Jump to ContentJump to Main Navigation
Philosophy and Model Theory$
Users without a subscription are not able to see the full content.

Tim Button and Sean Walsh

Print publication date: 2018

Print ISBN-13: 9780198790396

Published to Oxford Scholarship Online: May 2018

DOI: 10.1093/oso/9780198790396.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 28 October 2021

Quantifiers

Quantifiers

Chapter:
(p.387) 16 Quantifiers
Source:
Philosophy and Model Theory
Author(s):

Tim Button

Sean Walsh

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198790396.003.0016

Typically the existential and universal quantifiers are regarded as logical expressions. But there are straightforward semantic means for defining all sorts of new quantifiers that have roughly the same syntax as the more familiar quantifiers. This raises the question: Which of these new quantifiers are relevantly similar to the existential and universal quantifiers to count as logical? After introducing generalised quantifiers, we use notions of indiscernibility to investigate how to classify quantifiers as logical or non-logical, focussing especially on the famous Tarski-Sher thesis. Roughly, this thesis states that quantifiers are logical provided they exhibit a certain kind of invariance. We argue that intuitions about non-discrimination are insufficient to establish Tarski-Sher. Then, by considering infinitary logics and closure principles, we raise some further difficulties for attempts to establish Tarski-Sher.

Keywords:   Generalised quantifiers, Tarski’s thesis, Tarski-Sher, non-discrimatory, principle of closure, McGee’s squeezing argument

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 .