$
Users without a subscription are not able to see the full content.

Stewart Shapiro

Print publication date: 2005

Print ISBN-13: 9780195148770

Published to Oxford Scholarship Online: July 2005

DOI: 10.1093/0195148770.001.0001

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: 22 May 2019

Structuralism Reconsidered

Structuralism Reconsidered

Chapter:
(p.563) Structuralism Reconsidered
Source:
The Oxford Handbook of Philosophy of Mathematics and Logic
Author(s):

Fraser MacBride

Publisher:
Oxford University Press
DOI:10.1093/0195148770.003.0018

The basic relations and functions that mathematicians use to identify mathematical objects fail to settle whether mathematical objects of one kind are identical to or distinct from objects of an

apparently different kind, and what, if any, intrinsic properties mathematical objects possess. According to one influential interpretation of mathematical discourse, this is because the objects under study are themselves incomplete; they are positions or akin to positions in patterns or structures. Two versions of this idea are examined (Resnik, Shapiro). It is argued that the evidence adduced in favor of the incompleteness of mathematical objects underdetermines whether it is the objects themselves or our knowledge of them that is incomplete. Also, holding that mathematical objects are incomplete conflicts with the practice of mathematics. The objection that structuralism is committed to the identity of indiscernibles is evaluated and it is also argued that the identification of objects with positions is metaphysically suspect.

Keywords:   mathematical objects, identity, positions, structures, Resnik, Shapiro, incompleteness, structuralism, identity of indiscernibles

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 .