Jump to ContentJump to Main Navigation
Abstraction and Infinity$
Users without a subscription are not able to see the full content.

Paolo Mancosu

Print publication date: 2016

Print ISBN-13: 9780198746829

Published to Oxford Scholarship Online: January 2017

DOI: 10.1093/acprof:oso/9780198746829.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright 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 monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 21 September 2018

In good company? On Hume’s Principle and the assignment of numbers to infinite concepts

In good company? On Hume’s Principle and the assignment of numbers to infinite concepts

Chapter:
(p.154) 4 In good company? On Hume’s Principle and the assignment of numbers to infinite concepts
Source:
Abstraction and Infinity
Author(s):

Paolo Mancosu

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198746829.003.0005

In this chapter Mancosu generalizes some worries, raised by Richard Heck, emerging from the theory of numerosities (discussed in Chapter 3) to a line of thought resulting in what he calls a ‘good company’ objection to Hume’s Principle (HP). The chapter is centered around five main parts. The first takes a historical look at nineteenth-century attributions of equality of numbers in terms of one-one correlation and argues that there was no agreement as to how to extend such determinations to infinite sets of objects. This leads to the second part where Mancosu shows that there are countably-infinite many abstraction principles that are ‘good’, in the sense that they share the same virtues of HP and from which one can derive the axioms of second-order arithmetic. All the principles he presents agree with HP in the assignment of numbers to finite concepts but diverge from it in the assignment of numbers to infinite concepts. The third part connects this material to a debate on Finite Hume’s Principle between Heck and MacBride. The fourth part states the ‘good company’ objection as a generalization of Heck’s objection to the analyticity of HP based on the theory of numerosities. In the same section Mancosu offers a taxonomy of possible neo-logicist responses to the ‘good company’ objection. Finally, the fifth part makes a foray into the relevance of this material for the issue of cross-sortal identifications for abstractions.

Keywords:   Abstraction principles, Hume’s Principle, neo-logicism, cross-sortal identities, finite, infinite, good company objection, analyticity

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 .