Jump to ContentJump to Main Navigation
Mathematical Knowledge and the Interplay of Practices$
Users without a subscription are not able to see the full content.

José Ferreirós

Print publication date: 2015

Print ISBN-13: 9780691167510

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691167510.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton 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 HSO for personal use (for details see www.princeton.universitypressscholarship.com/page/privacy-policy).date: 15 October 2018

Objectivity in Mathematical Knowledge

Objectivity in Mathematical Knowledge

Chapter:
(p.247) 9 Objectivity in Mathematical Knowledge
Source:
Mathematical Knowledge and the Interplay of Practices
Author(s):

José Ferreirós

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691167510.003.0009

This chapter proposes an idea for reconciling the hypothetical conception of mathematics with the traditional idea of the objectivity of mathematical knowledge. The basic notion is that, because new hypotheses are embedded in the web of mathematical practices, they become systematically linked with previous strata of mathematical knowledge, and this forces upon us agents (for example, research mathematicians or students of math) certain results, be they principles or conclusions. The chapter first considers a simple case that illustrates objective features in the introduction of basic mathematical hypotheses. It then discusses Georg Cantor's “purely arithmetical” proofs of his set-theoretic results, along with the notion of arbitrary set in relation to the Axiom of Choice that has strong roots in the theory of real numbers. It also explores Cantor's ordinal numbers and the Continuum Hypothesis.

Keywords:   objectivity, mathematical knowledge, hypotheses, Georg Cantor, purely arithmetical proof, arbitrary set, Axiom of Choice, real numbers, ordinal numbers, Continuum Hypothesis

Princeton 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.