Show Summary Details

Page of

PRINTED FROM OXFORD HANDBOOKS ONLINE ( © 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: 25 November 2020

Abstract and Keywords

The properties and relations that perform a role in mathematical reasoning arise from the basic relations that obtain among mathematical objects. It is in terms of these basic relations that mathematicians identify the objects they intend to study. The way in which mathematicians identify these objects has led some philosophers to draw metaphysical conclusions about their nature. These philosophers have been led to claim that mathematical objects are positions in structures or akin to positions in patterns. This article retraces their route from (relatively uncontroversial) facts about the identification of mathematical objects to high metaphysical conclusions. Beginning with the natural numbers, how are they identified? The mathematically significant properties and relations of natural numbers arise from the successor function that orders them; the natural numbers are identified simply as the objects that answer to this basic function. But the relations (or functions) that are used to identify a class of mathematical objects may often be defined over what appear to be different kinds of objects.

Keywords: structuralism, mathematical reasoning, mathematical objects, metaphysical conclusions, natural numbers, mathematical properties

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.