Show Summary Details

Page of

PRINTED FROM OXFORD HANDBOOKS ONLINE (www.oxfordhandbooks.com). © 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: 21 February 2020

Abstract and Keywords

This article is organized around logicism's answers to the following questions: What is the basis for our knowledge of the infinity of the numbers? How is arithmetic applicable to reality? Why is reasoning by induction justified? Although there are, as is seen in this article, important differences, the common thread that runs through all three of the authors discussed in this article their opposition to the Kantian thesis that reflection on reasoning with mere concepts (i.e., without attention to intuitions formed a priori) can never succeed in providing satisfactory answers to these three questions. This description of the core of the view differs from more usual formulations which represent the opposition to Kant as an opposition to the contention that mathematics in general, and arithmetic in particular, are synthetic a priori rather than analytic.

Keywords: logicism, infinity of the numbers, arithmetic, Kantian thesis, mathematics, Russell

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.